id	sid	tid	token	lemma	pos
cana-2105	1	1	exploring	explore	VERB
cana-2105	1	2	the	the	DET
cana-2105	1	3	complex	complex	ADJ
cana-2105	1	4	dynamics	dynamic	NOUN
cana-2105	1	5	of	of	ADP
cana-2105	1	6	julia	julia	PROPN
cana-2105	1	7	and	and	CCONJ
cana-2105	1	8	mandelbrot	mandelbrot	PROPN
cana-2105	1	9	sets	set	VERB
cana-2105	1	10	for	for	ADP
cana-2105	1	11	the	the	DET
cana-2105	1	12	complex	complex	ADV
cana-2105	1	13	-	-	PUNCT
cana-2105	1	14	valued	value	VERB
cana-2105	1	15	mapping	mapping	NOUN
cana-2105	1	16	sin(zk	sin(zk	NOUN
cana-2105	1	17	)	)	PUNCT
cana-2105	2	1	+	+	CCONJ
cana-2105	2	2	az	az	PROPN
cana-2105	2	3	+	+	NOUN
cana-2105	2	4	c	c	VERB
cana-2105	2	5	using	use	VERB
cana-2105	2	6	four	four	NUM
cana-2105	2	7	-	-	PUNCT
cana-2105	2	8	step	step	NOUN
cana-2105	2	9	iterative	iterative	NOUN
cana-2105	2	10	scheme	scheme	NOUN
cana-2105	2	11	with	with	ADP
cana-2105	2	12	s	s	NOUN
cana-2105	2	13	-	-	PUNCT
cana-2105	2	14	convexity	convexity	NOUN
cana-2105	2	15	nabaraj	nabaraj	ADJ
cana-2105	2	16	adhikari	adhikari	PROPN
cana-2105	2	17	∗	∗	PROPN
cana-2105	2	18	central	central	PROPN
cana-2105	2	19	department	department	PROPN
cana-2105	2	20	of	of	ADP
cana-2105	2	21	mathematics	mathematics	PROPN
cana-2105	2	22	,	,	PUNCT
cana-2105	2	23	institute	institute	NOUN
cana-2105	2	24	of	of	ADP
cana-2105	2	25	science	science	PROPN
cana-2105	2	26	and	and	CCONJ
cana-2105	2	27	technology	technology	NOUN
cana-2105	2	28	tirbhuvan	tirbhuvan	PROPN
cana-2105	2	29	university	university	NOUN
cana-2105	2	30	,	,	PUNCT
cana-2105	2	31	kathmandu	kathmandu	NOUN
cana-2105	2	32	,	,	PUNCT
cana-2105	2	33	nepal	nepal	ADJ
cana-2105	2	34	e	e	NOUN
cana-2105	2	35	-	-	NOUN
cana-2105	2	36	mail	mail	NOUN
cana-2105	2	37	:	:	PUNCT
cana-2105	2	38	nabaraj.adhikari@cdmath.tu.edu.np	nabaraj.adhikari@cdmath.tu.edu.np	X
cana-2105	2	39	(	(	PUNCT
cana-2105	2	40	n.	n.	PROPN
cana-2105	2	41	adhikari	adhikari	PROPN
cana-2105	2	42	)	)	PUNCT
cana-2105	2	43	received	receive	VERB
cana-2105	2	44	:	:	PUNCT
cana-2105	2	45	07	07	NUM
cana-2105	2	46	-	-	SYM
cana-2105	2	47	08	08	NUM
cana-2105	2	48	-	-	PUNCT
cana-2105	2	49	2024	2024	NUM
cana-2105	2	50	,	,	PUNCT
cana-2105	2	51	revised	revise	VERB
cana-2105	2	52	:	:	PUNCT
cana-2105	2	53	25	25	NUM
cana-2105	2	54	-	-	PUNCT
cana-2105	2	55	09	09	NUM
cana-2105	2	56	-	-	PUNCT
cana-2105	2	57	2024	2024	NUM
cana-2105	2	58	,	,	PUNCT
cana-2105	2	59	accepted	accept	VERB
cana-2105	2	60	:	:	PUNCT
cana-2105	2	61	10	10	NUM
cana-2105	2	62	-	-	SYM
cana-2105	2	63	10	10	NUM
cana-2105	2	64	-	-	PUNCT
cana-2105	2	65	2024	2024	NUM
cana-2105	2	66	abstract	abstract	NOUN
cana-2105	2	67	in	in	ADP
cana-2105	2	68	this	this	DET
cana-2105	2	69	paper	paper	NOUN
cana-2105	2	70	,	,	PUNCT
cana-2105	2	71	we	we	PRON
cana-2105	2	72	investigate	investigate	VERB
cana-2105	2	73	unique	unique	ADJ
cana-2105	2	74	variations	variation	NOUN
cana-2105	2	75	of	of	ADP
cana-2105	2	76	the	the	DET
cana-2105	2	77	julia	julia	PROPN
cana-2105	2	78	and	and	CCONJ
cana-2105	2	79	mandelbrot	mandelbrot	PROPN
cana-2105	2	80	sets	set	NOUN
cana-2105	2	81	,	,	PUNCT
cana-2105	2	82	establishing	establish	VERB
cana-2105	2	83	criteria	criterion	NOUN
cana-2105	2	84	for	for	ADP
cana-2105	2	85	the	the	DET
cana-2105	2	86	escape	escape	NOUN
cana-2105	2	87	of	of	ADP
cana-2105	2	88	a	a	DET
cana-2105	2	89	function	function	NOUN
cana-2105	2	90	tcz	tcz	NOUN
cana-2105	2	91	=	=	SYM
cana-2105	2	92	sin(zk	sin(zk	NOUN
cana-2105	2	93	)	)	PUNCT
cana-2105	3	1	+	+	CCONJ
cana-2105	3	2	az	az	PROPN
cana-2105	3	3	+	+	CCONJ
cana-2105	3	4	c	c	PROPN
cana-2105	3	5	for	for	ADP
cana-2105	3	6	all	all	DET
cana-2105	3	7	z	z	NOUN
cana-2105	3	8	∈	∈	PROPN
cana-2105	4	1	c	c	NOUN
cana-2105	4	2	,	,	PUNCT
cana-2105	4	3	where	where	SCONJ
cana-2105	4	4	k	k	PROPN
cana-2105	4	5	∈	∈	PROPN
cana-2105	4	6	n	n	PRON
cana-2105	4	7	\	\	NOUN
cana-2105	4	8	{	{	PUNCT
cana-2105	4	9	1	1	NUM
cana-2105	4	10	}	}	PUNCT
cana-2105	4	11	and	and	CCONJ
cana-2105	4	12	a	a	PRON
cana-2105	4	13	,	,	PUNCT
cana-2105	4	14	c	c	PROPN
cana-2105	4	15	∈	∈	PROPN
cana-2105	4	16	c	c	NOUN
cana-2105	4	17	with	with	ADP
cana-2105	4	18	a	a	DET
cana-2105	4	19	̸=	̸=	PROPN
cana-2105	4	20	0	0	NUM
cana-2105	4	21	by	by	ADP
cana-2105	4	22	utilizing	utilize	VERB
cana-2105	4	23	a	a	DET
cana-2105	4	24	four	four	NUM
cana-2105	4	25	-	-	PUNCT
cana-2105	4	26	step	step	NOUN
cana-2105	4	27	iterative	iterative	NOUN
cana-2105	4	28	scheme	scheme	NOUN
cana-2105	4	29	extended	extend	VERB
cana-2105	4	30	with	with	ADP
cana-2105	4	31	s	s	NOUN
cana-2105	4	32	-	-	NOUN
cana-2105	4	33	convexity	convexity	NOUN
cana-2105	4	34	,	,	PUNCT
cana-2105	4	35	we	we	PRON
cana-2105	4	36	analyze	analyze	VERB
cana-2105	4	37	the	the	DET
cana-2105	4	38	dynamics	dynamic	NOUN
cana-2105	4	39	of	of	ADP
cana-2105	4	40	these	these	DET
cana-2105	4	41	fractals	fractal	NOUN
cana-2105	4	42	by	by	ADP
cana-2105	4	43	formulating	formulate	VERB
cana-2105	4	44	and	and	CCONJ
cana-2105	4	45	implementing	implement	VERB
cana-2105	4	46	the	the	DET
cana-2105	4	47	algorithms	algorithm	NOUN
cana-2105	4	48	.	.	PUNCT
cana-2105	5	1	our	our	PRON
cana-2105	5	2	exploration	exploration	NOUN
cana-2105	5	3	focuses	focus	VERB
cana-2105	5	4	on	on	ADP
cana-2105	5	5	understanding	understand	VERB
cana-2105	5	6	how	how	SCONJ
cana-2105	5	7	distinct	distinct	ADJ
cana-2105	5	8	parameters	parameter	NOUN
cana-2105	5	9	impact	impact	VERB
cana-2105	5	10	these	these	DET
cana-2105	5	11	fractals	fractal	NOUN
cana-2105	5	12	’	'	PUNCT
cana-2105	5	13	color	color	NOUN
cana-2105	5	14	,	,	PUNCT
cana-2105	5	15	dynamics	dynamic	NOUN
cana-2105	5	16	,	,	PUNCT
cana-2105	5	17	and	and	CCONJ
cana-2105	5	18	overall	overall	ADJ
cana-2105	5	19	visual	visual	ADJ
cana-2105	5	20	characteristics	characteristic	NOUN
cana-2105	5	21	.	.	PUNCT
cana-2105	6	1	our	our	PRON
cana-2105	6	2	findings	finding	NOUN
cana-2105	6	3	reveal	reveal	VERB
cana-2105	6	4	that	that	SCONJ
cana-2105	6	5	specific	specific	ADJ
cana-2105	6	6	fractal	fractal	ADJ
cana-2105	6	7	patterns	pattern	NOUN
cana-2105	6	8	resemble	resemble	VERB
cana-2105	6	9	exquisite	exquisite	ADJ
cana-2105	6	10	natural	natural	ADJ
cana-2105	6	11	objects	object	NOUN
cana-2105	6	12	like	like	ADP
cana-2105	6	13	flowers	flower	NOUN
cana-2105	6	14	and	and	CCONJ
cana-2105	6	15	spiders	spider	NOUN
cana-2105	6	16	.	.	PUNCT
cana-2105	7	1	these	these	DET
cana-2105	7	2	fractal	fractal	ADJ
cana-2105	7	3	designs	design	NOUN
cana-2105	7	4	are	be	AUX
cana-2105	7	5	also	also	ADV
cana-2105	7	6	employed	employ	VERB
cana-2105	7	7	as	as	ADP
cana-2105	7	8	visually	visually	ADV
cana-2105	7	9	striking	strike	VERB
cana-2105	7	10	artistic	artistic	ADJ
cana-2105	7	11	motifs	motif	NOUN
cana-2105	7	12	on	on	ADP
cana-2105	7	13	garments	garment	NOUN
cana-2105	7	14	and	and	CCONJ
cana-2105	7	15	textile	textile	NOUN
cana-2105	7	16	materials	material	NOUN
cana-2105	7	17	.	.	PUNCT
cana-2105	8	1	the	the	DET
cana-2105	8	2	captivating	captivating	ADJ
cana-2105	8	3	and	and	CCONJ
cana-2105	8	4	complex	complex	ADJ
cana-2105	8	5	properties	property	NOUN
cana-2105	8	6	of	of	ADP
cana-2105	8	7	fractal	fractal	ADJ
cana-2105	8	8	patterns	pattern	NOUN
cana-2105	8	9	within	within	ADP
cana-2105	8	10	dynamic	dynamic	ADJ
cana-2105	8	11	systems	system	NOUN
cana-2105	8	12	make	make	VERB
cana-2105	8	13	them	they	PRON
cana-2105	8	14	an	an	DET
cana-2105	8	15	enticing	enticing	ADJ
cana-2105	8	16	and	and	CCONJ
cana-2105	8	17	visually	visually	ADV
cana-2105	8	18	appealing	appealing	ADJ
cana-2105	8	19	area	area	NOUN
cana-2105	8	20	of	of	ADP
cana-2105	8	21	research	research	NOUN
cana-2105	8	22	.	.	PUNCT
cana-2105	9	1	keywords	keyword	NOUN
cana-2105	9	2	:	:	PUNCT
cana-2105	9	3	julia	julia	PROPN
cana-2105	9	4	set	set	PROPN
cana-2105	9	5	;	;	PUNCT
cana-2105	9	6	mandelbrot	mandelbrot	PROPN
cana-2105	9	7	set	set	VERB
cana-2105	9	8	;	;	PUNCT
cana-2105	9	9	four	four	NUM
cana-2105	9	10	-	-	PUNCT
cana-2105	9	11	step	step	NOUN
cana-2105	9	12	iteration	iteration	NOUN
cana-2105	9	13	scheme	scheme	NOUN
cana-2105	9	14	with	with	ADP
cana-2105	9	15	s	s	NOUN
cana-2105	9	16	-	-	NOUN
cana-2105	9	17	convexity	convexity	NOUN
cana-2105	9	18	.	.	PUNCT
cana-2105	10	1	mathematics	mathematic	NOUN
cana-2105	10	2	subject	subject	ADJ
cana-2105	10	3	classification	classification	NOUN
cana-2105	10	4	:	:	PUNCT
cana-2105	10	5	28a80	28a80	NUM
cana-2105	10	6	;	;	PUNCT
cana-2105	10	7	37f10	37f10	NUM
cana-2105	10	8	;	;	PUNCT
cana-2105	10	9	47h10	47h10	NUM
cana-2105	10	10	;	;	PUNCT
cana-2105	10	11	.	.	X
cana-2105	11	1	1	1	NUM
cana-2105	11	2	introduction	introduction	NOUN
cana-2105	11	3	fractals	fractal	NOUN
cana-2105	11	4	have	have	AUX
cana-2105	11	5	developed	develop	VERB
cana-2105	11	6	as	as	ADP
cana-2105	11	7	one	one	NUM
cana-2105	11	8	of	of	ADP
cana-2105	11	9	the	the	DET
cana-2105	11	10	most	most	ADV
cana-2105	11	11	exciting	exciting	ADJ
cana-2105	11	12	fields	field	NOUN
cana-2105	11	13	of	of	ADP
cana-2105	11	14	study	study	NOUN
cana-2105	11	15	because	because	SCONJ
cana-2105	11	16	of	of	ADP
cana-2105	11	17	its	its	PRON
cana-2105	11	18	selfsimilarity	selfsimilarity	NOUN
cana-2105	11	19	.	.	PUNCT
cana-2105	12	1	in	in	ADP
cana-2105	12	2	1917	1917	NUM
cana-2105	12	3	,	,	PUNCT
cana-2105	12	4	julia	julia	PROPN
cana-2105	13	1	[	[	X
cana-2105	13	2	6	6	NUM
cana-2105	13	3	]	]	PUNCT
cana-2105	13	4	and	and	CCONJ
cana-2105	13	5	fatou	fatou	NOUN
cana-2105	14	1	[	[	X
cana-2105	14	2	5	5	NUM
cana-2105	14	3	]	]	PUNCT
cana-2105	14	4	began	begin	VERB
cana-2105	14	5	researching	research	VERB
cana-2105	14	6	complex	complex	NOUN
cana-2105	14	7	-	-	PUNCT
cana-2105	14	8	valued	value	VERB
cana-2105	14	9	maps	map	NOUN
cana-2105	14	10	.	.	PUNCT
cana-2105	15	1	∗corresponding	∗corresponde	VERB
cana-2105	15	2	author	author	NOUN
cana-2105	15	3	e	e	NOUN
cana-2105	15	4	-	-	NOUN
cana-2105	15	5	mail	mail	NOUN
cana-2105	15	6	:	:	PUNCT
cana-2105	15	7	nabaraj.adhikari@camath.tu.edu.np	nabaraj.adhikari@camath.tu.edu.np	PROPN
cana-2105	15	8	communications	communication	NOUN
cana-2105	15	9	on	on	ADP
cana-2105	15	10	applied	apply	VERB
cana-2105	15	11	nonlinear	nonlinear	ADJ
cana-2105	15	12	analysis	analysis	NOUN
cana-2105	15	13	issn	issn	NOUN
cana-2105	15	14	:	:	PUNCT
cana-2105	15	15	1074	1074	NUM
cana-2105	15	16	-	-	PUNCT
cana-2105	15	17	133x	133x	NUM
cana-2105	15	18	vol	vol	NOUN
cana-2105	15	19	32	32	NUM
cana-2105	15	20	no	no	NOUN
cana-2105	15	21	.	.	PUNCT
cana-2105	16	1	1s	1s	NUM
cana-2105	16	2	(	(	PUNCT
cana-2105	16	3	2025	2025	NUM
cana-2105	16	4	)	)	PUNCT
cana-2105	16	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	16	6	63	63	NUM
cana-2105	16	7	they	they	PRON
cana-2105	16	8	focused	focus	VERB
cana-2105	16	9	on	on	ADP
cana-2105	16	10	exploring	explore	VERB
cana-2105	16	11	the	the	DET
cana-2105	16	12	complex	complex	ADJ
cana-2105	16	13	dynamics	dynamic	NOUN
cana-2105	16	14	of	of	ADP
cana-2105	16	15	complex	complex	NOUN
cana-2105	16	16	-	-	PUNCT
cana-2105	16	17	valued	value	VERB
cana-2105	16	18	map	map	NOUN
cana-2105	16	19	,	,	PUNCT
cana-2105	16	20	specifically	specifically	ADV
cana-2105	16	21	the	the	DET
cana-2105	16	22	iterative	iterative	ADJ
cana-2105	16	23	approximations	approximation	NOUN
cana-2105	16	24	of	of	ADP
cana-2105	16	25	the	the	DET
cana-2105	16	26	function	function	NOUN
cana-2105	16	27	z2	z2	PROPN
cana-2105	16	28	+	+	CCONJ
cana-2105	16	29	c	c	NOUN
cana-2105	16	30	,	,	PUNCT
cana-2105	16	31	where	where	SCONJ
cana-2105	16	32	z	z	NOUN
cana-2105	16	33	is	be	AUX
cana-2105	16	34	complex	complex	ADJ
cana-2105	16	35	variable	variable	NOUN
cana-2105	16	36	and	and	CCONJ
cana-2105	16	37	c	c	NOUN
cana-2105	16	38	is	be	AUX
cana-2105	16	39	a	a	DET
cana-2105	16	40	complex	complex	ADJ
cana-2105	16	41	constant	constant	ADJ
cana-2105	16	42	;	;	PUNCT
cana-2105	16	43	however	however	ADV
cana-2105	16	44	,	,	PUNCT
cana-2105	16	45	he	he	PRON
cana-2105	16	46	faced	face	VERB
cana-2105	16	47	challenges	challenge	NOUN
cana-2105	16	48	when	when	SCONJ
cana-2105	16	49	attempting	attempt	VERB
cana-2105	16	50	to	to	PART
cana-2105	16	51	visually	visually	ADV
cana-2105	16	52	present	present	VERB
cana-2105	16	53	it	it	PRON
cana-2105	16	54	due	due	ADP
cana-2105	16	55	to	to	ADP
cana-2105	16	56	the	the	DET
cana-2105	16	57	lack	lack	NOUN
cana-2105	16	58	of	of	ADP
cana-2105	16	59	computer	computer	NOUN
cana-2105	16	60	.	.	PUNCT
cana-2105	17	1	after	after	ADP
cana-2105	17	2	julia	julia	PROPN
cana-2105	17	3	’s	’s	PART
cana-2105	17	4	initial	initial	ADJ
cana-2105	17	5	exploration	exploration	NOUN
cana-2105	17	6	,	,	PUNCT
cana-2105	17	7	the	the	DET
cana-2105	17	8	field	field	NOUN
cana-2105	17	9	of	of	ADP
cana-2105	17	10	complex	complex	ADJ
cana-2105	17	11	dynamics	dynamic	NOUN
cana-2105	17	12	experienced	experience	VERB
cana-2105	17	13	a	a	DET
cana-2105	17	14	period	period	NOUN
cana-2105	17	15	of	of	ADP
cana-2105	17	16	decreased	decrease	VERB
cana-2105	17	17	activity	activity	NOUN
cana-2105	17	18	lasting	last	VERB
cana-2105	17	19	for	for	ADP
cana-2105	17	20	five	five	NUM
cana-2105	17	21	decades	decade	NOUN
cana-2105	17	22	.	.	PUNCT
cana-2105	18	1	however	however	ADV
cana-2105	18	2	,	,	PUNCT
cana-2105	18	3	in	in	ADP
cana-2105	18	4	the	the	DET
cana-2105	18	5	1980s	1980	NOUN
cana-2105	18	6	,	,	PUNCT
cana-2105	18	7	complex	complex	ADJ
cana-2105	18	8	dynamics	dynamic	NOUN
cana-2105	18	9	experienced	experience	VERB
cana-2105	18	10	a	a	DET
cana-2105	18	11	revival	revival	NOUN
cana-2105	18	12	,	,	PUNCT
cana-2105	18	13	spearheaded	spearhead	VERB
cana-2105	18	14	by	by	ADP
cana-2105	18	15	mandelbrot	mandelbrot	NOUN
cana-2105	18	16	[	[	X
cana-2105	18	17	11	11	NUM
cana-2105	18	18	]	]	PUNCT
cana-2105	18	19	,	,	PUNCT
cana-2105	18	20	re	re	VERB
cana-2105	18	21	-	-	VERB
cana-2105	18	22	emerging	emerge	VERB
cana-2105	18	23	as	as	ADP
cana-2105	18	24	a	a	DET
cana-2105	18	25	lively	lively	ADJ
cana-2105	18	26	area	area	NOUN
cana-2105	18	27	of	of	ADP
cana-2105	18	28	mathematical	mathematical	ADJ
cana-2105	18	29	research	research	NOUN
cana-2105	18	30	.	.	PUNCT
cana-2105	19	1	this	this	DET
cana-2105	19	2	resurgence	resurgence	NOUN
cana-2105	19	3	persists	persist	VERB
cana-2105	19	4	today	today	NOUN
cana-2105	19	5	,	,	PUNCT
cana-2105	19	6	driven	drive	VERB
cana-2105	19	7	in	in	ADP
cana-2105	19	8	part	part	NOUN
cana-2105	19	9	by	by	ADP
cana-2105	19	10	advancements	advancement	NOUN
cana-2105	19	11	in	in	ADP
cana-2105	19	12	computer	computer	NOUN
cana-2105	19	13	technology	technology	NOUN
cana-2105	19	14	that	that	PRON
cana-2105	19	15	provide	provide	VERB
cana-2105	19	16	substantial	substantial	ADJ
cana-2105	19	17	computational	computational	ADJ
cana-2105	19	18	power	power	NOUN
cana-2105	19	19	,	,	PUNCT
cana-2105	19	20	allowing	allow	VERB
cana-2105	19	21	for	for	ADP
cana-2105	19	22	the	the	DET
cana-2105	19	23	revelation	revelation	NOUN
cana-2105	19	24	of	of	ADP
cana-2105	19	25	the	the	DET
cana-2105	19	26	intricate	intricate	ADJ
cana-2105	19	27	beauty	beauty	NOUN
cana-2105	19	28	of	of	ADP
cana-2105	19	29	complex	complex	ADJ
cana-2105	19	30	dynamics	dynamic	NOUN
cana-2105	19	31	for	for	ADP
cana-2105	19	32	the	the	DET
cana-2105	19	33	first	first	ADJ
cana-2105	19	34	time	time	NOUN
cana-2105	19	35	.	.	PUNCT
cana-2105	20	1	he	he	PRON
cana-2105	20	2	named	name	VERB
cana-2105	20	3	these	these	DET
cana-2105	20	4	complex	complex	ADJ
cana-2105	20	5	structure	structure	NOUN
cana-2105	20	6	as	as	ADP
cana-2105	20	7	”	"	PUNCT
cana-2105	20	8	fractals	fractal	NOUN
cana-2105	20	9	”	"	PUNCT
cana-2105	20	10	and	and	CCONJ
cana-2105	20	11	discovered	discover	VERB
cana-2105	20	12	that	that	SCONJ
cana-2105	20	13	the	the	DET
cana-2105	20	14	julia	julia	PROPN
cana-2105	20	15	sets	set	NOUN
cana-2105	20	16	have	have	VERB
cana-2105	20	17	individually	individually	ADV
cana-2105	20	18	in	in	ADP
cana-2105	20	19	their	their	PRON
cana-2105	20	20	features	feature	NOUN
cana-2105	20	21	for	for	ADP
cana-2105	20	22	different	different	ADJ
cana-2105	20	23	values	value	NOUN
cana-2105	20	24	of	of	ADP
cana-2105	20	25	the	the	DET
cana-2105	20	26	parameter	parameter	NOUN
cana-2105	20	27	c.	c.	PROPN
cana-2105	20	28	furthermore	furthermore	ADV
cana-2105	20	29	,	,	PUNCT
cana-2105	20	30	by	by	ADP
cana-2105	20	31	interchanging	interchange	VERB
cana-2105	20	32	the	the	DET
cana-2105	20	33	role	role	NOUN
cana-2105	20	34	of	of	ADP
cana-2105	20	35	z	z	PROPN
cana-2105	20	36	and	and	CCONJ
cana-2105	20	37	c	c	NOUN
cana-2105	20	38	,	,	PUNCT
cana-2105	20	39	a	a	DET
cana-2105	20	40	new	new	ADJ
cana-2105	20	41	set	set	NOUN
cana-2105	20	42	obtained	obtain	VERB
cana-2105	20	43	using	use	VERB
cana-2105	20	44	same	same	ADJ
cana-2105	20	45	iterative	iterative	NOUN
cana-2105	20	46	scheme	scheme	NOUN
cana-2105	20	47	,	,	PUNCT
cana-2105	20	48	which	which	PRON
cana-2105	20	49	is	be	AUX
cana-2105	20	50	called	call	VERB
cana-2105	20	51	the	the	DET
cana-2105	20	52	mandelbrot	mandelbrot	NOUN
cana-2105	20	53	set	set	VERB
cana-2105	20	54	.	.	PUNCT
cana-2105	21	1	in	in	ADP
cana-2105	21	2	1987s	1987	NOUN
cana-2105	21	3	,	,	PUNCT
cana-2105	21	4	lakhtakia	lakhtakia	NOUN
cana-2105	21	5	et	et	NOUN
cana-2105	21	6	al.[9	al.[9	PROPN
cana-2105	21	7	]	]	PUNCT
cana-2105	21	8	extended	extend	VERB
cana-2105	21	9	the	the	DET
cana-2105	21	10	work	work	NOUN
cana-2105	21	11	of	of	ADP
cana-2105	21	12	julia	julia	PROPN
cana-2105	21	13	and	and	CCONJ
cana-2105	21	14	mandelbrot	mandelbrot	NOUN
cana-2105	21	15	for	for	ADP
cana-2105	21	16	the	the	DET
cana-2105	21	17	complex	complex	ADJ
cana-2105	21	18	valued	value	VERB
cana-2105	21	19	function	function	NOUN
cana-2105	21	20	zk	zk	PROPN
cana-2105	21	21	+	+	CCONJ
cana-2105	22	1	c	c	PROPN
cana-2105	23	1	for	for	ADP
cana-2105	23	2	all	all	DET
cana-2105	23	3	z	z	NOUN
cana-2105	23	4	∈	∈	PROPN
cana-2105	23	5	c	c	NOUN
cana-2105	23	6	,	,	PUNCT
cana-2105	23	7	k	k	PROPN
cana-2105	23	8	∈	∈	PROPN
cana-2105	23	9	n	n	PRON
cana-2105	23	10	\	\	NOUN
cana-2105	23	11	{	{	PUNCT
cana-2105	23	12	1	1	NUM
cana-2105	23	13	}	}	PUNCT
cana-2105	23	14	and	and	CCONJ
cana-2105	23	15	c	c	PROPN
cana-2105	23	16	is	be	AUX
cana-2105	23	17	complex	complex	ADJ
cana-2105	23	18	parameter	parameter	NOUN
cana-2105	23	19	.	.	PUNCT
cana-2105	24	1	many	many	ADJ
cana-2105	24	2	academics	academic	NOUN
cana-2105	24	3	have	have	AUX
cana-2105	24	4	studied	study	VERB
cana-2105	24	5	the	the	DET
cana-2105	24	6	julia	julia	PROPN
cana-2105	24	7	and	and	CCONJ
cana-2105	24	8	mandelbrot	mandelbrot	PROPN
cana-2105	24	9	set	set	VERB
cana-2105	24	10	in	in	ADP
cana-2105	24	11	depth	depth	NOUN
cana-2105	24	12	from	from	ADP
cana-2105	24	13	different	different	ADJ
cana-2105	24	14	angles	angle	NOUN
cana-2105	24	15	ever	ever	ADV
cana-2105	24	16	since	since	SCONJ
cana-2105	24	17	it	it	PRON
cana-2105	24	18	was	be	AUX
cana-2105	24	19	first	first	ADV
cana-2105	24	20	introduced	introduce	VERB
cana-2105	24	21	.	.	PUNCT
cana-2105	25	1	in	in	ADP
cana-2105	25	2	2004	2004	NUM
cana-2105	25	3	,	,	PUNCT
cana-2105	25	4	rani	rani	PROPN
cana-2105	25	5	and	and	CCONJ
cana-2105	25	6	kumar	kumar	PROPN
cana-2105	26	1	[	[	X
cana-2105	26	2	14	14	NUM
cana-2105	26	3	]	]	PUNCT
cana-2105	26	4	,	,	PUNCT
cana-2105	26	5	began	begin	VERB
cana-2105	26	6	an	an	DET
cana-2105	26	7	approach	approach	NOUN
cana-2105	26	8	that	that	PRON
cana-2105	26	9	included	include	VERB
cana-2105	26	10	using	use	VERB
cana-2105	26	11	iteration	iteration	NOUN
cana-2105	26	12	algorithms	algorithm	NOUN
cana-2105	26	13	based	base	VERB
cana-2105	26	14	on	on	ADP
cana-2105	26	15	fixed	fix	VERB
cana-2105	26	16	-	-	PUNCT
cana-2105	26	17	point	point	NOUN
cana-2105	26	18	theory	theory	NOUN
cana-2105	26	19	.	.	PUNCT
cana-2105	27	1	this	this	DET
cana-2105	27	2	strategy	strategy	NOUN
cana-2105	27	3	was	be	AUX
cana-2105	27	4	one	one	NUM
cana-2105	27	5	of	of	ADP
cana-2105	27	6	the	the	DET
cana-2105	27	7	avenues	avenue	NOUN
cana-2105	27	8	explored	explore	VERB
cana-2105	27	9	in	in	ADP
cana-2105	27	10	the	the	DET
cana-2105	27	11	analysis	analysis	NOUN
cana-2105	27	12	of	of	ADP
cana-2105	27	13	the	the	DET
cana-2105	27	14	julia	julia	PROPN
cana-2105	27	15	and	and	CCONJ
cana-2105	27	16	mandelbrot	mandelbrot	PROPN
cana-2105	27	17	set	set	VERB
cana-2105	27	18	.	.	PUNCT
cana-2105	28	1	after	after	ADP
cana-2105	28	2	that	that	PRON
cana-2105	28	3	,	,	PUNCT
cana-2105	28	4	different	different	ADJ
cana-2105	28	5	iterative	iterative	NOUN
cana-2105	28	6	methods	method	NOUN
cana-2105	28	7	are	be	AUX
cana-2105	28	8	used	use	VERB
cana-2105	28	9	to	to	PART
cana-2105	28	10	create	create	VERB
cana-2105	28	11	different	different	ADJ
cana-2105	28	12	sorts	sort	NOUN
cana-2105	28	13	of	of	ADP
cana-2105	28	14	fractals	fractal	NOUN
cana-2105	28	15	,	,	PUNCT
cana-2105	28	16	like	like	ADP
cana-2105	28	17	as	as	ADP
cana-2105	28	18	ishikawa	ishikawa	NOUN
cana-2105	28	19	-	-	PUNCT
cana-2105	28	20	iteration	iteration	NOUN
cana-2105	29	1	[	[	X
cana-2105	29	2	13	13	NUM
cana-2105	29	3	]	]	PUNCT
cana-2105	29	4	,	,	PUNCT
cana-2105	29	5	noor	noor	PROPN
cana-2105	29	6	-	-	PUNCT
cana-2105	29	7	iteration	iteration	NOUN
cana-2105	30	1	[	[	X
cana-2105	30	2	4	4	NUM
cana-2105	30	3	]	]	PUNCT
cana-2105	30	4	,	,	PUNCT
cana-2105	30	5	abbas	abbas	PROPN
cana-2105	30	6	iteration[7	iteration[7	PROPN
cana-2105	30	7	]	]	PUNCT
cana-2105	30	8	.	.	PUNCT
cana-2105	31	1	many	many	ADJ
cana-2105	31	2	researcher	researcher	NOUN
cana-2105	31	3	use	use	VERB
cana-2105	31	4	various	various	ADJ
cana-2105	31	5	iterative	iterative	NOUN
cana-2105	31	6	methods	method	NOUN
cana-2105	31	7	such	such	ADJ
cana-2105	31	8	as	as	ADP
cana-2105	31	9	picard	picard	NOUN
cana-2105	31	10	-	-	PUNCT
cana-2105	31	11	mann	mann	PROPN
cana-2105	31	12	iteration	iteration	NOUN
cana-2105	32	1	[	[	X
cana-2105	32	2	21	21	NUM
cana-2105	32	3	]	]	PUNCT
cana-2105	32	4	,	,	PUNCT
cana-2105	32	5	the	the	DET
cana-2105	32	6	picard	picard	NOUN
cana-2105	32	7	-	-	PUNCT
cana-2105	32	8	mann	mann	PROPN
cana-2105	32	9	iteration	iteration	NOUN
cana-2105	32	10	with	with	ADP
cana-2105	32	11	s	s	NOUN
cana-2105	32	12	-	-	NOUN
cana-2105	32	13	convexity	convexity	NOUN
cana-2105	32	14	[	[	X
cana-2105	32	15	15	15	NUM
cana-2105	32	16	]	]	PUNCT
cana-2105	32	17	,	,	PUNCT
cana-2105	32	18	and	and	CCONJ
cana-2105	32	19	the	the	DET
cana-2105	32	20	picard	picard	NOUN
cana-2105	32	21	-	-	PUNCT
cana-2105	32	22	ishikawa	ishikawa	PROPN
cana-2105	32	23	iteration	iteration	NOUN
cana-2105	33	1	[	[	X
cana-2105	33	2	1	1	NUM
cana-2105	33	3	]	]	PUNCT
cana-2105	33	4	,	,	PUNCT
cana-2105	33	5	viscosity	viscosity	NOUN
cana-2105	33	6	approximation	approximation	NOUN
cana-2105	33	7	method	method	NOUN
cana-2105	33	8	[	[	X
cana-2105	33	9	8	8	NUM
cana-2105	33	10	]	]	PUNCT
cana-2105	33	11	,	,	PUNCT
cana-2105	33	12	jungck	jungck	PROPN
cana-2105	33	13	-	-	PUNCT
cana-2105	33	14	noor	noor	PROPN
cana-2105	33	15	iteration	iteration	NOUN
cana-2105	33	16	with	with	ADP
cana-2105	33	17	s	s	NOUN
cana-2105	33	18	-	-	NOUN
cana-2105	33	19	convexity	convexity	NOUN
cana-2105	33	20	[	[	X
cana-2105	33	21	18	18	NUM
cana-2105	33	22	]	]	PUNCT
cana-2105	33	23	,	,	PUNCT
cana-2105	33	24	jungck	jungck	PROPN
cana-2105	33	25	-	-	PUNCT
cana-2105	33	26	cr	cr	PROPN
cana-2105	34	1	[	[	X
cana-2105	34	2	17	17	NUM
cana-2105	34	3	]	]	PUNCT
cana-2105	34	4	,	,	PUNCT
cana-2105	34	5	have	have	AUX
cana-2105	34	6	all	all	PRON
cana-2105	34	7	been	be	AUX
cana-2105	34	8	used	use	VERB
cana-2105	34	9	to	to	PART
cana-2105	34	10	generate	generate	VERB
cana-2105	34	11	the	the	DET
cana-2105	34	12	julia	julia	PROPN
cana-2105	34	13	and	and	CCONJ
cana-2105	34	14	mandelbrot	mandelbrot	PROPN
cana-2105	34	15	sets	set	VERB
cana-2105	34	16	.	.	PUNCT
cana-2105	35	1	tomar	tomar	NOUN
cana-2105	35	2	et	et	PROPN
cana-2105	35	3	al	al	PROPN
cana-2105	35	4	.	.	PUNCT
cana-2105	36	1	[	[	X
cana-2105	36	2	19	19	NUM
cana-2105	36	3	]	]	PUNCT
cana-2105	36	4	flourished	flourish	VERB
cana-2105	36	5	escape	escape	NOUN
cana-2105	36	6	criteria	criterion	NOUN
cana-2105	36	7	for	for	ADP
cana-2105	36	8	the	the	DET
cana-2105	36	9	complex	complex	ADV
cana-2105	36	10	-	-	PUNCT
cana-2105	36	11	valued	value	VERB
cana-2105	36	12	function	function	NOUN
cana-2105	36	13	sin(zk)−az+	sin(zk)−az+	NOUN
cana-2105	37	1	c	c	X
cana-2105	37	2	,	,	PUNCT
cana-2105	37	3	for	for	ADP
cana-2105	37	4	all	all	DET
cana-2105	37	5	k	k	PROPN
cana-2105	37	6	∈	∈	PROPN
cana-2105	37	7	n\{1	n\{1	PROPN
cana-2105	37	8	}	}	PUNCT
cana-2105	37	9	using	use	VERB
cana-2105	37	10	noor	noor	NOUN
cana-2105	37	11	-	-	PUNCT
cana-2105	37	12	iteration	iteration	NOUN
cana-2105	37	13	,	,	PUNCT
cana-2105	37	14	created	create	VERB
cana-2105	37	15	and	and	CCONJ
cana-2105	37	16	examined	examine	VERB
cana-2105	37	17	numerous	numerous	ADJ
cana-2105	37	18	mandelbrot	mandelbrot	NOUN
cana-2105	37	19	sets	set	NOUN
cana-2105	37	20	.	.	PUNCT
cana-2105	38	1	in	in	ADP
cana-2105	38	2	order	order	NOUN
cana-2105	38	3	to	to	PART
cana-2105	38	4	estimate	estimate	VERB
cana-2105	38	5	a	a	DET
cana-2105	38	6	fixed	fix	VERB
cana-2105	38	7	point	point	NOUN
cana-2105	38	8	for	for	ADP
cana-2105	38	9	a	a	DET
cana-2105	38	10	contraction	contraction	NOUN
cana-2105	38	11	mapping	mapping	NOUN
cana-2105	38	12	with	with	ADP
cana-2105	38	13	a	a	DET
cana-2105	38	14	weak	weak	ADJ
cana-2105	38	15	type	type	NOUN
cana-2105	38	16	,	,	PUNCT
cana-2105	38	17	shatanawi	shatanawi	ADJ
cana-2105	38	18	et	et	NOUN
cana-2105	38	19	al.[16	al.[16	PROPN
cana-2105	38	20	]	]	PUNCT
cana-2105	38	21	have	have	AUX
cana-2105	38	22	been	be	AUX
cana-2105	38	23	introduced	introduce	VERB
cana-2105	38	24	a	a	DET
cana-2105	38	25	four	four	NUM
cana-2105	38	26	-	-	PUNCT
cana-2105	38	27	step	step	NOUN
cana-2105	38	28	iterative	iterative	NOUN
cana-2105	38	29	technique	technique	NOUN
cana-2105	38	30	.	.	PUNCT
cana-2105	39	1	by	by	ADP
cana-2105	39	2	incorporating	incorporate	VERB
cana-2105	39	3	s	s	NOUN
cana-2105	39	4	-	-	NOUN
cana-2105	39	5	convexity	convexity	NOUN
cana-2105	39	6	into	into	ADP
cana-2105	39	7	a	a	DET
cana-2105	39	8	four	four	NUM
cana-2105	39	9	-	-	PUNCT
cana-2105	39	10	step	step	NOUN
cana-2105	39	11	iterative	iterative	NOUN
cana-2105	39	12	technique	technique	NOUN
cana-2105	39	13	,	,	PUNCT
cana-2105	39	14	tomar	tomar	NOUN
cana-2105	39	15	et	et	NOUN
cana-2105	39	16	al	al	PROPN
cana-2105	39	17	.	.	PUNCT
cana-2105	40	1	[	[	X
cana-2105	40	2	20	20	NUM
cana-2105	40	3	]	]	PUNCT
cana-2105	40	4	proved	prove	VERB
cana-2105	40	5	an	an	DET
cana-2105	40	6	escape	escape	NOUN
cana-2105	40	7	criterion	criterion	NOUN
cana-2105	40	8	for	for	ADP
cana-2105	40	9	complex	complex	ADV
cana-2105	40	10	-	-	PUNCT
cana-2105	40	11	valued	value	VERB
cana-2105	40	12	cosine	cosine	NOUN
cana-2105	40	13	function	function	NOUN
cana-2105	40	14	and	and	CCONJ
cana-2105	40	15	generate	generate	VERB
cana-2105	40	16	fascinating	fascinating	ADJ
cana-2105	40	17	fractal	fractal	ADJ
cana-2105	40	18	formations	formation	NOUN
cana-2105	40	19	,	,	PUNCT
cana-2105	40	20	including	include	VERB
cana-2105	40	21	julia	julia	PROPN
cana-2105	40	22	and	and	CCONJ
cana-2105	40	23	mandelbrot	mandelbrot	PROPN
cana-2105	40	24	sets	set	NOUN
cana-2105	40	25	.	.	PUNCT
cana-2105	41	1	recently	recently	ADV
cana-2105	41	2	adhikari	adhikari	PROPN
cana-2105	41	3	and	and	CCONJ
cana-2105	41	4	sintunavarat	sintunavarat	NOUN
cana-2105	41	5	create	create	VERB
cana-2105	41	6	and	and	CCONJ
cana-2105	41	7	analyze	analyze	VERB
cana-2105	41	8	the	the	DET
cana-2105	41	9	properties	property	NOUN
cana-2105	41	10	of	of	ADP
cana-2105	41	11	fractal	fractal	NOUN
cana-2105	41	12	for	for	ADP
cana-2105	41	13	modified	modify	VERB
cana-2105	41	14	functions	function	NOUN
cana-2105	41	15	(	(	PUNCT
cana-2105	41	16	see	see	VERB
cana-2105	41	17	details	detail	NOUN
cana-2105	41	18	in	in	ADP
cana-2105	41	19	[	[	X
cana-2105	41	20	3	3	X
cana-2105	41	21	]	]	X
cana-2105	41	22	[	[	X
cana-2105	41	23	2	2	NUM
cana-2105	41	24	]	]	PUNCT
cana-2105	41	25	)	)	PUNCT
cana-2105	41	26	.	.	PUNCT
cana-2105	42	1	the	the	DET
cana-2105	42	2	paper	paper	NOUN
cana-2105	42	3	employs	employ	VERB
cana-2105	42	4	a	a	DET
cana-2105	42	5	systematic	systematic	ADJ
cana-2105	42	6	approach	approach	NOUN
cana-2105	42	7	,	,	PUNCT
cana-2105	42	8	integrating	integrate	VERB
cana-2105	42	9	the	the	DET
cana-2105	42	10	four	four	NUM
cana-2105	42	11	-	-	PUNCT
cana-2105	42	12	step	step	NOUN
cana-2105	42	13	iterative	iterative	NOUN
cana-2105	42	14	method	method	NOUN
cana-2105	42	15	with	with	ADP
cana-2105	42	16	s	s	NOUN
cana-2105	42	17	-	-	NOUN
cana-2105	42	18	convexity	convexity	NOUN
cana-2105	42	19	,	,	PUNCT
cana-2105	42	20	to	to	PART
cana-2105	42	21	investigate	investigate	VERB
cana-2105	42	22	novel	novel	ADJ
cana-2105	42	23	variations	variation	NOUN
cana-2105	42	24	of	of	ADP
cana-2105	42	25	the	the	DET
cana-2105	42	26	julia	julia	PROPN
cana-2105	42	27	and	and	CCONJ
cana-2105	42	28	mandelbrot	mandelbrot	PROPN
cana-2105	42	29	sets	set	VERB
cana-2105	42	30	.	.	PUNCT
cana-2105	43	1	the	the	DET
cana-2105	43	2	primary	primary	ADJ
cana-2105	43	3	objective	objective	NOUN
cana-2105	43	4	is	be	AUX
cana-2105	43	5	to	to	PART
cana-2105	43	6	define	define	VERB
cana-2105	43	7	criteria	criterion	NOUN
cana-2105	43	8	for	for	ADP
cana-2105	43	9	determining	determine	VERB
cana-2105	43	10	escape	escape	NOUN
cana-2105	43	11	conditions	condition	NOUN
cana-2105	43	12	for	for	ADP
cana-2105	43	13	the	the	DET
cana-2105	43	14	function	function	NOUN
cana-2105	43	15	sin(zk	sin(zk	NOUN
cana-2105	43	16	)	)	PUNCT
cana-2105	44	1	+	+	CCONJ
cana-2105	44	2	az	az	PROPN
cana-2105	44	3	+	+	CCONJ
cana-2105	44	4	c	c	PROPN
cana-2105	44	5	for	for	ADP
cana-2105	44	6	all	all	DET
cana-2105	44	7	z	z	NOUN
cana-2105	44	8	∈	∈	PROPN
cana-2105	44	9	c	c	PROPN
cana-2105	44	10	and	and	CCONJ
cana-2105	44	11	k	k	PROPN
cana-2105	44	12	is	be	AUX
cana-2105	44	13	a	a	DET
cana-2105	44	14	natural	natural	ADJ
cana-2105	44	15	number	number	NOUN
cana-2105	44	16	excluding	exclude	VERB
cana-2105	44	17	1	1	NUM
cana-2105	44	18	,	,	PUNCT
cana-2105	44	19	and	and	CCONJ
cana-2105	44	20	a	a	PRON
cana-2105	44	21	,	,	PUNCT
cana-2105	44	22	c	c	PROPN
cana-2105	44	23	are	be	AUX
cana-2105	44	24	complex	complex	ADJ
cana-2105	44	25	constants	constant	NOUN
cana-2105	44	26	with	with	ADP
cana-2105	44	27	a	a	DET
cana-2105	44	28	̸=	̸=	PROPN
cana-2105	44	29	0	0	NUM
cana-2105	44	30	.	.	PUNCT
cana-2105	45	1	the	the	DET
cana-2105	45	2	study	study	NOUN
cana-2105	45	3	aims	aim	VERB
cana-2105	45	4	to	to	PART
cana-2105	45	5	devise	devise	VERB
cana-2105	45	6	and	and	CCONJ
cana-2105	45	7	execute	execute	VERB
cana-2105	45	8	algorithms	algorithm	NOUN
cana-2105	45	9	capable	capable	ADJ
cana-2105	45	10	of	of	ADP
cana-2105	45	11	generating	generate	VERB
cana-2105	45	12	these	these	DET
cana-2105	45	13	fractal	fractal	ADJ
cana-2105	45	14	patterns	pattern	NOUN
cana-2105	45	15	,	,	PUNCT
cana-2105	45	16	thereby	thereby	ADV
cana-2105	45	17	expanding	expand	VERB
cana-2105	45	18	the	the	DET
cana-2105	45	19	scope	scope	NOUN
cana-2105	45	20	for	for	ADP
cana-2105	45	21	analyzing	analyze	VERB
cana-2105	45	22	these	these	DET
cana-2105	45	23	captivating	captivating	ADJ
cana-2105	45	24	fractal	fractal	ADJ
cana-2105	45	25	structures	structure	NOUN
cana-2105	45	26	.	.	PUNCT
cana-2105	46	1	the	the	DET
cana-2105	46	2	paper	paper	NOUN
cana-2105	46	3	is	be	AUX
cana-2105	46	4	structured	structure	VERB
cana-2105	46	5	into	into	ADP
cana-2105	46	6	several	several	ADJ
cana-2105	46	7	sections	section	NOUN
cana-2105	46	8	.	.	PUNCT
cana-2105	47	1	section	section	NOUN
cana-2105	47	2	2	2	NUM
cana-2105	47	3	offers	offer	VERB
cana-2105	47	4	an	an	DET
cana-2105	47	5	overview	overview	NOUN
cana-2105	47	6	of	of	ADP
cana-2105	47	7	the	the	DET
cana-2105	47	8	notation	notation	NOUN
cana-2105	47	9	and	and	CCONJ
cana-2105	47	10	definitions	definition	NOUN
cana-2105	47	11	employed	employ	VERB
cana-2105	47	12	throughout	throughout	ADP
cana-2105	47	13	the	the	DET
cana-2105	47	14	article	article	NOUN
cana-2105	47	15	.	.	PUNCT
cana-2105	48	1	section	section	NOUN
cana-2105	48	2	3	3	NUM
cana-2105	48	3	introduces	introduce	VERB
cana-2105	48	4	the	the	DET
cana-2105	48	5	definition	definition	NOUN
cana-2105	48	6	and	and	CCONJ
cana-2105	48	7	proves	prove	VERB
cana-2105	48	8	the	the	DET
cana-2105	48	9	escape	escape	NOUN
cana-2105	48	10	criterion	criterion	NOUN
cana-2105	48	11	and	and	CCONJ
cana-2105	48	12	algorithm	algorithm	NOUN
cana-2105	48	13	used	use	VERB
cana-2105	48	14	for	for	ADP
cana-2105	48	15	fractal	fractal	ADJ
cana-2105	48	16	generation	generation	NOUN
cana-2105	48	17	.	.	PUNCT
cana-2105	49	1	communications	communication	NOUN
cana-2105	49	2	on	on	ADP
cana-2105	49	3	applied	apply	VERB
cana-2105	49	4	nonlinear	nonlinear	ADJ
cana-2105	49	5	analysis	analysis	NOUN
cana-2105	49	6	issn	issn	NOUN
cana-2105	49	7	:	:	PUNCT
cana-2105	49	8	1074	1074	NUM
cana-2105	49	9	-	-	PUNCT
cana-2105	49	10	133x	133x	NUM
cana-2105	49	11	vol	vol	NOUN
cana-2105	49	12	32	32	NUM
cana-2105	49	13	no	no	NOUN
cana-2105	49	14	.	.	PUNCT
cana-2105	50	1	1s	1s	NUM
cana-2105	50	2	(	(	PUNCT
cana-2105	50	3	2025	2025	NUM
cana-2105	50	4	)	)	PUNCT
cana-2105	50	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	50	6	64	64	NUM
cana-2105	50	7	section	section	NOUN
cana-2105	50	8	4	4	NUM
cana-2105	50	9	provides	provide	VERB
cana-2105	50	10	visual	visual	ADJ
cana-2105	50	11	examples	example	NOUN
cana-2105	50	12	that	that	PRON
cana-2105	50	13	illustrate	illustrate	VERB
cana-2105	50	14	the	the	DET
cana-2105	50	15	behavior	behavior	NOUN
cana-2105	50	16	and	and	CCONJ
cana-2105	50	17	patterns	pattern	NOUN
cana-2105	50	18	produced	produce	VERB
cana-2105	50	19	by	by	ADP
cana-2105	50	20	the	the	DET
cana-2105	50	21	proposed	propose	VERB
cana-2105	50	22	methodology	methodology	NOUN
cana-2105	50	23	.	.	PUNCT
cana-2105	51	1	finally	finally	ADV
cana-2105	51	2	,	,	PUNCT
cana-2105	51	3	section	section	NOUN
cana-2105	51	4	5	5	NUM
cana-2105	51	5	summarizes	summarize	NOUN
cana-2105	51	6	the	the	DET
cana-2105	51	7	main	main	ADJ
cana-2105	51	8	results	result	NOUN
cana-2105	51	9	and	and	CCONJ
cana-2105	51	10	contributions	contribution	NOUN
cana-2105	51	11	of	of	ADP
cana-2105	51	12	the	the	DET
cana-2105	51	13	research	research	NOUN
cana-2105	51	14	.	.	PUNCT
cana-2105	52	1	2	2	NUM
cana-2105	52	2	preliminaries	preliminary	NOUN
cana-2105	52	3	in	in	ADP
cana-2105	52	4	this	this	DET
cana-2105	52	5	paper	paper	NOUN
cana-2105	52	6	,	,	PUNCT
cana-2105	52	7	c	c	X
cana-2105	52	8	,	,	PUNCT
cana-2105	52	9	r	r	NOUN
cana-2105	52	10	,	,	PUNCT
cana-2105	52	11	n	n	CCONJ
cana-2105	52	12	,	,	PUNCT
cana-2105	52	13	always	always	ADV
cana-2105	52	14	stand	stand	VERB
cana-2105	52	15	for	for	ADP
cana-2105	52	16	the	the	DET
cana-2105	52	17	set	set	NOUN
cana-2105	52	18	of	of	ADP
cana-2105	52	19	complex	complex	ADJ
cana-2105	52	20	numbers	number	NOUN
cana-2105	52	21	,	,	PUNCT
cana-2105	52	22	all	all	DET
cana-2105	52	23	real	real	ADJ
cana-2105	52	24	numbers	number	NOUN
cana-2105	52	25	,	,	PUNCT
cana-2105	52	26	all	all	DET
cana-2105	52	27	positive	positive	ADJ
cana-2105	52	28	integers	integer	NOUN
cana-2105	52	29	,	,	PUNCT
cana-2105	52	30	respectively	respectively	ADV
cana-2105	52	31	.	.	PUNCT
cana-2105	53	1	in	in	ADP
cana-2105	53	2	this	this	DET
cana-2105	53	3	section	section	NOUN
cana-2105	53	4	,	,	PUNCT
cana-2105	53	5	we	we	PRON
cana-2105	53	6	define	define	VERB
cana-2105	53	7	julia	julia	PROPN
cana-2105	53	8	set	set	PROPN
cana-2105	53	9	,	,	PUNCT
cana-2105	53	10	mandelbrot	mandelbrot	PROPN
cana-2105	53	11	set	set	PROPN
cana-2105	53	12	,	,	PUNCT
cana-2105	53	13	sconvexity	sconvexity	NOUN
cana-2105	53	14	and	and	CCONJ
cana-2105	53	15	four	four	NUM
cana-2105	53	16	-	-	PUNCT
cana-2105	53	17	step	step	NOUN
cana-2105	53	18	iteration	iteration	NOUN
cana-2105	53	19	which	which	PRON
cana-2105	53	20	is	be	AUX
cana-2105	53	21	use	use	NOUN
cana-2105	53	22	in	in	ADP
cana-2105	53	23	this	this	DET
cana-2105	53	24	research	research	NOUN
cana-2105	53	25	paper	paper	NOUN
cana-2105	53	26	.	.	PUNCT
cana-2105	54	1	definition	definition	NOUN
cana-2105	54	2	2.1	2.1	NUM
cana-2105	54	3	(	(	PUNCT
cana-2105	54	4	[	[	X
cana-2105	54	5	6	6	NUM
cana-2105	54	6	]	]	NUM
cana-2105	54	7	)	)	PUNCT
cana-2105	54	8	.	.	PUNCT
cana-2105	55	1	the	the	DET
cana-2105	55	2	set	set	NOUN
cana-2105	55	3	of	of	ADP
cana-2105	55	4	complex	complex	ADJ
cana-2105	55	5	numbers	number	NOUN
cana-2105	55	6	in	in	ADP
cana-2105	55	7	which	which	PRON
cana-2105	55	8	the	the	DET
cana-2105	55	9	orbit	orbit	NOUN
cana-2105	55	10	of	of	ADP
cana-2105	55	11	function	function	NOUN
cana-2105	55	12	tc	tc	INTJ
cana-2105	55	13	:	:	PUNCT
cana-2105	55	14	c	c	X
cana-2105	55	15	→	→	SYM
cana-2105	55	16	c	c	X
cana-2105	55	17	,	,	PUNCT
cana-2105	55	18	where	where	SCONJ
cana-2105	55	19	c	c	AUX
cana-2105	55	20	∈	∈	PROPN
cana-2105	55	21	c	c	AUX
cana-2105	55	22	not	not	PART
cana-2105	55	23	diverges	diverge	VERB
cana-2105	55	24	towards	towards	ADP
cana-2105	55	25	infinity	infinity	NOUN
cana-2105	55	26	is	be	AUX
cana-2105	55	27	referred	refer	VERB
cana-2105	55	28	to	to	ADP
cana-2105	55	29	as	as	ADP
cana-2105	55	30	the	the	DET
cana-2105	55	31	filled	fill	VERB
cana-2105	55	32	julia	julia	PROPN
cana-2105	55	33	set	set	PROPN
cana-2105	55	34	of	of	ADP
cana-2105	55	35	tc	tc	NOUN
cana-2105	55	36	.	.	PUNCT
cana-2105	56	1	it	it	PRON
cana-2105	56	2	is	be	AUX
cana-2105	56	3	denoted	denote	VERB
cana-2105	56	4	by	by	ADP
cana-2105	56	5	jtc	jtc	PROPN
cana-2105	56	6	and	and	CCONJ
cana-2105	56	7	write	write	VERB
cana-2105	56	8	jtc	jtc	PROPN
cana-2105	57	1	=	=	PUNCT
cana-2105	57	2	{	{	PUNCT
cana-2105	57	3	z	z	PROPN
cana-2105	57	4	∈	∈	PROPN
cana-2105	57	5	c	c	NOUN
cana-2105	57	6	:	:	PUNCT
cana-2105	57	7	{	{	PUNCT
cana-2105	57	8	|t	|t	PROPN
cana-2105	57	9	n	n	ADV
cana-2105	57	10	c	c	NOUN
cana-2105	58	1	(	(	PUNCT
cana-2105	58	2	z)|}∞n=0	z)|}∞n=0	PROPN
cana-2105	58	3	is	be	AUX
cana-2105	58	4	bounded	bound	VERB
cana-2105	58	5	}	}	PUNCT
cana-2105	58	6	.	.	PUNCT
cana-2105	59	1	definition	definition	NOUN
cana-2105	59	2	2.2	2.2	NUM
cana-2105	59	3	(	(	PUNCT
cana-2105	59	4	[	[	X
cana-2105	59	5	11	11	NUM
cana-2105	59	6	]	]	NUM
cana-2105	59	7	)	)	PUNCT
cana-2105	59	8	.	.	PUNCT
cana-2105	60	1	let	let	VERB
cana-2105	60	2	tc	tc	NOUN
cana-2105	60	3	:	:	PUNCT
cana-2105	60	4	c	c	X
cana-2105	60	5	→	→	PUNCT
cana-2105	60	6	c	c	X
cana-2105	60	7	be	be	AUX
cana-2105	60	8	a	a	DET
cana-2105	60	9	complex	complex	ADJ
cana-2105	60	10	mapping	mapping	NOUN
cana-2105	60	11	,	,	PUNCT
cana-2105	60	12	where	where	SCONJ
cana-2105	60	13	c	c	PROPN
cana-2105	60	14	∈	∈	PROPN
cana-2105	60	15	c	c	NOUN
cana-2105	60	16	is	be	AUX
cana-2105	60	17	a	a	DET
cana-2105	60	18	parameter	parameter	NOUN
cana-2105	60	19	.	.	PUNCT
cana-2105	61	1	the	the	DET
cana-2105	61	2	mandelbrot	mandelbrot	PROPN
cana-2105	61	3	set	set	VERB
cana-2105	61	4	is	be	AUX
cana-2105	61	5	defined	define	VERB
cana-2105	61	6	as	as	ADP
cana-2105	61	7	m	m	NOUN
cana-2105	61	8	=	=	PUNCT
cana-2105	62	1	{	{	PUNCT
cana-2105	62	2	c	c	NOUN
cana-2105	62	3	∈	∈	PROPN
cana-2105	62	4	c	c	NOUN
cana-2105	62	5	:	:	PUNCT
cana-2105	63	1	jtc	jtc	PROPN
cana-2105	63	2	is	be	AUX
cana-2105	63	3	connected	connect	VERB
cana-2105	63	4	}	}	PUNCT
cana-2105	63	5	.	.	PUNCT
cana-2105	64	1	equivalently	equivalently	ADV
cana-2105	64	2	,	,	PUNCT
cana-2105	64	3	the	the	DET
cana-2105	64	4	mandelbrot	mandelbrot	NOUN
cana-2105	64	5	set	set	VERB
cana-2105	64	6	m	m	NOUN
cana-2105	64	7	can	can	AUX
cana-2105	64	8	be	be	AUX
cana-2105	64	9	defined	define	VERB
cana-2105	64	10	in	in	ADP
cana-2105	64	11	[	[	X
cana-2105	64	12	10	10	NUM
cana-2105	64	13	]	]	PUNCT
cana-2105	64	14	as	as	ADP
cana-2105	64	15	:	:	PUNCT
cana-2105	64	16	m	m	VERB
cana-2105	64	17	=	=	PUNCT
cana-2105	64	18	{	{	PUNCT
cana-2105	64	19	c	c	NOUN
cana-2105	64	20	∈	∈	PROPN
cana-2105	64	21	c	c	NOUN
cana-2105	64	22	:	:	PUNCT
cana-2105	64	23	t	t	PROPN
cana-2105	64	24	n(κ	n(κ	PROPN
cana-2105	64	25	)	)	PUNCT
cana-2105	64	26	↛	↛	NUM
cana-2105	64	27	∞	∞	NUM
cana-2105	64	28	as	as	ADP
cana-2105	64	29	n	n	PROPN
cana-2105	64	30	→	→	SYM
cana-2105	64	31	∞	∞	NOUN
cana-2105	64	32	}	}	PUNCT
cana-2105	64	33	where	where	SCONJ
cana-2105	64	34	,	,	PUNCT
cana-2105	64	35	κ	κ	PROPN
cana-2105	64	36	is	be	AUX
cana-2105	64	37	any	any	DET
cana-2105	64	38	critical	critical	ADJ
cana-2105	64	39	point	point	NOUN
cana-2105	64	40	of	of	ADP
cana-2105	64	41	tc	tc	NOUN
cana-2105	64	42	.	.	PUNCT
cana-2105	65	1	in	in	ADP
cana-2105	65	2	the	the	DET
cana-2105	65	3	year	year	NOUN
cana-2105	65	4	2020	2020	NUM
cana-2105	65	5	,	,	PUNCT
cana-2105	65	6	the	the	DET
cana-2105	65	7	following	follow	VERB
cana-2105	65	8	four	four	NUM
cana-2105	65	9	-	-	PUNCT
cana-2105	65	10	step	step	NOUN
cana-2105	65	11	iterative	iterative	NOUN
cana-2105	65	12	approach	approach	NOUN
cana-2105	65	13	was	be	AUX
cana-2105	65	14	proposed	propose	VERB
cana-2105	65	15	by	by	ADP
cana-2105	65	16	shatanawi	shatanawi	PROPN
cana-2105	65	17	et	et	PROPN
cana-2105	65	18	al	al	PROPN
cana-2105	65	19	.	.	PUNCT
cana-2105	66	1	[	[	X
cana-2105	66	2	16	16	NUM
cana-2105	66	3	]	]	PUNCT
cana-2105	66	4	for	for	ADP
cana-2105	66	5	the	the	DET
cana-2105	66	6	approximating	approximate	VERB
cana-2105	66	7	a	a	DET
cana-2105	66	8	fixed	fix	VERB
cana-2105	66	9	point	point	NOUN
cana-2105	66	10	within	within	ADP
cana-2105	66	11	a	a	DET
cana-2105	66	12	weak	weak	ADJ
cana-2105	66	13	-	-	PUNCT
cana-2105	66	14	type	type	NOUN
cana-2105	66	15	contraction	contraction	NOUN
cana-2105	66	16	mapping	mapping	NOUN
cana-2105	66	17	.	.	PUNCT
cana-2105	67	1	definition	definition	NOUN
cana-2105	67	2	2.3	2.3	NUM
cana-2105	67	3	(	(	PUNCT
cana-2105	67	4	[	[	X
cana-2105	67	5	16	16	NUM
cana-2105	67	6	]	]	PUNCT
cana-2105	67	7	)	)	PUNCT
cana-2105	67	8	.	.	PUNCT
cana-2105	68	1	let	let	VERB
cana-2105	68	2	tc	tc	NOUN
cana-2105	68	3	:	:	PUNCT
cana-2105	68	4	c	c	X
cana-2105	68	5	→	→	SYM
cana-2105	68	6	c	c	NOUN
cana-2105	68	7	to	to	PART
cana-2105	68	8	be	be	AUX
cana-2105	68	9	a	a	DET
cana-2105	68	10	complex	complex	ADV
cana-2105	68	11	-	-	PUNCT
cana-2105	68	12	valued	value	VERB
cana-2105	68	13	self	self	NOUN
cana-2105	68	14	-	-	PUNCT
cana-2105	68	15	mapping	mapping	NOUN
cana-2105	68	16	.	.	PUNCT
cana-2105	69	1	for	for	ADP
cana-2105	69	2	initial	initial	ADJ
cana-2105	69	3	point	point	NOUN
cana-2105	69	4	z0	z0	PROPN
cana-2105	69	5	∈	∈	PROPN
cana-2105	69	6	c	c	NOUN
cana-2105	69	7	the	the	DET
cana-2105	69	8	four	four	NUM
cana-2105	69	9	-	-	PUNCT
cana-2105	69	10	step	step	NOUN
cana-2105	69	11	iteration	iteration	NOUN
cana-2105	69	12	scheme	scheme	NOUN
cana-2105	69	13	for	for	ADP
cana-2105	69	14	sequence	sequence	NOUN
cana-2105	69	15	{	{	PUNCT
cana-2105	69	16	zn	zn	NOUN
cana-2105	69	17	}	}	PUNCT
cana-2105	69	18	with	with	ADP
cana-2105	69	19	constant	constant	ADJ
cana-2105	69	20	parameter	parameter	NOUN
cana-2105	69	21	is	be	AUX
cana-2105	69	22	defined	define	VERB
cana-2105	69	23	as	as	ADP
cana-2105	69	24	:	:	PUNCT
cana-2105	69	25			PROPN
cana-2105	69	26	un	un	PROPN
cana-2105	69	27	=	=	PRON
cana-2105	69	28	(	(	PUNCT
cana-2105	69	29	1−	1−	NUM
cana-2105	69	30	δ)zn	δ)zn	PROPN
cana-2105	69	31	+	+	CCONJ
cana-2105	69	32	δtczn	δtczn	ADJ
cana-2105	69	33	vn	vn	PROPN
cana-2105	69	34	=	=	SYM
cana-2105	69	35	(	(	PUNCT
cana-2105	69	36	1−	1−	NUM
cana-2105	69	37	γ)zn	γ)zn	NOUN
cana-2105	69	38	+	+	CCONJ
cana-2105	69	39	γtcun	γtcun	PROPN
cana-2105	69	40	wn	wn	PROPN
cana-2105	69	41	=	=	PRON
cana-2105	69	42	(	(	PUNCT
cana-2105	69	43	1−	1−	NUM
cana-2105	69	44	β)zn	β)zn	NOUN
cana-2105	69	45	+	+	NUM
cana-2105	69	46	βtcvn	βtcvn	NOUN
cana-2105	69	47	zn+1	zn+1	X
cana-2105	69	48	=	=	SYM
cana-2105	69	49	(	(	PUNCT
cana-2105	69	50	1−	1−	NUM
cana-2105	69	51	α)zn	α)zn	NOUN
cana-2105	69	52	+	+	CCONJ
cana-2105	69	53	αtcwn	αtcwn	NOUN
cana-2105	69	54	(	(	PUNCT
cana-2105	69	55	2.1	2.1	NUM
cana-2105	69	56	)	)	PUNCT
cana-2105	69	57	for	for	ADP
cana-2105	69	58	all	all	PRON
cana-2105	69	59	n	n	PRON
cana-2105	69	60	∈	∈	NOUN
cana-2105	69	61	n	n	NOUN
cana-2105	69	62	∪	∪	X
cana-2105	69	63	{	{	PUNCT
cana-2105	69	64	0	0	NUM
cana-2105	69	65	}	}	PUNCT
cana-2105	69	66	and	and	CCONJ
cana-2105	69	67	α	α	NOUN
cana-2105	69	68	,	,	PUNCT
cana-2105	69	69	β	β	X
cana-2105	69	70	,	,	PUNCT
cana-2105	69	71	γ	γ	PROPN
cana-2105	69	72	,	,	PUNCT
cana-2105	69	73	δ	δ	PROPN
cana-2105	69	74	∈	∈	PROPN
cana-2105	69	75	(	(	PUNCT
cana-2105	69	76	0	0	NUM
cana-2105	69	77	,	,	PUNCT
cana-2105	69	78	1	1	NUM
cana-2105	69	79	]	]	PUNCT
cana-2105	69	80	.	.	PUNCT
cana-2105	70	1	definition	definition	NOUN
cana-2105	70	2	2.4	2.4	NUM
cana-2105	70	3	(	(	PUNCT
cana-2105	70	4	[	[	X
cana-2105	70	5	12	12	NUM
cana-2105	70	6	]	]	PUNCT
cana-2105	70	7	)	)	PUNCT
cana-2105	70	8	.	.	PUNCT
cana-2105	71	1	let	let	VERB
cana-2105	71	2	z1	z1	NOUN
cana-2105	71	3	,	,	PUNCT
cana-2105	71	4	z2	z2	PROPN
cana-2105	71	5	,	,	PUNCT
cana-2105	71	6	z3	z3	PROPN
cana-2105	71	7	,	,	PUNCT
cana-2105	71	8	·	·	PUNCT
cana-2105	71	9	·	·	PUNCT
cana-2105	71	10	·	·	PUNCT
cana-2105	71	11	,	,	PUNCT
cana-2105	71	12	zn	zn	PROPN
cana-2105	71	13	∈	∈	PROPN
cana-2105	71	14	c	c	PROPN
cana-2105	71	15	and	and	CCONJ
cana-2105	71	16	s	s	PROPN
cana-2105	71	17	∈	∈	PROPN
cana-2105	71	18	(	(	PUNCT
cana-2105	71	19	0	0	NUM
cana-2105	71	20	,	,	PUNCT
cana-2105	71	21	1	1	NUM
cana-2105	71	22	]	]	PUNCT
cana-2105	71	23	.	.	PUNCT
cana-2105	72	1	the	the	DET
cana-2105	72	2	s	s	ADJ
cana-2105	72	3	-	-	ADJ
cana-2105	72	4	convex	convex	ADJ
cana-2105	72	5	combination	combination	NOUN
cana-2105	72	6	is	be	AUX
cana-2105	72	7	defined	define	VERB
cana-2105	72	8	by	by	ADP
cana-2105	72	9	λs	λs	ADP
cana-2105	72	10	1	1	NUM
cana-2105	72	11	·	·	PUNCT
cana-2105	72	12	z1	z1	NOUN
cana-2105	72	13	+	+	CCONJ
cana-2105	72	14	λs	λs	PROPN
cana-2105	72	15	2	2	NUM
cana-2105	72	16	·	·	PUNCT
cana-2105	72	17	z2	z2	NOUN
cana-2105	72	18	+	+	CCONJ
cana-2105	72	19	λs	λs	PROPN
cana-2105	72	20	3	3	NUM
cana-2105	72	21	·	·	PUNCT
cana-2105	72	22	z3	z3	PROPN
cana-2105	72	23	+	+	CCONJ
cana-2105	72	24	·	·	PUNCT
cana-2105	72	25	·	·	PUNCT
cana-2105	72	26	·	·	PUNCT
cana-2105	73	1	+	+	NUM
cana-2105	73	2	λs	λs	NOUN
cana-2105	73	3	n	n	PROPN
cana-2105	73	4	·	·	PUNCT
cana-2105	73	5	zn	zn	X
cana-2105	73	6	(	(	PUNCT
cana-2105	73	7	2.2	2.2	NUM
cana-2105	73	8	)	)	PUNCT
cana-2105	73	9	where	where	SCONJ
cana-2105	73	10	,	,	PUNCT
cana-2105	73	11	λk	λk	PRON
cana-2105	73	12	≥	≥	NOUN
cana-2105	73	13	0	0	NUM
cana-2105	73	14	and	and	CCONJ
cana-2105	73	15	∑n	∑n	PROPN
cana-2105	73	16	k=1	k=1	X
cana-2105	73	17	λk	λk	X
cana-2105	73	18	=	=	NOUN
cana-2105	73	19	1	1	X
cana-2105	73	20	.	.	PUNCT
cana-2105	74	1	when	when	SCONJ
cana-2105	74	2	s	s	VERB
cana-2105	74	3	=	=	SYM
cana-2105	74	4	1	1	NUM
cana-2105	74	5	,	,	PUNCT
cana-2105	74	6	the	the	DET
cana-2105	74	7	s	s	NOUN
cana-2105	74	8	-	-	ADJ
cana-2105	74	9	convex	convex	ADJ
cana-2105	74	10	combination	combination	NOUN
cana-2105	74	11	reduced	reduce	VERB
cana-2105	74	12	to	to	ADP
cana-2105	74	13	the	the	DET
cana-2105	74	14	standard	standard	ADJ
cana-2105	74	15	combination	combination	NOUN
cana-2105	74	16	.	.	PUNCT
cana-2105	75	1	communications	communication	NOUN
cana-2105	75	2	on	on	ADP
cana-2105	75	3	applied	apply	VERB
cana-2105	75	4	nonlinear	nonlinear	ADJ
cana-2105	75	5	analysis	analysis	NOUN
cana-2105	75	6	issn	issn	NOUN
cana-2105	75	7	:	:	PUNCT
cana-2105	75	8	1074	1074	NUM
cana-2105	75	9	-	-	PUNCT
cana-2105	75	10	133x	133x	NUM
cana-2105	75	11	vol	vol	NOUN
cana-2105	75	12	32	32	NUM
cana-2105	75	13	no	no	NOUN
cana-2105	75	14	.	.	PUNCT
cana-2105	76	1	1s	1s	NUM
cana-2105	76	2	(	(	PUNCT
cana-2105	76	3	2025	2025	NUM
cana-2105	76	4	)	)	PUNCT
cana-2105	76	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	77	1	65	65	NUM
cana-2105	77	2	recently	recently	ADV
cana-2105	77	3	,	,	PUNCT
cana-2105	77	4	tomar	tomar	PROPN
cana-2105	77	5	et	et	PROPN
cana-2105	77	6	al	al	PROPN
cana-2105	77	7	.	.	PUNCT
cana-2105	78	1	[	[	X
cana-2105	78	2	20	20	NUM
cana-2105	78	3	]	]	PUNCT
cana-2105	78	4	added	add	VERB
cana-2105	78	5	the	the	DET
cana-2105	78	6	s	s	NOUN
cana-2105	78	7	-	-	ADJ
cana-2105	78	8	convex	convex	ADJ
cana-2105	78	9	combination	combination	NOUN
cana-2105	78	10	to	to	ADP
cana-2105	78	11	the	the	DET
cana-2105	78	12	four	four	NUM
cana-2105	78	13	-	-	PUNCT
cana-2105	78	14	step	step	NOUN
cana-2105	78	15	iteration	iteration	NOUN
cana-2105	78	16	,	,	PUNCT
cana-2105	78	17	which	which	PRON
cana-2105	78	18	is	be	AUX
cana-2105	78	19	defined	define	VERB
cana-2105	78	20	as	as	SCONJ
cana-2105	78	21	follows	follow	VERB
cana-2105	78	22	:	:	PUNCT
cana-2105	78	23	definition	definition	NOUN
cana-2105	78	24	2.5	2.5	NUM
cana-2105	78	25	(	(	PUNCT
cana-2105	78	26	[	[	X
cana-2105	78	27	20	20	NUM
cana-2105	78	28	]	]	NUM
cana-2105	78	29	)	)	PUNCT
cana-2105	78	30	.	.	PUNCT
cana-2105	79	1	tc	tc	NOUN
cana-2105	79	2	:	:	PUNCT
cana-2105	80	1	c	c	X
cana-2105	80	2	→	→	SYM
cana-2105	80	3	c	c	NOUN
cana-2105	80	4	to	to	PART
cana-2105	80	5	be	be	AUX
cana-2105	80	6	a	a	DET
cana-2105	80	7	complex	complex	ADV
cana-2105	80	8	-	-	PUNCT
cana-2105	80	9	valued	value	VERB
cana-2105	80	10	self	self	NOUN
cana-2105	80	11	-	-	PUNCT
cana-2105	80	12	mapping	mapping	NOUN
cana-2105	80	13	.	.	PUNCT
cana-2105	81	1	for	for	ADP
cana-2105	81	2	initial	initial	ADJ
cana-2105	81	3	point	point	NOUN
cana-2105	81	4	z0	z0	PROPN
cana-2105	81	5	∈	∈	PROPN
cana-2105	81	6	c	c	NOUN
cana-2105	81	7	,	,	PUNCT
cana-2105	81	8	the	the	DET
cana-2105	81	9	four	four	NUM
cana-2105	81	10	-	-	PUNCT
cana-2105	81	11	step	step	NOUN
cana-2105	81	12	iteration	iteration	NOUN
cana-2105	81	13	scheme	scheme	NOUN
cana-2105	81	14	with	with	ADP
cana-2105	81	15	s	s	NOUN
cana-2105	81	16	-	-	NOUN
cana-2105	81	17	convexity	convexity	NOUN
cana-2105	81	18	for	for	ADP
cana-2105	81	19	sequence	sequence	NOUN
cana-2105	81	20	{	{	PUNCT
cana-2105	81	21	zn}∞n=0	zn}∞n=0	NUM
cana-2105	81	22	with	with	ADP
cana-2105	81	23	constant	constant	ADJ
cana-2105	81	24	parameter	parameter	NOUN
cana-2105	81	25	is	be	AUX
cana-2105	81	26	defined	define	VERB
cana-2105	82	1	as:	as:	ADJ
cana-2105	82	2	un	un	PROPN
cana-2105	82	3	=	=	SYM
cana-2105	82	4	(	(	PUNCT
cana-2105	82	5	1−	1−	NUM
cana-2105	82	6	δ)szn	δ)szn	PROPN
cana-2105	82	7	+	+	CCONJ
cana-2105	82	8	δstczn	δstczn	ADV
cana-2105	82	9	vn	vn	PROPN
cana-2105	82	10	=	=	SYM
cana-2105	82	11	(	(	PUNCT
cana-2105	82	12	1−	1−	NUM
cana-2105	82	13	γ)szn	γ)szn	NOUN
cana-2105	82	14	+	+	CCONJ
cana-2105	82	15	γstcun	γstcun	NOUN
cana-2105	82	16	wn	wn	NOUN
cana-2105	82	17	=	=	SYM
cana-2105	82	18	(	(	PUNCT
cana-2105	82	19	1−	1−	NUM
cana-2105	82	20	β)szn	β)szn	NOUN
cana-2105	83	1	+	+	CCONJ
cana-2105	83	2	βstcvn	βstcvn	ADJ
cana-2105	83	3	zn+1	zn+1	X
cana-2105	83	4	=	=	SYM
cana-2105	83	5	(	(	PUNCT
cana-2105	83	6	1−	1−	NUM
cana-2105	83	7	α)szn	α)szn	NUM
cana-2105	83	8	+	+	NUM
cana-2105	83	9	αstcwn	αstcwn	NOUN
cana-2105	83	10	(	(	PUNCT
cana-2105	83	11	2.3	2.3	NUM
cana-2105	83	12	)	)	PUNCT
cana-2105	83	13	for	for	ADP
cana-2105	83	14	all	all	PRON
cana-2105	83	15	n	n	PRON
cana-2105	83	16	∈	∈	NOUN
cana-2105	83	17	n	n	NOUN
cana-2105	83	18	∪	∪	X
cana-2105	83	19	{	{	PUNCT
cana-2105	83	20	0	0	NUM
cana-2105	83	21	}	}	PUNCT
cana-2105	83	22	and	and	CCONJ
cana-2105	83	23	α	α	NOUN
cana-2105	83	24	,	,	PUNCT
cana-2105	83	25	β	β	X
cana-2105	83	26	,	,	PUNCT
cana-2105	83	27	γ	γ	PROPN
cana-2105	83	28	,	,	PUNCT
cana-2105	83	29	δ	δ	PROPN
cana-2105	83	30	,	,	PUNCT
cana-2105	83	31	s	s	PART
cana-2105	83	32	∈	∈	PROPN
cana-2105	83	33	(	(	PUNCT
cana-2105	83	34	0	0	NUM
cana-2105	83	35	,	,	PUNCT
cana-2105	83	36	1	1	NUM
cana-2105	83	37	]	]	PUNCT
cana-2105	83	38	.	.	PUNCT
cana-2105	84	1	using	use	VERB
cana-2105	84	2	the	the	DET
cana-2105	84	3	iterative	iterative	NOUN
cana-2105	84	4	scheme	scheme	NOUN
cana-2105	84	5	(	(	PUNCT
cana-2105	84	6	2.3	2.3	NUM
cana-2105	84	7	)	)	PUNCT
cana-2105	84	8	they	they	PRON
cana-2105	84	9	prove	prove	VERB
cana-2105	84	10	the	the	DET
cana-2105	84	11	escape	escape	NOUN
cana-2105	84	12	criterion	criterion	NOUN
cana-2105	84	13	for	for	ADP
cana-2105	84	14	the	the	DET
cana-2105	84	15	complexvalued	complexvalue	VERB
cana-2105	84	16	cosine	cosine	NOUN
cana-2105	84	17	function	function	NOUN
cana-2105	84	18	cos(zk)+az+c	cos(zk)+az+c	PROPN
cana-2105	84	19	for	for	ADP
cana-2105	84	20	all	all	DET
cana-2105	84	21	z	z	NOUN
cana-2105	84	22	∈	∈	PROPN
cana-2105	84	23	c	c	NOUN
cana-2105	84	24	,	,	PUNCT
cana-2105	84	25	k	k	PROPN
cana-2105	84	26	∈	∈	PROPN
cana-2105	84	27	n\{1	n\{1	PROPN
cana-2105	84	28	}	}	PUNCT
cana-2105	84	29	and	and	CCONJ
cana-2105	84	30	a	a	DET
cana-2105	84	31	,	,	PUNCT
cana-2105	84	32	c	c	PROPN
cana-2105	84	33	∈	∈	PROPN
cana-2105	84	34	c	c	NOUN
cana-2105	84	35	and	and	CCONJ
cana-2105	84	36	create	create	VERB
cana-2105	84	37	the	the	DET
cana-2105	84	38	julia	julia	PROPN
cana-2105	84	39	sets	set	NOUN
cana-2105	84	40	,	,	PUNCT
cana-2105	84	41	along	along	ADP
cana-2105	84	42	with	with	ADP
cana-2105	84	43	mandelbrot	mandelbrot	NOUN
cana-2105	84	44	sets	set	NOUN
cana-2105	84	45	.	.	PUNCT
cana-2105	85	1	if	if	SCONJ
cana-2105	85	2	u	u	PROPN
cana-2105	85	3	,	,	PUNCT
cana-2105	85	4	v	v	NOUN
cana-2105	85	5	,	,	PUNCT
cana-2105	85	6	w	w	PROPN
cana-2105	85	7	,	,	PUNCT
cana-2105	85	8	z	z	PROPN
cana-2105	85	9	∈	∈	PROPN
cana-2105	85	10	c	c	NOUN
cana-2105	85	11	then	then	ADV
cana-2105	85	12	by	by	ADP
cana-2105	85	13	taylor	taylor	PROPN
cana-2105	85	14	series	series	PROPN
cana-2105	85	15	expansion	expansion	NOUN
cana-2105	85	16	for	for	ADP
cana-2105	85	17	the	the	DET
cana-2105	85	18	sine	sine	ADJ
cana-2105	85	19	function	function	NOUN
cana-2105	85	20	,	,	PUNCT
cana-2105	85	21	we	we	PRON
cana-2105	85	22	have	have	VERB
cana-2105	85	23	|	|	ADV
cana-2105	85	24	sin(uk)|	sin(uk)|	NOUN
cana-2105	85	25	=	=	NOUN
cana-2105	85	26	∣∣∣∣uk	∣∣∣∣uk	PROPN
cana-2105	85	27	−	−	PROPN
cana-2105	85	28	u3k	u3k	PROPN
cana-2105	85	29	3	3	X
cana-2105	85	30	!	!	PUNCT
cana-2105	86	1	+	+	CCONJ
cana-2105	86	2	u5k	u5k	PROPN
cana-2105	86	3	5	5	NUM
cana-2105	86	4	!	!	PUNCT
cana-2105	86	5	−	−	PROPN
cana-2105	86	6	·	·	PUNCT
cana-2105	86	7	·	·	PUNCT
cana-2105	86	8	·	·	PUNCT
cana-2105	87	1	∣∣∣∣	∣∣∣∣	PROPN
cana-2105	88	1	=	=	PRON
cana-2105	88	2	|uk|	|uk|	VERB
cana-2105	88	3	∣∣∣∣1−	∣∣∣∣1−	X
cana-2105	88	4	u2k	u2k	NUM
cana-2105	88	5	3	3	NUM
cana-2105	88	6	!	!	PUNCT
cana-2105	89	1	+	+	CCONJ
cana-2105	89	2	u4k	u4k	PRON
cana-2105	89	3	5	5	NUM
cana-2105	89	4	!	!	PUNCT
cana-2105	89	5	−	−	PROPN
cana-2105	90	1	·	·	PUNCT
cana-2105	90	2	·	·	PUNCT
cana-2105	90	3	·	·	PUNCT
cana-2105	90	4	∣∣∣∣	∣∣∣∣	NOUN
cana-2105	90	5	|	|	ADV
cana-2105	90	6	sin(vk)|	sin(vk)|	VERB
cana-2105	90	7	=	=	NOUN
cana-2105	90	8	|vk|	|vk|	NUM
cana-2105	90	9	∣∣∣∣1−	∣∣∣∣1−	NOUN
cana-2105	90	10	v2k	v2k	NOUN
cana-2105	90	11	3	3	NUM
cana-2105	90	12	!	!	PUNCT
cana-2105	91	1	+	+	CCONJ
cana-2105	91	2	v4k	v4k	NOUN
cana-2105	91	3	5	5	NUM
cana-2105	91	4	!	!	PUNCT
cana-2105	91	5	−	−	PROPN
cana-2105	91	6	·	·	PUNCT
cana-2105	91	7	·	·	PUNCT
cana-2105	91	8	·	·	PUNCT
cana-2105	92	1	∣∣∣∣	∣∣∣∣	NOUN
cana-2105	92	2	|	|	NOUN
cana-2105	92	3	sin(wk)|	sin(wk)|	VERB
cana-2105	92	4	=	=	NOUN
cana-2105	92	5	|wk|	|wk|	NOUN
cana-2105	92	6	∣∣∣∣1−	∣∣∣∣1−	VERB
cana-2105	92	7	w2k	w2k	PROPN
cana-2105	92	8	3	3	NUM
cana-2105	92	9	!	!	PUNCT
cana-2105	93	1	+	+	CCONJ
cana-2105	93	2	w4k	w4k	ADP
cana-2105	93	3	5	5	NUM
cana-2105	93	4	!	!	PUNCT
cana-2105	93	5	−	−	PROPN
cana-2105	93	6	·	·	PUNCT
cana-2105	93	7	·	·	PUNCT
cana-2105	93	8	·	·	PUNCT
cana-2105	93	9	∣∣∣∣	∣∣∣∣	NOUN
cana-2105	93	10	|	|	ADV
cana-2105	93	11	sin(zk)|	sin(zk)|	VERB
cana-2105	93	12	=	=	NOUN
cana-2105	93	13	|zk|	|zk|	NOUN
cana-2105	93	14	∣∣∣∣1−	∣∣∣∣1−	NOUN
cana-2105	93	15	z2k	z2k	NOUN
cana-2105	93	16	3	3	NUM
cana-2105	93	17	!	!	PUNCT
cana-2105	94	1	+	+	CCONJ
cana-2105	94	2	z4k	z4k	NUM
cana-2105	94	3	5	5	NUM
cana-2105	94	4	!	!	PUNCT
cana-2105	94	5	−	−	PROPN
cana-2105	94	6	·	·	PUNCT
cana-2105	94	7	·	·	PUNCT
cana-2105	94	8	·	·	PUNCT
cana-2105	95	1	∣∣∣∣	∣∣∣∣	NOUN
cana-2105	95	2	suppose	suppose	VERB
cana-2105	95	3	(	(	PUNCT
cana-2105	95	4	i	i	NOUN
cana-2105	95	5	)	)	PUNCT
cana-2105	95	6	∣∣∣1−	∣∣∣1−	PROPN
cana-2105	95	7	u2k	u2k	PROPN
cana-2105	95	8	3	3	NUM
cana-2105	95	9	!	!	PUNCT
cana-2105	96	1	+	+	CCONJ
cana-2105	96	2	u4k	u4k	PRON
cana-2105	96	3	5	5	NUM
cana-2105	96	4	!	!	PUNCT
cana-2105	96	5	−	−	PROPN
cana-2105	96	6	·	·	PUNCT
cana-2105	96	7	·	·	PUNCT
cana-2105	96	8	·	·	PUNCT
cana-2105	96	9	∣∣∣	∣∣∣	ADJ
cana-2105	96	10	≥	≥	NUM
cana-2105	96	11	|ω1|	|ω1|	PROPN
cana-2105	96	12	(	(	PUNCT
cana-2105	96	13	ii	ii	PROPN
cana-2105	96	14	)	)	PUNCT
cana-2105	96	15	∣∣∣1−	∣∣∣1−	NUM
cana-2105	96	16	v2k	v2k	NOUN
cana-2105	96	17	3	3	NUM
cana-2105	96	18	!	!	PUNCT
cana-2105	97	1	+	+	CCONJ
cana-2105	97	2	v4k	v4k	NOUN
cana-2105	97	3	5	5	NUM
cana-2105	97	4	!	!	PUNCT
cana-2105	97	5	−	−	PROPN
cana-2105	97	6	·	·	PUNCT
cana-2105	97	7	·	·	PUNCT
cana-2105	97	8	·	·	PUNCT
cana-2105	98	1	∣∣∣	∣∣∣	ADJ
cana-2105	98	2	≥	≥	NUM
cana-2105	98	3	|ω2|	|ω2|	PROPN
cana-2105	98	4	(	(	PUNCT
cana-2105	98	5	iii	iii	NOUN
cana-2105	98	6	)	)	PUNCT
cana-2105	98	7	∣∣∣1−	∣∣∣1−	PROPN
cana-2105	98	8	w2k	w2k	PROPN
cana-2105	98	9	3	3	NUM
cana-2105	98	10	!	!	PUNCT
cana-2105	99	1	+	+	CCONJ
cana-2105	99	2	w4k	w4k	ADP
cana-2105	99	3	5	5	NUM
cana-2105	99	4	!	!	PUNCT
cana-2105	99	5	−	−	PROPN
cana-2105	99	6	·	·	PUNCT
cana-2105	99	7	·	·	PUNCT
cana-2105	99	8	·	·	PUNCT
cana-2105	99	9	∣∣∣	∣∣∣	ADJ
cana-2105	99	10	≥	≥	NUM
cana-2105	99	11	|ω3|	|ω3|	NOUN
cana-2105	99	12	(	(	PUNCT
cana-2105	99	13	iv	iv	X
cana-2105	99	14	)	)	PUNCT
cana-2105	99	15	∣∣∣1−	∣∣∣1−	NUM
cana-2105	99	16	z2k	z2k	NOUN
cana-2105	99	17	3	3	NUM
cana-2105	99	18	!	!	PUNCT
cana-2105	100	1	+	+	CCONJ
cana-2105	100	2	z4k	z4k	NUM
cana-2105	100	3	5	5	NUM
cana-2105	100	4	!	!	PUNCT
cana-2105	100	5	−	−	PROPN
cana-2105	100	6	·	·	PUNCT
cana-2105	100	7	·	·	PUNCT
cana-2105	100	8	·	·	PUNCT
cana-2105	100	9	∣∣∣	∣∣∣	X
cana-2105	100	10	≥	≥	NUM
cana-2105	100	11	|ω4|	|ω4|	NOUN
cana-2105	100	12	where	where	SCONJ
cana-2105	100	13	,	,	PUNCT
cana-2105	100	14	|ω1|	|ω1|	PROPN
cana-2105	100	15	,	,	PUNCT
cana-2105	100	16	|ω2|	|ω2|	NOUN
cana-2105	100	17	,	,	PUNCT
cana-2105	100	18	|ω3|	|ω3|	NOUN
cana-2105	100	19	,	,	PUNCT
cana-2105	100	20	|ω4|	|ω4|	NOUN
cana-2105	100	21	∈	∈	PROPN
cana-2105	100	22	(	(	PUNCT
cana-2105	100	23	0	0	NUM
cana-2105	100	24	,	,	PUNCT
cana-2105	100	25	1	1	NUM
cana-2105	100	26	]	]	PUNCT
cana-2105	100	27	.	.	PUNCT
cana-2105	101	1	communications	communication	NOUN
cana-2105	101	2	on	on	ADP
cana-2105	101	3	applied	apply	VERB
cana-2105	101	4	nonlinear	nonlinear	ADJ
cana-2105	101	5	analysis	analysis	NOUN
cana-2105	101	6	issn	issn	NOUN
cana-2105	101	7	:	:	PUNCT
cana-2105	101	8	1074	1074	NUM
cana-2105	101	9	-	-	PUNCT
cana-2105	101	10	133x	133x	NUM
cana-2105	101	11	vol	vol	NOUN
cana-2105	101	12	32	32	NUM
cana-2105	101	13	no	no	NOUN
cana-2105	101	14	.	.	PUNCT
cana-2105	102	1	1s	1s	NUM
cana-2105	102	2	(	(	PUNCT
cana-2105	102	3	2025	2025	NUM
cana-2105	102	4	)	)	PUNCT
cana-2105	103	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	103	2	66	66	NUM
cana-2105	103	3	3	3	NUM
cana-2105	103	4	main	main	ADJ
cana-2105	103	5	results	result	NOUN
cana-2105	103	6	in	in	ADP
cana-2105	103	7	this	this	DET
cana-2105	103	8	section	section	NOUN
cana-2105	103	9	,	,	PUNCT
cana-2105	103	10	we	we	PRON
cana-2105	103	11	prove	prove	VERB
cana-2105	103	12	the	the	DET
cana-2105	103	13	escaping	escaping	NOUN
cana-2105	103	14	criteria	criterion	NOUN
cana-2105	103	15	,	,	PUNCT
cana-2105	103	16	which	which	PRON
cana-2105	103	17	plays	play	VERB
cana-2105	103	18	a	a	DET
cana-2105	103	19	vital	vital	ADJ
cana-2105	103	20	role	role	NOUN
cana-2105	103	21	in	in	ADP
cana-2105	103	22	creating	create	VERB
cana-2105	103	23	the	the	DET
cana-2105	103	24	julia	julia	PROPN
cana-2105	103	25	and	and	CCONJ
cana-2105	103	26	mandelbrot	mandelbrot	PROPN
cana-2105	103	27	sets	set	NOUN
cana-2105	103	28	.	.	PUNCT
cana-2105	104	1	3.1	3.1	NUM
cana-2105	104	2	escape	escape	NOUN
cana-2105	104	3	criteria	criterion	NOUN
cana-2105	104	4	for	for	ADP
cana-2105	104	5	complex	complex	ADJ
cana-2105	104	6	sine	sine	ADJ
cana-2105	104	7	functions	function	NOUN
cana-2105	104	8	theorem	theorem	VERB
cana-2105	104	9	3.1	3.1	NUM
cana-2105	104	10	.	.	PUNCT
cana-2105	105	1	let	let	VERB
cana-2105	105	2	tc	tc	NOUN
cana-2105	105	3	:	:	PUNCT
cana-2105	105	4	c	c	X
cana-2105	105	5	→	→	PUNCT
cana-2105	105	6	c	c	X
cana-2105	105	7	be	be	AUX
cana-2105	105	8	a	a	DET
cana-2105	105	9	complex	complex	ADV
cana-2105	105	10	-	-	PUNCT
cana-2105	105	11	valued	value	VERB
cana-2105	105	12	map	map	NOUN
cana-2105	105	13	defined	define	VERB
cana-2105	105	14	by	by	ADP
cana-2105	105	15	tc(z	tc(z	NOUN
cana-2105	105	16	)	)	PUNCT
cana-2105	105	17	=	=	PUNCT
cana-2105	106	1	sin(zk	sin(zk	X
cana-2105	106	2	)	)	PUNCT
cana-2105	107	1	+	+	CCONJ
cana-2105	107	2	az	az	PROPN
cana-2105	107	3	+	+	CCONJ
cana-2105	107	4	c	c	PROPN
cana-2105	107	5	for	for	ADP
cana-2105	107	6	all	all	DET
cana-2105	107	7	z	z	NOUN
cana-2105	107	8	∈	∈	PROPN
cana-2105	107	9	c	c	NOUN
cana-2105	107	10	,	,	PUNCT
cana-2105	107	11	k	k	PROPN
cana-2105	107	12	∈	∈	PROPN
cana-2105	107	13	n	n	PRON
cana-2105	107	14	\	\	NOUN
cana-2105	107	15	{	{	PUNCT
cana-2105	107	16	1	1	NUM
cana-2105	107	17	}	}	PUNCT
cana-2105	107	18	and	and	CCONJ
cana-2105	107	19	a	a	DET
cana-2105	107	20	,	,	PUNCT
cana-2105	107	21	c	c	PROPN
cana-2105	107	22	∈	∈	PROPN
cana-2105	107	23	c	c	NOUN
cana-2105	107	24	such	such	ADJ
cana-2105	107	25	that	that	SCONJ
cana-2105	107	26	a	a	DET
cana-2105	107	27	̸=	̸=	PROPN
cana-2105	107	28	0	0	NUM
cana-2105	107	29	.	.	PUNCT
cana-2105	108	1	consider	consider	VERB
cana-2105	108	2	the	the	DET
cana-2105	108	3	iterative	iterative	NOUN
cana-2105	108	4	sequence	sequence	NOUN
cana-2105	108	5	defined	define	VERB
cana-2105	108	6	in	in	ADP
cana-2105	108	7	(	(	PUNCT
cana-2105	108	8	2.3	2.3	NUM
cana-2105	108	9	)	)	PUNCT
cana-2105	108	10	and	and	CCONJ
cana-2105	108	11	|ω1|	|ω1|	PROPN
cana-2105	108	12	,	,	PUNCT
cana-2105	108	13	|ω2|	|ω2|	NOUN
cana-2105	108	14	,	,	PUNCT
cana-2105	108	15	|ω3|	|ω3|	NOUN
cana-2105	108	16	,	,	PUNCT
cana-2105	108	17	|ω4|	|ω4|	NOUN
cana-2105	108	18	∈	∈	PROPN
cana-2105	108	19	(	(	PUNCT
cana-2105	108	20	0	0	NUM
cana-2105	108	21	,	,	PUNCT
cana-2105	108	22	1	1	NUM
cana-2105	108	23	]	]	PUNCT
cana-2105	108	24	if	if	SCONJ
cana-2105	108	25	|z0|	|z0|	X
cana-2105	108	26	>	>	X
cana-2105	108	27	max	max	PROPN
cana-2105	108	28	{	{	PUNCT
cana-2105	108	29	|c|	|c|	PROPN
cana-2105	108	30	,	,	PUNCT
cana-2105	108	31	(	(	PUNCT
cana-2105	108	32	2(1	2(1	NUM
cana-2105	108	33	+	+	CCONJ
cana-2105	108	34	|a|	|a|	NOUN
cana-2105	108	35	)	)	PUNCT
cana-2105	108	36	sα|ω1|	sα|ω1|	PROPN
cana-2105	108	37	)	)	PUNCT
cana-2105	108	38	1	1	NUM
cana-2105	108	39	k−1	k−1	PROPN
cana-2105	108	40	,	,	PUNCT
cana-2105	108	41	(	(	PUNCT
cana-2105	108	42	2(1	2(1	NUM
cana-2105	108	43	+	+	CCONJ
cana-2105	108	44	|a|	|a|	NOUN
cana-2105	108	45	)	)	PUNCT
cana-2105	108	46	sβ|ω2|	sβ|ω2|	NOUN
cana-2105	108	47	)	)	PUNCT
cana-2105	108	48	1	1	NUM
cana-2105	108	49	k−1	k−1	PROPN
cana-2105	108	50	,	,	PUNCT
cana-2105	108	51	(	(	PUNCT
cana-2105	108	52	2(1	2(1	NUM
cana-2105	108	53	+	+	CCONJ
cana-2105	108	54	|a|	|a|	NOUN
cana-2105	108	55	)	)	PUNCT
cana-2105	108	56	sγ|ω3|	sγ|ω3|	NUM
cana-2105	108	57	)	)	PUNCT
cana-2105	108	58	1	1	NUM
cana-2105	108	59	k−1	k−1	PROPN
cana-2105	108	60	,	,	PUNCT
cana-2105	108	61	(	(	PUNCT
cana-2105	108	62	2(1	2(1	NUM
cana-2105	108	63	+	+	CCONJ
cana-2105	108	64	|a|	|a|	NOUN
cana-2105	108	65	)	)	PUNCT
cana-2105	108	66	sδ|ω4|	sδ|ω4|	PROPN
cana-2105	108	67	)	)	PUNCT
cana-2105	108	68	1	1	NUM
cana-2105	108	69	k−1	k−1	PROPN
cana-2105	108	70	}	}	PUNCT
cana-2105	108	71	then	then	ADV
cana-2105	108	72	lim	lim	PROPN
cana-2105	108	73	n→∞	n→∞	PRON
cana-2105	108	74	|zn|	|zn|	NOUN
cana-2105	108	75	=	=	PUNCT
cana-2105	108	76	∞.	∞.	PROPN
cana-2105	108	77	proof	proof	NOUN
cana-2105	108	78	.	.	PUNCT
cana-2105	109	1	for	for	ADP
cana-2105	109	2	n	n	NOUN
cana-2105	109	3	=	=	SYM
cana-2105	109	4	0	0	NUM
cana-2105	109	5	in	in	ADP
cana-2105	109	6	(	(	PUNCT
cana-2105	109	7	2.3	2.3	NUM
cana-2105	109	8	)	)	PUNCT
cana-2105	109	9	and	and	CCONJ
cana-2105	109	10	using	use	VERB
cana-2105	109	11	the	the	DET
cana-2105	109	12	binomial	binomial	ADJ
cana-2105	109	13	expansion	expansion	NOUN
cana-2105	109	14	for	for	ADP
cana-2105	109	15	any	any	DET
cana-2105	109	16	index	index	NOUN
cana-2105	109	17	,	,	PUNCT
cana-2105	109	18	we	we	PRON
cana-2105	109	19	obtain	obtain	VERB
cana-2105	109	20	|u0|	|u0|	X
cana-2105	109	21	=	=	PUNCT
cana-2105	109	22	|(1−	|(1−	NOUN
cana-2105	109	23	δ)sz0	δ)sz0	NOUN
cana-2105	109	24	+	+	CCONJ
cana-2105	109	25	δstcz0|	δstcz0|	NOUN
cana-2105	109	26	=	=	SYM
cana-2105	109	27	|(1−	|(1−	PROPN
cana-2105	109	28	δ)sz0	δ)sz0	NOUN
cana-2105	109	29	+	+	X
cana-2105	109	30	δs(sin(zk0	δs(sin(zk0	NOUN
cana-2105	109	31	)	)	PUNCT
cana-2105	110	1	+	+	CCONJ
cana-2105	110	2	az0	az0	NOUN
cana-2105	111	1	+	+	CCONJ
cana-2105	111	2	c)|	c)|	NOUN
cana-2105	111	3	≥	≥	PRON
cana-2105	111	4	δs|	δs|	VERB
cana-2105	111	5	sin	sin	NOUN
cana-2105	111	6	zk0	zk0	NOUN
cana-2105	111	7	+	+	CCONJ
cana-2105	111	8	az0	az0	NOUN
cana-2105	112	1	+	+	CCONJ
cana-2105	112	2	c|	c|	PROPN
cana-2105	112	3	−	−	PROPN
cana-2105	112	4	(	(	PUNCT
cana-2105	112	5	1−	1−	NUM
cana-2105	112	6	δ)s|z0|	δ)s|z0|	NOUN
cana-2105	112	7	≥	≥	PRON
cana-2105	112	8	δs|	δs|	VERB
cana-2105	112	9	sin(zk0	sin(zk0	ADV
cana-2105	112	10	)	)	PUNCT
cana-2105	113	1	+	+	CCONJ
cana-2105	113	2	az0	az0	NOUN
cana-2105	114	1	+	+	CCONJ
cana-2105	114	2	c|	c|	PROPN
cana-2105	114	3	−	−	PROPN
cana-2105	114	4	(	(	PUNCT
cana-2105	114	5	1−	1−	NUM
cana-2105	114	6	sδ)|z0|	sδ)|z0|	NOUN
cana-2105	114	7	[	[	X
cana-2105	114	8	∵	∵	X
cana-2105	114	9	(	(	PUNCT
cana-2105	114	10	1−	1−	NUM
cana-2105	114	11	δ)s	δ)s	NOUN
cana-2105	114	12	≤	≤	NOUN
cana-2105	114	13	1−	1−	NUM
cana-2105	114	14	δs	δs	NOUN
cana-2105	114	15	]	]	PUNCT
cana-2105	114	16	≥	≥	NOUN
cana-2105	114	17	δs[|	δs[|	PROPN
cana-2105	114	18	sin(zk0	sin(zk0	PROPN
cana-2105	114	19	)	)	PUNCT
cana-2105	115	1	|	|	ADV
cana-2105	115	2	−	−	ADP
cana-2105	115	3	|a||z0|	|a||z0|	NOUN
cana-2105	115	4	−	−	NOUN
cana-2105	115	5	|c|]−	|c|]−	NUM
cana-2105	115	6	|z0|+	|z0|+	NUM
cana-2105	115	7	sδ|z0|	sδ|z0|	NUM
cana-2105	115	8	≥	≥	NOUN
cana-2105	115	9	sδ[|	sδ[|	PROPN
cana-2105	115	10	sin(zk0	sin(zk0	PROPN
cana-2105	115	11	)	)	PUNCT
cana-2105	115	12	|	|	ADV
cana-2105	115	13	−	−	ADP
cana-2105	115	14	|a||z0|	|a||z0|	NOUN
cana-2105	115	15	−	−	NOUN
cana-2105	115	16	|z0|]−	|z0|]−	SYM
cana-2105	115	17	|z0|+	|z0|+	NUM
cana-2105	115	18	sδ|z0|	sδ|z0|	SYM
cana-2105	115	19	=	=	SYM
cana-2105	115	20	sδ|	sδ|	NOUN
cana-2105	115	21	sin(zk0	sin(zk0	NOUN
cana-2105	115	22	)	)	PUNCT
cana-2105	116	1	|	|	ADV
cana-2105	116	2	−	−	PROPN
cana-2105	116	3	sδ|a||z0|	sδ|a||z0|	PROPN
cana-2105	116	4	−	−	ADP
cana-2105	116	5	sδ|z0|	sδ|z0|	NUM
cana-2105	116	6	−	−	PROPN
cana-2105	116	7	|z0|+	|z0|+	SYM
cana-2105	116	8	sδ|z0|	sδ|z0|	PRON
cana-2105	116	9	≥	≥	NOUN
cana-2105	116	10	sδ|	sδ|	NOUN
cana-2105	116	11	sin(zk0	sin(zk0	NOUN
cana-2105	116	12	)	)	PUNCT
cana-2105	116	13	|	|	ADV
cana-2105	116	14	−	−	NOUN
cana-2105	116	15	|a||z0|	|a||z0|	NOUN
cana-2105	116	16	−	−	PROPN
cana-2105	116	17	|z0|	|z0|	NOUN
cana-2105	116	18	.	.	PUNCT
cana-2105	117	1	(	(	PUNCT
cana-2105	117	2	3.1	3.1	NUM
cana-2105	117	3	)	)	PUNCT
cana-2105	117	4	we	we	PRON
cana-2105	117	5	have	have	AUX
cana-2105	117	6	|	|	ADV
cana-2105	117	7	sin(zk0	sin(zk0	VERB
cana-2105	117	8	)	)	PUNCT
cana-2105	118	1	|	|	ADV
cana-2105	118	2	=	=	SYM
cana-2105	118	3	|zk0	|zk0	PROPN
cana-2105	118	4	|	|	ADV
cana-2105	118	5	∣∣∣1−	∣∣∣1−	NUM
cana-2105	118	6	z2k0	z2k0	NOUN
cana-2105	118	7	3	3	X
cana-2105	118	8	!	!	PUNCT
cana-2105	119	1	+	+	CCONJ
cana-2105	119	2	z4k0	z4k0	NUM
cana-2105	119	3	5	5	NUM
cana-2105	119	4	!	!	PUNCT
cana-2105	119	5	−	−	PROPN
cana-2105	119	6	·	·	PUNCT
cana-2105	119	7	·	·	PUNCT
cana-2105	119	8	·	·	PUNCT
cana-2105	119	9	∣∣∣	∣∣∣	X
cana-2105	119	10	≥	≥	X
cana-2105	119	11	|zk0	|zk0	PROPN
cana-2105	119	12	||ω4|	||ω4|	PROPN
cana-2105	119	13	,	,	PUNCT
cana-2105	119	14	where	where	SCONJ
cana-2105	119	15	|ω4|	|ω4|	NOUN
cana-2105	119	16	∈	∈	PROPN
cana-2105	119	17	(	(	PUNCT
cana-2105	119	18	0	0	NUM
cana-2105	119	19	,	,	PUNCT
cana-2105	119	20	1	1	NUM
cana-2105	119	21	]	]	PUNCT
cana-2105	119	22	except	except	SCONJ
cana-2105	119	23	the	the	DET
cana-2105	119	24	value	value	NOUN
cana-2105	119	25	for	for	ADP
cana-2105	119	26	which	which	PRON
cana-2105	119	27	|ω4|	|ω4|	NOUN
cana-2105	119	28	=	=	SYM
cana-2105	119	29	0	0	NUM
cana-2105	119	30	and	and	CCONJ
cana-2105	119	31	|z0|	|z0|	X
cana-2105	119	32	>	>	X
cana-2105	119	33	(	(	PUNCT
cana-2105	119	34	2(1+|a|	2(1+|a|	NUM
cana-2105	119	35	)	)	PUNCT
cana-2105	119	36	sδ|ω4|	sδ|ω4|	PROPN
cana-2105	119	37	)	)	PUNCT
cana-2105	119	38	1	1	NUM
cana-2105	119	39	k−1	k−1	PROPN
cana-2105	119	40	,	,	PUNCT
cana-2105	119	41	from	from	ADP
cana-2105	119	42	inequality	inequality	NOUN
cana-2105	119	43	3.1	3.1	NUM
cana-2105	119	44	we	we	PRON
cana-2105	119	45	obtain	obtain	VERB
cana-2105	119	46	|u0|	|u0|	NOUN
cana-2105	119	47	≥sδ|ω4||zk0	≥sδ|ω4||zk0	ADJ
cana-2105	119	48	|	|	ADV
cana-2105	119	49	−	−	PROPN
cana-2105	119	50	(	(	PUNCT
cana-2105	119	51	1	1	NUM
cana-2105	119	52	+	+	NUM
cana-2105	119	53	|a|)|z0|	|a|)|z0|	NOUN
cana-2105	119	54	=	=	PRON
cana-2105	119	55	|z0|[sδ|ω4||zk−1	|z0|[sδ|ω4||zk−1	NOUN
cana-2105	119	56	0	0	NUM
cana-2105	120	1	|	|	ADV
cana-2105	120	2	−	−	PROPN
cana-2105	120	3	(	(	PUNCT
cana-2105	120	4	1	1	NUM
cana-2105	120	5	+	+	CCONJ
cana-2105	120	6	|a|	|a|	NOUN
cana-2105	120	7	)	)	PUNCT
cana-2105	120	8	]	]	PUNCT
cana-2105	120	9	≥|z0|[2(1	≥|z0|[2(1	NOUN
cana-2105	120	10	+	+	CCONJ
cana-2105	120	11	|a|)−	|a|)−	PUNCT
cana-2105	120	12	(	(	PUNCT
cana-2105	120	13	1	1	NUM
cana-2105	120	14	+	+	NUM
cana-2105	120	15	|a|	|a|	NOUN
cana-2105	120	16	)	)	PUNCT
cana-2105	120	17	]	]	PUNCT
cana-2105	121	1	=	=	X
cana-2105	121	2	(	(	PUNCT
cana-2105	121	3	1	1	NUM
cana-2105	121	4	+	+	NUM
cana-2105	121	5	|a|)|z0|	|a|)|z0|	NOUN
cana-2105	121	6	≥|z0|	≥|z0|	NOUN
cana-2105	121	7	.	.	PUNCT
cana-2105	122	1	(	(	PUNCT
cana-2105	122	2	3.2	3.2	NUM
cana-2105	122	3	)	)	PUNCT
cana-2105	122	4	communications	communication	NOUN
cana-2105	122	5	on	on	ADP
cana-2105	122	6	applied	apply	VERB
cana-2105	122	7	nonlinear	nonlinear	ADJ
cana-2105	122	8	analysis	analysis	NOUN
cana-2105	122	9	issn	issn	NOUN
cana-2105	122	10	:	:	PUNCT
cana-2105	122	11	1074	1074	NUM
cana-2105	122	12	-	-	PUNCT
cana-2105	122	13	133x	133x	NUM
cana-2105	122	14	vol	vol	NOUN
cana-2105	122	15	32	32	NUM
cana-2105	122	16	no	no	NOUN
cana-2105	122	17	.	.	PUNCT
cana-2105	123	1	1s	1s	NUM
cana-2105	123	2	(	(	PUNCT
cana-2105	123	3	2025	2025	NUM
cana-2105	123	4	)	)	PUNCT
cana-2105	123	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	123	6	67	67	NUM
cana-2105	123	7	moving	move	VERB
cana-2105	123	8	forward	forward	ADV
cana-2105	123	9	to	to	ADP
cana-2105	123	10	the	the	DET
cana-2105	123	11	subsequent	subsequent	ADJ
cana-2105	123	12	stage	stage	NOUN
cana-2105	123	13	of	of	ADP
cana-2105	123	14	the	the	DET
cana-2105	123	15	four	four	NUM
cana-2105	123	16	-	-	PUNCT
cana-2105	123	17	step	step	NOUN
cana-2105	123	18	iteration	iteration	NOUN
cana-2105	123	19	,	,	PUNCT
cana-2105	123	20	we	we	PRON
cana-2105	123	21	have	have	VERB
cana-2105	123	22	|v0|	|v0|	NOUN
cana-2105	123	23	=	=	SYM
cana-2105	123	24	|(1−	|(1−	NOUN
cana-2105	123	25	γ)sz0	γ)sz0	NOUN
cana-2105	123	26	+	+	CCONJ
cana-2105	123	27	γstcu0|	γstcu0|	X
cana-2105	123	28	=	=	PUNCT
cana-2105	123	29	|(1−	|(1−	PROPN
cana-2105	123	30	γ)sz0	γ)sz0	NOUN
cana-2105	123	31	+	+	CCONJ
cana-2105	123	32	γs(sin(uk	γs(sin(uk	PROPN
cana-2105	123	33	0	0	NUM
cana-2105	123	34	)	)	PUNCT
cana-2105	124	1	+	+	CCONJ
cana-2105	124	2	au0	au0	NOUN
cana-2105	124	3	+	+	X
cana-2105	124	4	c)|	c)|	NOUN
cana-2105	124	5	≥	≥	NOUN
cana-2105	124	6	γs|	γs|	NOUN
cana-2105	124	7	sin(uk	sin(uk	NUM
cana-2105	124	8	0	0	NUM
cana-2105	124	9	)	)	PUNCT
cana-2105	125	1	+	+	CCONJ
cana-2105	125	2	au0	au0	NOUN
cana-2105	125	3	+	+	X
cana-2105	125	4	c|	c|	PROPN
cana-2105	125	5	−	−	PROPN
cana-2105	125	6	(	(	PUNCT
cana-2105	125	7	1−	1−	NUM
cana-2105	125	8	γ)s|z0|	γ)s|z0|	NOUN
cana-2105	125	9	≥	≥	NOUN
cana-2105	125	10	γs|	γs|	NOUN
cana-2105	125	11	sin(uk	sin(uk	NUM
cana-2105	125	12	0	0	NUM
cana-2105	125	13	)	)	PUNCT
cana-2105	126	1	+	+	CCONJ
cana-2105	126	2	au0	au0	NOUN
cana-2105	126	3	+	+	X
cana-2105	126	4	c|	c|	PROPN
cana-2105	126	5	−	−	PROPN
cana-2105	126	6	(	(	PUNCT
cana-2105	126	7	1−	1−	NUM
cana-2105	126	8	sγ)|z0|	sγ)|z0|	NOUN
cana-2105	126	9	≥	≥	NOUN
cana-2105	126	10	γs[|	γs[|	NOUN
cana-2105	126	11	sin(uk	sin(uk	VERB
cana-2105	126	12	0)|	0)|	NOUN
cana-2105	126	13	−	−	NOUN
cana-2105	126	14	|a||u0|	|a||u0|	SYM
cana-2105	126	15	−	−	NOUN
cana-2105	126	16	|c|]−	|c|]−	NUM
cana-2105	126	17	|z0|+	|z0|+	NUM
cana-2105	126	18	sγ|z0|	sγ|z0|	NUM
cana-2105	126	19	≥	≥	NOUN
cana-2105	126	20	sδ[|	sδ[|	NOUN
cana-2105	126	21	sin(uk	sin(uk	NUM
cana-2105	126	22	0)|	0)|	NOUN
cana-2105	126	23	−	−	NOUN
cana-2105	126	24	|a||u0|	|a||u0|	SYM
cana-2105	126	25	−	−	ADP
cana-2105	126	26	|z0|]−	|z0|]−	SYM
cana-2105	126	27	|z0|+	|z0|+	NUM
cana-2105	126	28	sγ|z0|	sγ|z0|	NUM
cana-2105	126	29	=	=	SYM
cana-2105	126	30	sδ|	sδ|	ADJ
cana-2105	126	31	sin(uk	sin(uk	NOUN
cana-2105	126	32	0)|	0)|	NOUN
cana-2105	126	33	−	−	NOUN
cana-2105	126	34	sδ|a||z0|	sδ|a||z0|	PROPN
cana-2105	126	35	−	−	ADP
cana-2105	126	36	sδ|z0|	sδ|z0|	NUM
cana-2105	126	37	−	−	PROPN
cana-2105	126	38	|z0|+	|z0|+	NUM
cana-2105	126	39	sγ|z0|	sγ|z0|	NUM
cana-2105	126	40	≥	≥	NOUN
cana-2105	126	41	sγ|	sγ|	VERB
cana-2105	126	42	sin(uk	sin(uk	NUM
cana-2105	126	43	0)|	0)|	NOUN
cana-2105	126	44	−	−	NOUN
cana-2105	126	45	|a||z0|	|a||z0|	NOUN
cana-2105	126	46	−	−	PROPN
cana-2105	126	47	|z0|	|z0|	NOUN
cana-2105	126	48	.	.	PUNCT
cana-2105	127	1	(	(	PUNCT
cana-2105	127	2	3.3	3.3	NUM
cana-2105	127	3	)	)	PUNCT
cana-2105	127	4	we	we	PRON
cana-2105	127	5	have	have	AUX
cana-2105	127	6	|	|	ADV
cana-2105	127	7	sin(uk	sin(uk	NUM
cana-2105	127	8	0)|	0)|	NOUN
cana-2105	127	9	=	=	SYM
cana-2105	127	10	|uk	|uk	X
cana-2105	127	11	0|	0|	NUM
cana-2105	127	12	∣∣∣1−	∣∣∣1−	NUM
cana-2105	127	13	u2k	u2k	PROPN
cana-2105	127	14	0	0	NUM
cana-2105	127	15	3	3	NUM
cana-2105	127	16	!	!	PUNCT
cana-2105	128	1	+	+	CCONJ
cana-2105	128	2	u4k	u4k	NOUN
cana-2105	128	3	0	0	NUM
cana-2105	128	4	5	5	NUM
cana-2105	128	5	!	!	PUNCT
cana-2105	128	6	−	−	PROPN
cana-2105	129	1	·	·	PUNCT
cana-2105	129	2	·	·	PUNCT
cana-2105	129	3	·	·	PUNCT
cana-2105	129	4	∣∣∣	∣∣∣	X
cana-2105	129	5	≥	≥	PROPN
cana-2105	129	6	|uk	|uk	X
cana-2105	129	7	0||ω3|	0||ω3|	PROPN
cana-2105	129	8	,	,	PUNCT
cana-2105	129	9	where	where	SCONJ
cana-2105	129	10	|ω3|	|ω3|	NOUN
cana-2105	129	11	∈	∈	PROPN
cana-2105	129	12	(	(	PUNCT
cana-2105	129	13	0	0	NUM
cana-2105	129	14	,	,	PUNCT
cana-2105	129	15	1	1	NUM
cana-2105	129	16	]	]	PUNCT
cana-2105	129	17	except	except	SCONJ
cana-2105	129	18	the	the	DET
cana-2105	129	19	value	value	NOUN
cana-2105	129	20	for	for	ADP
cana-2105	129	21	which	which	PRON
cana-2105	129	22	|ω3|	|ω3|	NOUN
cana-2105	129	23	=	=	SYM
cana-2105	129	24	0	0	NUM
cana-2105	129	25	and	and	CCONJ
cana-2105	129	26	|z0|	|z0|	X
cana-2105	129	27	>	>	X
cana-2105	129	28	(	(	PUNCT
cana-2105	129	29	2(1+|a|	2(1+|a|	X
cana-2105	129	30	)	)	PUNCT
cana-2105	129	31	sγ|ω3|	sγ|ω3|	NUM
cana-2105	129	32	)	)	PUNCT
cana-2105	129	33	1	1	NUM
cana-2105	129	34	k−1	k−1	PROPN
cana-2105	129	35	,	,	PUNCT
cana-2105	129	36	from	from	ADP
cana-2105	129	37	inequality	inequality	NOUN
cana-2105	129	38	3.3	3.3	NUM
cana-2105	129	39	we	we	PRON
cana-2105	129	40	obtain	obtain	VERB
cana-2105	129	41	|v0|	|v0|	NOUN
cana-2105	129	42	≥sγ|ω3||uk	≥sγ|ω3||uk	NOUN
cana-2105	129	43	0|	0|	VERB
cana-2105	129	44	−	−	PROPN
cana-2105	130	1	(	(	PUNCT
cana-2105	130	2	1	1	NUM
cana-2105	130	3	+	+	NUM
cana-2105	130	4	|a|)|z0|	|a|)|z0|	NOUN
cana-2105	130	5	=	=	NOUN
cana-2105	130	6	|z0|[sγ|ω3||zk−1	|z0|[sγ|ω3||zk−1	NUM
cana-2105	130	7	0	0	NUM
cana-2105	131	1	|	|	ADV
cana-2105	131	2	−	−	PROPN
cana-2105	131	3	(	(	PUNCT
cana-2105	131	4	1	1	NUM
cana-2105	131	5	+	+	CCONJ
cana-2105	131	6	|a|	|a|	NOUN
cana-2105	131	7	)	)	PUNCT
cana-2105	131	8	]	]	PUNCT
cana-2105	131	9	≥|z0|[2(1	≥|z0|[2(1	NOUN
cana-2105	131	10	+	+	CCONJ
cana-2105	131	11	|a|)−	|a|)−	PUNCT
cana-2105	131	12	(	(	PUNCT
cana-2105	131	13	1	1	NUM
cana-2105	131	14	+	+	NUM
cana-2105	131	15	|a|	|a|	NOUN
cana-2105	131	16	)	)	PUNCT
cana-2105	131	17	]	]	PUNCT
cana-2105	132	1	=	=	X
cana-2105	132	2	(	(	PUNCT
cana-2105	132	3	1	1	NUM
cana-2105	132	4	+	+	NUM
cana-2105	132	5	|a|)|z0|	|a|)|z0|	NOUN
cana-2105	132	6	≥|z0|	≥|z0|	NOUN
cana-2105	132	7	.	.	PUNCT
cana-2105	133	1	(	(	PUNCT
cana-2105	133	2	3.4	3.4	NUM
cana-2105	133	3	)	)	PUNCT
cana-2105	133	4	for	for	ADP
cana-2105	133	5	the	the	DET
cana-2105	133	6	next	next	ADJ
cana-2105	133	7	step	step	NOUN
cana-2105	133	8	of	of	ADP
cana-2105	133	9	the	the	DET
cana-2105	133	10	four	four	NUM
cana-2105	133	11	-	-	PUNCT
cana-2105	133	12	step	step	NOUN
cana-2105	133	13	iteration	iteration	NOUN
cana-2105	133	14	,	,	PUNCT
cana-2105	133	15	we	we	PRON
cana-2105	133	16	have	have	AUX
cana-2105	133	17	|w0|	|w0|	VERB
cana-2105	133	18	=	=	NOUN
cana-2105	133	19	|(1−	|(1−	NOUN
cana-2105	133	20	β)sz0	β)sz0	NOUN
cana-2105	133	21	+	+	NOUN
cana-2105	133	22	βstcv0|	βstcv0|	ADV
cana-2105	133	23	=	=	SYM
cana-2105	133	24	|(1−	|(1−	NOUN
cana-2105	133	25	β)sz0	β)sz0	NOUN
cana-2105	133	26	+	+	X
cana-2105	133	27	βs(sin(vk0	βs(sin(vk0	ADJ
cana-2105	133	28	)	)	PUNCT
cana-2105	133	29	+	+	NUM
cana-2105	133	30	av0	av0	PROPN
cana-2105	134	1	+	+	CCONJ
cana-2105	134	2	c)|	c)|	PROPN
cana-2105	134	3	≥	≥	NOUN
cana-2105	134	4	βs|	βs|	NOUN
cana-2105	134	5	sin(vk0	sin(vk0	NUM
cana-2105	134	6	)	)	PUNCT
cana-2105	134	7	+	+	NUM
cana-2105	134	8	av0	av0	PROPN
cana-2105	134	9	+	+	CCONJ
cana-2105	134	10	c|	c|	PROPN
cana-2105	134	11	−	−	PROPN
cana-2105	134	12	(	(	PUNCT
cana-2105	134	13	1−	1−	NUM
cana-2105	134	14	β)s|z0|	β)s|z0|	SYM
cana-2105	134	15	≥	≥	X
cana-2105	135	1	βs|	βs|	NOUN
cana-2105	135	2	sin(vk0	sin(vk0	NUM
cana-2105	135	3	)	)	PUNCT
cana-2105	136	1	+	+	NUM
cana-2105	137	1	av0	av0	PROPN
cana-2105	137	2	+	+	CCONJ
cana-2105	137	3	c|	c|	PROPN
cana-2105	137	4	−	−	PROPN
cana-2105	137	5	(	(	PUNCT
cana-2105	137	6	1−	1−	NUM
cana-2105	137	7	sβ)|z0|	sβ)|z0|	PROPN
cana-2105	137	8	≥	≥	NOUN
cana-2105	137	9	βs[|	βs[|	PROPN
cana-2105	137	10	sin(vk0)|	sin(vk0)|	PROPN
cana-2105	137	11	−	−	PROPN
cana-2105	137	12	|a||v0|	|a||v0|	PROPN
cana-2105	137	13	−	−	PROPN
cana-2105	137	14	|c|]−	|c|]−	NUM
cana-2105	137	15	|z0|+	|z0|+	NUM
cana-2105	137	16	sγ|z0|	sγ|z0|	X
cana-2105	137	17	≥	≥	NOUN
cana-2105	137	18	sβ[|	sβ[|	PROPN
cana-2105	137	19	sin(vk0)|	sin(vk0)|	NUM
cana-2105	137	20	−	−	PROPN
cana-2105	137	21	|a||v0|	|a||v0|	ADP
cana-2105	137	22	−	−	PROPN
cana-2105	137	23	|z0|]−	|z0|]−	SYM
cana-2105	137	24	|z0|+	|z0|+	NUM
cana-2105	137	25	sβ|z0|	sβ|z0|	NOUN
cana-2105	137	26	=	=	SYM
cana-2105	137	27	sβ|	sβ|	PROPN
cana-2105	137	28	sin(vk0)|	sin(vk0)|	PROPN
cana-2105	137	29	−	−	PROPN
cana-2105	137	30	sβ|a||z0|	sβ|a||z0|	PROPN
cana-2105	137	31	−	−	ADP
cana-2105	137	32	sδ|z0|	sδ|z0|	NUM
cana-2105	137	33	−	−	PROPN
cana-2105	137	34	|z0|+	|z0|+	NUM
cana-2105	137	35	sβ|z0|	sβ|z0|	X
cana-2105	137	36	≥	≥	X
cana-2105	137	37	sβ|	sβ|	PROPN
cana-2105	137	38	sin(vk0)|	sin(vk0)|	NUM
cana-2105	137	39	−	−	NOUN
cana-2105	137	40	|a||z0|	|a||z0|	NOUN
cana-2105	137	41	−	−	PROPN
cana-2105	137	42	|z0|	|z0|	NOUN
cana-2105	137	43	.	.	PUNCT
cana-2105	138	1	(	(	PUNCT
cana-2105	138	2	3.5	3.5	NUM
cana-2105	138	3	)	)	PUNCT
cana-2105	138	4	we	we	PRON
cana-2105	138	5	have	have	VERB
cana-2105	138	6	|	|	ADV
cana-2105	138	7	sin(vk0)|	sin(vk0)|	NOUN
cana-2105	138	8	=	=	SYM
cana-2105	138	9	|vk0	|vk0	PROPN
cana-2105	139	1	|	|	CCONJ
cana-2105	139	2	∣∣∣1−	∣∣∣1−	NUM
cana-2105	139	3	v2k0	v2k0	NOUN
cana-2105	139	4	3	3	NUM
cana-2105	139	5	!	!	PUNCT
cana-2105	139	6	+	+	CCONJ
cana-2105	139	7	v4k0	v4k0	PROPN
cana-2105	139	8	5	5	NUM
cana-2105	139	9	!	!	PUNCT
cana-2105	139	10	−	−	PROPN
cana-2105	139	11	·	·	PUNCT
cana-2105	139	12	·	·	PUNCT
cana-2105	139	13	·	·	PUNCT
cana-2105	139	14	∣∣∣	∣∣∣	ADJ
cana-2105	139	15	≥	≥	PROPN
cana-2105	139	16	|vk0	|vk0	PROPN
cana-2105	139	17	||ω2|	||ω2|	NOUN
cana-2105	139	18	,	,	PUNCT
cana-2105	139	19	where	where	SCONJ
cana-2105	139	20	|ω2|	|ω2|	NOUN
cana-2105	139	21	∈	∈	PROPN
cana-2105	139	22	(	(	PUNCT
cana-2105	139	23	0	0	NUM
cana-2105	139	24	,	,	PUNCT
cana-2105	139	25	1	1	NUM
cana-2105	139	26	]	]	PUNCT
cana-2105	139	27	except	except	SCONJ
cana-2105	139	28	the	the	DET
cana-2105	139	29	communications	communication	NOUN
cana-2105	139	30	on	on	ADP
cana-2105	139	31	applied	apply	VERB
cana-2105	139	32	nonlinear	nonlinear	ADJ
cana-2105	139	33	analysis	analysis	NOUN
cana-2105	139	34	issn	issn	NOUN
cana-2105	139	35	:	:	PUNCT
cana-2105	139	36	1074	1074	NUM
cana-2105	139	37	-	-	PUNCT
cana-2105	139	38	133x	133x	NUM
cana-2105	139	39	vol	vol	NOUN
cana-2105	139	40	32	32	NUM
cana-2105	140	1	no	no	NOUN
cana-2105	140	2	.	.	PUNCT
cana-2105	141	1	1s	1s	NUM
cana-2105	141	2	(	(	PUNCT
cana-2105	141	3	2025	2025	NUM
cana-2105	141	4	)	)	PUNCT
cana-2105	141	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	141	6	68	68	NUM
cana-2105	141	7	value	value	NOUN
cana-2105	141	8	for	for	ADP
cana-2105	141	9	which	which	PRON
cana-2105	141	10	|ω2|	|ω2|	NOUN
cana-2105	141	11	=	=	SYM
cana-2105	141	12	0	0	NUM
cana-2105	141	13	and	and	CCONJ
cana-2105	141	14	|z0|	|z0|	X
cana-2105	141	15	>	>	X
cana-2105	141	16	(	(	PUNCT
cana-2105	141	17	2(1+|a|	2(1+|a|	X
cana-2105	141	18	)	)	PUNCT
cana-2105	141	19	sβ|ω2|	sβ|ω2|	NOUN
cana-2105	141	20	)	)	PUNCT
cana-2105	141	21	1	1	NUM
cana-2105	141	22	k−1	k−1	PROPN
cana-2105	141	23	,	,	PUNCT
cana-2105	141	24	from	from	ADP
cana-2105	141	25	inequality	inequality	NOUN
cana-2105	141	26	3.5	3.5	NUM
cana-2105	141	27	we	we	PRON
cana-2105	141	28	obtain	obtain	VERB
cana-2105	141	29	|w0|	|w0|	NOUN
cana-2105	141	30	≥sβ|ω2||vk0	≥sβ|ω2||vk0	PROPN
cana-2105	141	31	|	|	ADV
cana-2105	141	32	−	−	PROPN
cana-2105	141	33	(	(	PUNCT
cana-2105	141	34	1	1	NUM
cana-2105	141	35	+	+	NUM
cana-2105	141	36	|a|)|z0|	|a|)|z0|	NOUN
cana-2105	141	37	≥sβ|ω2||zk0	≥sβ|ω2||zk0	X
cana-2105	141	38	|	|	ADV
cana-2105	141	39	−	−	PROPN
cana-2105	141	40	(	(	PUNCT
cana-2105	141	41	1	1	NUM
cana-2105	141	42	+	+	NUM
cana-2105	141	43	|a|)|z0|	|a|)|z0|	NOUN
cana-2105	141	44	=	=	AUX
cana-2105	141	45	|z0|[sβ|ω2||zk−1	|z0|[sβ|ω2||zk−1	NOUN
cana-2105	141	46	0	0	NUM
cana-2105	142	1	|	|	ADV
cana-2105	142	2	−	−	PROPN
cana-2105	142	3	(	(	PUNCT
cana-2105	142	4	1	1	NUM
cana-2105	142	5	+	+	CCONJ
cana-2105	142	6	|a|	|a|	NOUN
cana-2105	142	7	)	)	PUNCT
cana-2105	142	8	]	]	PUNCT
cana-2105	142	9	≥|z0|[2(1	≥|z0|[2(1	NOUN
cana-2105	142	10	+	+	CCONJ
cana-2105	142	11	|a|)−	|a|)−	PUNCT
cana-2105	142	12	(	(	PUNCT
cana-2105	142	13	1	1	NUM
cana-2105	142	14	+	+	NUM
cana-2105	142	15	|a|	|a|	NOUN
cana-2105	142	16	)	)	PUNCT
cana-2105	142	17	]	]	PUNCT
cana-2105	143	1	=	=	X
cana-2105	143	2	(	(	PUNCT
cana-2105	143	3	1	1	NUM
cana-2105	143	4	+	+	NUM
cana-2105	143	5	|a|)|z0|	|a|)|z0|	NOUN
cana-2105	143	6	≥|z0|	≥|z0|	NOUN
cana-2105	143	7	.	.	PUNCT
cana-2105	144	1	(	(	PUNCT
cana-2105	144	2	3.6	3.6	NUM
cana-2105	144	3	)	)	PUNCT
cana-2105	144	4	for	for	ADP
cana-2105	144	5	the	the	DET
cana-2105	144	6	last	last	ADJ
cana-2105	144	7	step	step	NOUN
cana-2105	144	8	of	of	ADP
cana-2105	144	9	the	the	DET
cana-2105	144	10	four	four	NUM
cana-2105	144	11	-	-	PUNCT
cana-2105	144	12	step	step	NOUN
cana-2105	144	13	iteration	iteration	NOUN
cana-2105	144	14	,	,	PUNCT
cana-2105	144	15	we	we	PRON
cana-2105	144	16	have	have	VERB
cana-2105	144	17	|z1|	|z1|	NOUN
cana-2105	144	18	=	=	PUNCT
cana-2105	144	19	|(1−	|(1−	NOUN
cana-2105	144	20	α)sz0	α)sz0	NOUN
cana-2105	144	21	+	+	CCONJ
cana-2105	144	22	αstcv0|	αstcv0|	NOUN
cana-2105	144	23	=	=	SYM
cana-2105	144	24	|(1−	|(1−	X
cana-2105	145	1	β)sz0	β)sz0	NOUN
cana-2105	146	1	+	+	CCONJ
cana-2105	146	2	βs(sin(wk	βs(sin(wk	NOUN
cana-2105	146	3	0	0	NUM
cana-2105	146	4	)	)	PUNCT
cana-2105	146	5	+	+	CCONJ
cana-2105	147	1	aw0	aw0	NOUN
cana-2105	147	2	+	+	CCONJ
cana-2105	147	3	c)|	c)|	PROPN
cana-2105	147	4	≥	≥	NOUN
cana-2105	147	5	αs|	αs|	NOUN
cana-2105	147	6	sin(wk	sin(wk	NOUN
cana-2105	147	7	0	0	NUM
cana-2105	147	8	)	)	PUNCT
cana-2105	148	1	+	+	CCONJ
cana-2105	148	2	aw0	aw0	NOUN
cana-2105	148	3	+	+	CCONJ
cana-2105	148	4	c|	c|	PROPN
cana-2105	148	5	−	−	PROPN
cana-2105	148	6	(	(	PUNCT
cana-2105	148	7	1−	1−	NUM
cana-2105	148	8	β)s|z0|	β)s|z0|	SYM
cana-2105	148	9	≥	≥	AUX
cana-2105	148	10	βs|	βs|	NOUN
cana-2105	148	11	sin(wk	sin(wk	NOUN
cana-2105	148	12	0	0	NUM
cana-2105	148	13	)	)	PUNCT
cana-2105	149	1	+	+	CCONJ
cana-2105	149	2	aw0	aw0	NOUN
cana-2105	149	3	+	+	CCONJ
cana-2105	149	4	c|	c|	PROPN
cana-2105	149	5	−	−	PROPN
cana-2105	149	6	(	(	PUNCT
cana-2105	149	7	1−	1−	NUM
cana-2105	149	8	sβ)|z0|	sβ)|z0|	PROPN
cana-2105	149	9	≥	≥	NOUN
cana-2105	149	10	βs[|	βs[|	ADJ
cana-2105	149	11	sin(wk	sin(wk	NOUN
cana-2105	149	12	0)|	0)|	NOUN
cana-2105	149	13	−	−	NOUN
cana-2105	149	14	|a||w0|	|a||w0|	ADJ
cana-2105	149	15	−	−	PROPN
cana-2105	149	16	|c|]−	|c|]−	NUM
cana-2105	149	17	|z0|+	|z0|+	NUM
cana-2105	149	18	sγ|z0|	sγ|z0|	X
cana-2105	149	19	≥	≥	NOUN
cana-2105	149	20	sβ[|	sβ[|	NOUN
cana-2105	149	21	sin(wk	sin(wk	NOUN
cana-2105	149	22	0)|	0)|	NOUN
cana-2105	149	23	−	−	NOUN
cana-2105	149	24	|a||w0|	|a||w0|	ADJ
cana-2105	149	25	−	−	PROPN
cana-2105	149	26	|z0|]−	|z0|]−	SYM
cana-2105	149	27	|z0|+	|z0|+	NUM
cana-2105	149	28	sβ|z0|	sβ|z0|	NOUN
cana-2105	149	29	=	=	SYM
cana-2105	149	30	sβ|	sβ|	PROPN
cana-2105	149	31	sin(wk	sin(wk	NOUN
cana-2105	149	32	0)|	0)|	NOUN
cana-2105	149	33	−	−	NOUN
cana-2105	149	34	sβ|a||w0|	sβ|a||w0|	PROPN
cana-2105	149	35	−	−	ADP
cana-2105	149	36	sδ|z0|	sδ|z0|	NUM
cana-2105	149	37	−	−	PROPN
cana-2105	149	38	|z0|+	|z0|+	NUM
cana-2105	149	39	sβ|z0|	sβ|z0|	NOUN
cana-2105	149	40	≥	≥	X
cana-2105	149	41	sβ|	sβ|	PROPN
cana-2105	149	42	sin(wk	sin(wk	NOUN
cana-2105	149	43	0)|	0)|	NOUN
cana-2105	149	44	−	−	NOUN
cana-2105	149	45	|a||z0|	|a||z0|	NOUN
cana-2105	149	46	−	−	PROPN
cana-2105	149	47	|z0|	|z0|	NOUN
cana-2105	149	48	.	.	PUNCT
cana-2105	150	1	(	(	PUNCT
cana-2105	150	2	3.7	3.7	NUM
cana-2105	150	3	)	)	PUNCT
cana-2105	150	4	we	we	PRON
cana-2105	150	5	have	have	VERB
cana-2105	150	6	|	|	ADV
cana-2105	150	7	sin(wk	sin(wk	NOUN
cana-2105	150	8	0)|	0)|	NOUN
cana-2105	150	9	=	=	SYM
cana-2105	150	10	|wk	|wk	SYM
cana-2105	150	11	0	0	NUM
cana-2105	151	1	|	|	CCONJ
cana-2105	151	2	∣∣∣1−	∣∣∣1−	PROPN
cana-2105	151	3	w2k	w2k	PROPN
cana-2105	151	4	0	0	NUM
cana-2105	151	5	3	3	NUM
cana-2105	151	6	!	!	PUNCT
cana-2105	152	1	+	+	CCONJ
cana-2105	152	2	w4k	w4k	ADP
cana-2105	152	3	0	0	NUM
cana-2105	152	4	5	5	NUM
cana-2105	152	5	!	!	PUNCT
cana-2105	152	6	−	−	PROPN
cana-2105	152	7	·	·	PUNCT
cana-2105	152	8	·	·	PUNCT
cana-2105	152	9	·	·	PUNCT
cana-2105	152	10	∣∣∣	∣∣∣	X
cana-2105	152	11	≥	≥	NUM
cana-2105	152	12	|wk	|wk	ADP
cana-2105	152	13	0	0	NUM
cana-2105	152	14	||ω1|	||ω1|	NOUN
cana-2105	152	15	,	,	PUNCT
cana-2105	152	16	where	where	SCONJ
cana-2105	152	17	|ω1|	|ω1|	VERB
cana-2105	152	18	∈	∈	PROPN
cana-2105	152	19	(	(	PUNCT
cana-2105	152	20	0	0	NUM
cana-2105	152	21	,	,	PUNCT
cana-2105	152	22	1	1	NUM
cana-2105	152	23	]	]	PUNCT
cana-2105	152	24	except	except	SCONJ
cana-2105	152	25	the	the	DET
cana-2105	152	26	value	value	NOUN
cana-2105	152	27	for	for	ADP
cana-2105	152	28	which	which	PRON
cana-2105	152	29	|ω1|	|ω1|	VERB
cana-2105	152	30	=	=	SYM
cana-2105	152	31	0	0	NUM
cana-2105	152	32	and	and	CCONJ
cana-2105	152	33	|z0|	|z0|	X
cana-2105	152	34	>	>	X
cana-2105	152	35	(	(	PUNCT
cana-2105	152	36	2(1+|a|	2(1+|a|	NUM
cana-2105	152	37	)	)	PUNCT
cana-2105	152	38	sα|ω1|	sα|ω1|	PROPN
cana-2105	152	39	)	)	PUNCT
cana-2105	152	40	1	1	NUM
cana-2105	152	41	k−1	k−1	PROPN
cana-2105	152	42	,	,	PUNCT
cana-2105	152	43	from	from	ADP
cana-2105	152	44	inequality	inequality	NOUN
cana-2105	152	45	3.7	3.7	NUM
cana-2105	152	46	we	we	PRON
cana-2105	152	47	obtain	obtain	VERB
cana-2105	152	48	|z1|	|z1|	NOUN
cana-2105	152	49	≥sα|ω1||wk	≥sα|ω1||wk	ADJ
cana-2105	152	50	0	0	NUM
cana-2105	153	1	|	|	ADV
cana-2105	153	2	−	−	PROPN
cana-2105	153	3	(	(	PUNCT
cana-2105	153	4	1	1	NUM
cana-2105	153	5	+	+	NUM
cana-2105	153	6	|a|)|z0|	|a|)|z0|	NOUN
cana-2105	153	7	≥sα|ω1||zk0	≥sα|ω1||zk0	NOUN
cana-2105	153	8	|	|	ADV
cana-2105	153	9	−	−	PROPN
cana-2105	153	10	(	(	PUNCT
cana-2105	153	11	1	1	NUM
cana-2105	153	12	+	+	NUM
cana-2105	153	13	|a|)|z0|	|a|)|z0|	NOUN
cana-2105	153	14	=	=	NOUN
cana-2105	153	15	|z0|[sα|ω1||zk−1	|z0|[sα|ω1||zk−1	NUM
cana-2105	153	16	0	0	NUM
cana-2105	154	1	|	|	ADV
cana-2105	154	2	−	−	PROPN
cana-2105	154	3	(	(	PUNCT
cana-2105	154	4	1	1	NUM
cana-2105	154	5	+	+	CCONJ
cana-2105	154	6	|a|	|a|	NOUN
cana-2105	154	7	)	)	PUNCT
cana-2105	154	8	]	]	PUNCT
cana-2105	154	9	≥|z0|[2(1	≥|z0|[2(1	NOUN
cana-2105	154	10	+	+	CCONJ
cana-2105	154	11	|a|)−	|a|)−	PUNCT
cana-2105	154	12	(	(	PUNCT
cana-2105	154	13	1	1	NUM
cana-2105	154	14	+	+	NUM
cana-2105	154	15	|a|	|a|	NOUN
cana-2105	154	16	)	)	PUNCT
cana-2105	154	17	]	]	PUNCT
cana-2105	155	1	=	=	X
cana-2105	155	2	(	(	PUNCT
cana-2105	155	3	1	1	NUM
cana-2105	155	4	+	+	NUM
cana-2105	155	5	|a|)|z0|	|a|)|z0|	NOUN
cana-2105	155	6	.	.	PUNCT
cana-2105	156	1	(	(	PUNCT
cana-2105	156	2	3.8	3.8	NUM
cana-2105	156	3	)	)	PUNCT
cana-2105	156	4	from	from	ADP
cana-2105	156	5	equation	equation	NOUN
cana-2105	156	6	(	(	PUNCT
cana-2105	156	7	3.8	3.8	NUM
cana-2105	156	8	)	)	PUNCT
cana-2105	156	9	|z1|	|z1|	NOUN
cana-2105	156	10	≥(1	≥(1	PROPN
cana-2105	156	11	+	+	CCONJ
cana-2105	156	12	|a|)|z0|	|a|)|z0|	PROPN
cana-2105	156	13	>	>	X
cana-2105	156	14	|z0|	|z0|	PROPN
cana-2105	156	15	>	>	X
cana-2105	156	16	max	max	PROPN
cana-2105	156	17	{	{	PUNCT
cana-2105	156	18	|c|	|c|	PROPN
cana-2105	156	19	,	,	PUNCT
cana-2105	156	20	(	(	PUNCT
cana-2105	156	21	2(1	2(1	NUM
cana-2105	156	22	+	+	CCONJ
cana-2105	156	23	|a|	|a|	NOUN
cana-2105	156	24	)	)	PUNCT
cana-2105	156	25	sα|ω1|	sα|ω1|	PROPN
cana-2105	156	26	)	)	PUNCT
cana-2105	156	27	1	1	NUM
cana-2105	156	28	k−1	k−1	PROPN
cana-2105	156	29	,	,	PUNCT
cana-2105	156	30	(	(	PUNCT
cana-2105	156	31	2(1	2(1	NUM
cana-2105	156	32	+	+	CCONJ
cana-2105	156	33	|a|	|a|	NOUN
cana-2105	156	34	)	)	PUNCT
cana-2105	156	35	sβ|ω2|	sβ|ω2|	NOUN
cana-2105	156	36	)	)	PUNCT
cana-2105	156	37	1	1	NUM
cana-2105	156	38	k−1	k−1	PROPN
cana-2105	156	39	,	,	PUNCT
cana-2105	156	40	(	(	PUNCT
cana-2105	156	41	2(1	2(1	NUM
cana-2105	156	42	+	+	CCONJ
cana-2105	156	43	|a|	|a|	NOUN
cana-2105	156	44	)	)	PUNCT
cana-2105	156	45	sγ|ω3|	sγ|ω3|	NUM
cana-2105	156	46	)	)	PUNCT
cana-2105	156	47	1	1	NUM
cana-2105	156	48	k−1	k−1	PROPN
cana-2105	156	49	,	,	PUNCT
cana-2105	156	50	(	(	PUNCT
cana-2105	156	51	2(1	2(1	NUM
cana-2105	156	52	+	+	CCONJ
cana-2105	156	53	|a|	|a|	NOUN
cana-2105	156	54	)	)	PUNCT
cana-2105	156	55	sδ|ω4|	sδ|ω4|	PROPN
cana-2105	156	56	)	)	PUNCT
cana-2105	156	57	1	1	NUM
cana-2105	156	58	k−1	k−1	PROPN
cana-2105	156	59	}	}	PUNCT
cana-2105	156	60	.	.	PUNCT
cana-2105	157	1	therefore	therefore	ADV
cana-2105	157	2	,	,	PUNCT
cana-2105	157	3	|z1|	|z1|	NOUN
cana-2105	157	4	satisfied	satisfy	VERB
cana-2105	157	5	all	all	DET
cana-2105	157	6	the	the	DET
cana-2105	157	7	conditions	condition	NOUN
cana-2105	157	8	as	as	ADP
cana-2105	157	9	|z0|	|z0|	NOUN
cana-2105	157	10	.	.	PUNCT
cana-2105	158	1	so	so	ADV
cana-2105	158	2	,	,	PUNCT
cana-2105	158	3	by	by	ADP
cana-2105	158	4	using	use	VERB
cana-2105	158	5	the	the	DET
cana-2105	158	6	same	same	ADJ
cana-2105	158	7	technique	technique	NOUN
cana-2105	158	8	for	for	ADP
cana-2105	158	9	n	n	NOUN
cana-2105	158	10	=	=	SYM
cana-2105	158	11	0	0	NUM
cana-2105	158	12	,	,	PUNCT
cana-2105	158	13	we	we	PRON
cana-2105	158	14	obtain	obtain	VERB
cana-2105	158	15	the	the	DET
cana-2105	158	16	result	result	NOUN
cana-2105	158	17	for	for	ADP
cana-2105	158	18	for	for	ADP
cana-2105	158	19	n	n	NOUN
cana-2105	158	20	=	=	SYM
cana-2105	158	21	1	1	NUM
cana-2105	158	22	,	,	PUNCT
cana-2105	158	23	as	as	ADP
cana-2105	158	24	|z2|	|z2|	PROPN
cana-2105	158	25	≥(1	≥(1	PROPN
cana-2105	158	26	+	+	PROPN
cana-2105	158	27	|a|)|z1|	|a|)|z1|	X
cana-2105	158	28	>	>	PUNCT
cana-2105	158	29	(	(	PUNCT
cana-2105	158	30	1	1	NUM
cana-2105	158	31	+	+	NUM
cana-2105	158	32	|a|)2|z0|	|a|)2|z0|	NOUN
cana-2105	158	33	communications	communication	NOUN
cana-2105	158	34	on	on	ADP
cana-2105	158	35	applied	apply	VERB
cana-2105	158	36	nonlinear	nonlinear	ADJ
cana-2105	158	37	analysis	analysis	NOUN
cana-2105	158	38	issn	issn	NOUN
cana-2105	158	39	:	:	PUNCT
cana-2105	158	40	1074	1074	NUM
cana-2105	158	41	-	-	PUNCT
cana-2105	158	42	133x	133x	NUM
cana-2105	158	43	vol	vol	NOUN
cana-2105	158	44	32	32	NUM
cana-2105	158	45	no	no	NOUN
cana-2105	158	46	.	.	PUNCT
cana-2105	159	1	1s	1s	NUM
cana-2105	159	2	(	(	PUNCT
cana-2105	159	3	2025	2025	NUM
cana-2105	159	4	)	)	PUNCT
cana-2105	159	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	159	6	69	69	NUM
cana-2105	159	7	continuing	continue	VERB
cana-2105	159	8	the	the	DET
cana-2105	159	9	iteration	iteration	NOUN
cana-2105	159	10	process	process	NOUN
cana-2105	159	11	up	up	ADP
cana-2105	159	12	to	to	ADP
cana-2105	159	13	the	the	DET
cana-2105	159	14	nth	nth	NOUN
cana-2105	159	15	steps	step	NOUN
cana-2105	159	16	,	,	PUNCT
cana-2105	159	17	we	we	PRON
cana-2105	159	18	obtain	obtain	VERB
cana-2105	159	19	|zn|	|zn|	ADJ
cana-2105	159	20	>	>	X
cana-2105	159	21	(	(	PUNCT
cana-2105	159	22	1	1	NUM
cana-2105	159	23	+	+	NUM
cana-2105	159	24	|a|)n|z0|	|a|)n|z0|	X
cana-2105	159	25	.	.	PUNCT
cana-2105	160	1	since	since	SCONJ
cana-2105	160	2	1	1	NUM
cana-2105	160	3	+	+	CCONJ
cana-2105	160	4	|a|	|a|	PROPN
cana-2105	160	5	>	>	SYM
cana-2105	160	6	1	1	NUM
cana-2105	160	7	,	,	PUNCT
cana-2105	160	8	we	we	PRON
cana-2105	160	9	obtain	obtain	VERB
cana-2105	160	10	lim	lim	PROPN
cana-2105	160	11	n→∞	n→∞	PRON
cana-2105	160	12	|zn|	|zn|	NOUN
cana-2105	160	13	=	=	SYM
cana-2105	160	14	∞.	∞.	PROPN
cana-2105	160	15	theorem	theorem	VERB
cana-2105	160	16	3.2	3.2	NUM
cana-2105	160	17	.	.	PUNCT
cana-2105	161	1	let	let	VERB
cana-2105	161	2	tc	tc	NOUN
cana-2105	161	3	:	:	PUNCT
cana-2105	161	4	c	c	X
cana-2105	161	5	→	→	PUNCT
cana-2105	161	6	c	c	X
cana-2105	161	7	be	be	AUX
cana-2105	161	8	a	a	DET
cana-2105	161	9	complex	complex	ADV
cana-2105	161	10	-	-	PUNCT
cana-2105	161	11	valued	value	VERB
cana-2105	161	12	map	map	NOUN
cana-2105	161	13	defined	define	VERB
cana-2105	161	14	by	by	ADP
cana-2105	161	15	tc(z	tc(z	NOUN
cana-2105	161	16	)	)	PUNCT
cana-2105	161	17	=	=	PUNCT
cana-2105	162	1	sin(zk	sin(zk	X
cana-2105	162	2	)	)	PUNCT
cana-2105	163	1	+	+	CCONJ
cana-2105	163	2	az	az	PROPN
cana-2105	163	3	+	+	CCONJ
cana-2105	163	4	c	c	PROPN
cana-2105	163	5	for	for	ADP
cana-2105	163	6	all	all	DET
cana-2105	163	7	z	z	NOUN
cana-2105	163	8	∈	∈	PROPN
cana-2105	163	9	c	c	NOUN
cana-2105	163	10	,	,	PUNCT
cana-2105	163	11	k	k	PROPN
cana-2105	163	12	∈	∈	PROPN
cana-2105	163	13	n	n	PRON
cana-2105	163	14	\	\	NOUN
cana-2105	163	15	{	{	PUNCT
cana-2105	163	16	1	1	NUM
cana-2105	163	17	}	}	PUNCT
cana-2105	163	18	and	and	CCONJ
cana-2105	163	19	a	a	DET
cana-2105	163	20	,	,	PUNCT
cana-2105	163	21	c	c	PROPN
cana-2105	163	22	∈	∈	PROPN
cana-2105	163	23	c	c	NOUN
cana-2105	163	24	such	such	ADJ
cana-2105	163	25	that	that	SCONJ
cana-2105	163	26	a	a	DET
cana-2105	163	27	̸=	̸=	PROPN
cana-2105	163	28	0	0	NUM
cana-2105	163	29	.	.	PUNCT
cana-2105	164	1	consider	consider	VERB
cana-2105	164	2	the	the	DET
cana-2105	164	3	iterative	iterative	NOUN
cana-2105	164	4	sequence	sequence	NOUN
cana-2105	164	5	defined	define	VERB
cana-2105	164	6	in	in	ADP
cana-2105	164	7	(	(	PUNCT
cana-2105	164	8	2.3	2.3	NUM
cana-2105	164	9	)	)	PUNCT
cana-2105	164	10	and	and	CCONJ
cana-2105	164	11	|ω1|	|ω1|	PROPN
cana-2105	164	12	,	,	PUNCT
cana-2105	164	13	|ω2|	|ω2|	NOUN
cana-2105	164	14	,	,	PUNCT
cana-2105	164	15	|ω3|	|ω3|	NOUN
cana-2105	164	16	,	,	PUNCT
cana-2105	164	17	|ω4|	|ω4|	NOUN
cana-2105	164	18	∈	∈	PROPN
cana-2105	164	19	(	(	PUNCT
cana-2105	164	20	0	0	NUM
cana-2105	164	21	,	,	PUNCT
cana-2105	164	22	1	1	NUM
cana-2105	164	23	]	]	PUNCT
cana-2105	164	24	if	if	SCONJ
cana-2105	164	25	|zm|	|zm|	PROPN
cana-2105	164	26	>	>	X
cana-2105	164	27	max	max	PROPN
cana-2105	164	28	{	{	PUNCT
cana-2105	164	29	|c|	|c|	PROPN
cana-2105	164	30	,	,	PUNCT
cana-2105	164	31	(	(	PUNCT
cana-2105	164	32	2(1	2(1	NUM
cana-2105	164	33	+	+	CCONJ
cana-2105	164	34	|a|	|a|	NOUN
cana-2105	164	35	)	)	PUNCT
cana-2105	164	36	sα|ω1|	sα|ω1|	PROPN
cana-2105	164	37	)	)	PUNCT
cana-2105	164	38	1	1	NUM
cana-2105	164	39	k−1	k−1	PROPN
cana-2105	164	40	,	,	PUNCT
cana-2105	164	41	(	(	PUNCT
cana-2105	164	42	2(1	2(1	NUM
cana-2105	164	43	+	+	CCONJ
cana-2105	164	44	|a|	|a|	NOUN
cana-2105	164	45	)	)	PUNCT
cana-2105	164	46	sβ|ω2|	sβ|ω2|	NOUN
cana-2105	164	47	)	)	PUNCT
cana-2105	164	48	1	1	NUM
cana-2105	164	49	k−1	k−1	PROPN
cana-2105	164	50	,	,	PUNCT
cana-2105	164	51	(	(	PUNCT
cana-2105	164	52	2(1	2(1	NUM
cana-2105	164	53	+	+	CCONJ
cana-2105	164	54	|a|	|a|	NOUN
cana-2105	164	55	)	)	PUNCT
cana-2105	164	56	sγ|ω3|	sγ|ω3|	NUM
cana-2105	164	57	)	)	PUNCT
cana-2105	164	58	1	1	NUM
cana-2105	164	59	k−1	k−1	PROPN
cana-2105	164	60	,	,	PUNCT
cana-2105	164	61	(	(	PUNCT
cana-2105	164	62	2(1	2(1	NUM
cana-2105	164	63	+	+	CCONJ
cana-2105	164	64	|a|	|a|	NOUN
cana-2105	164	65	)	)	PUNCT
cana-2105	164	66	sδ|ω4|	sδ|ω4|	PROPN
cana-2105	164	67	)	)	PUNCT
cana-2105	164	68	1	1	NUM
cana-2105	164	69	k−1	k−1	PROPN
cana-2105	164	70	}	}	PUNCT
cana-2105	164	71	for	for	ADP
cana-2105	164	72	some	some	DET
cana-2105	164	73	m	m	NOUN
cana-2105	164	74	∈	∈	NOUN
cana-2105	164	75	n	n	ADV
cana-2105	164	76	∪	∪	X
cana-2105	164	77	{	{	PUNCT
cana-2105	164	78	0	0	NUM
cana-2105	164	79	}	}	PUNCT
cana-2105	164	80	,	,	PUNCT
cana-2105	164	81	then	then	ADV
cana-2105	164	82	lim	lim	PROPN
cana-2105	164	83	n→∞	n→∞	PRON
cana-2105	164	84	|zn|	|zn|	NOUN
cana-2105	164	85	=	=	PUNCT
cana-2105	164	86	∞.	∞.	PROPN
cana-2105	164	87	proof	proof	NOUN
cana-2105	164	88	.	.	PUNCT
cana-2105	165	1	by	by	ADP
cana-2105	165	2	using	use	VERB
cana-2105	165	3	a	a	DET
cana-2105	165	4	similar	similar	ADJ
cana-2105	165	5	technique	technique	NOUN
cana-2105	165	6	of	of	ADP
cana-2105	165	7	the	the	DET
cana-2105	165	8	theorem	theorem	NOUN
cana-2105	165	9	3.1	3.1	NUM
cana-2105	165	10	,	,	PUNCT
cana-2105	165	11	we	we	PRON
cana-2105	165	12	have	have	AUX
cana-2105	165	13	sα|ω1||z0|k−1|	sα|ω1||z0|k−1|	VERB
cana-2105	165	14	−	−	NOUN
cana-2105	165	15	(	(	PUNCT
cana-2105	165	16	1	1	NUM
cana-2105	165	17	+	+	CCONJ
cana-2105	165	18	|a|	|a|	NOUN
cana-2105	165	19	)	)	PUNCT
cana-2105	165	20	>	>	SYM
cana-2105	165	21	1	1	NUM
cana-2105	165	22	and	and	CCONJ
cana-2105	165	23	|zm+n|	|zm+n|	PROPN
cana-2105	165	24	>	>	CCONJ
cana-2105	165	25	|z0|(1	|z0|(1	PROPN
cana-2105	165	26	+	+	CCONJ
cana-2105	165	27	|a|)m+n	|a|)m+n	X
cana-2105	165	28	hence	hence	ADV
cana-2105	165	29	,	,	PUNCT
cana-2105	165	30	|zn|	|zn|	ADJ
cana-2105	165	31	→	→	SYM
cana-2105	165	32	∞	∞	NUM
cana-2105	165	33	as	as	ADP
cana-2105	165	34	n	n	PROPN
cana-2105	165	35	→	→	SYM
cana-2105	165	36	∞.	∞.	PROPN
cana-2105	165	37	remark	remark	VERB
cana-2105	165	38	3.3	3.3	NUM
cana-2105	165	39	.	.	PUNCT
cana-2105	166	1	we	we	PRON
cana-2105	166	2	have	have	VERB
cana-2105	166	3	r	r	NOUN
cana-2105	166	4	=	=	SYM
cana-2105	166	5	max	max	X
cana-2105	166	6	{	{	PUNCT
cana-2105	166	7	|c|	|c|	PROPN
cana-2105	166	8	,	,	PUNCT
cana-2105	166	9	(	(	PUNCT
cana-2105	166	10	2(1	2(1	NUM
cana-2105	166	11	+	+	CCONJ
cana-2105	166	12	|a|	|a|	NOUN
cana-2105	166	13	)	)	PUNCT
cana-2105	166	14	sα|ω1|	sα|ω1|	PROPN
cana-2105	166	15	)	)	PUNCT
cana-2105	166	16	1	1	NUM
cana-2105	166	17	k−1	k−1	PROPN
cana-2105	166	18	,	,	PUNCT
cana-2105	166	19	(	(	PUNCT
cana-2105	166	20	2(1	2(1	NUM
cana-2105	166	21	+	+	CCONJ
cana-2105	166	22	|a|	|a|	NOUN
cana-2105	166	23	)	)	PUNCT
cana-2105	166	24	sβ|ω2|	sβ|ω2|	NOUN
cana-2105	166	25	)	)	PUNCT
cana-2105	166	26	1	1	NUM
cana-2105	166	27	k−1	k−1	PROPN
cana-2105	166	28	,	,	PUNCT
cana-2105	166	29	(	(	PUNCT
cana-2105	166	30	2(1	2(1	NUM
cana-2105	166	31	+	+	CCONJ
cana-2105	166	32	|a|	|a|	NOUN
cana-2105	166	33	)	)	PUNCT
cana-2105	166	34	sγ|ω3|	sγ|ω3|	NUM
cana-2105	166	35	)	)	PUNCT
cana-2105	166	36	1	1	NUM
cana-2105	166	37	k−1	k−1	PROPN
cana-2105	166	38	,	,	PUNCT
cana-2105	166	39	(	(	PUNCT
cana-2105	166	40	2(1	2(1	NUM
cana-2105	166	41	+	+	CCONJ
cana-2105	166	42	|a|	|a|	NOUN
cana-2105	166	43	)	)	PUNCT
cana-2105	166	44	sδ|ω4|	sδ|ω4|	PROPN
cana-2105	166	45	)	)	PUNCT
cana-2105	166	46	1	1	NUM
cana-2105	166	47	k−1	k−1	PROPN
cana-2105	166	48	}	}	PUNCT
cana-2105	166	49	is	be	AUX
cana-2105	166	50	called	call	VERB
cana-2105	166	51	escape	escape	NOUN
cana-2105	166	52	radius	radius	NOUN
cana-2105	166	53	that	that	PRON
cana-2105	166	54	enable	enable	VERB
cana-2105	166	55	the	the	DET
cana-2105	166	56	generation	generation	NOUN
cana-2105	166	57	of	of	ADP
cana-2105	166	58	novel	novel	ADJ
cana-2105	166	59	julia	julia	PROPN
cana-2105	166	60	and	and	CCONJ
cana-2105	166	61	mandelbrot	mandelbrot	PROPN
cana-2105	166	62	sets	set	NOUN
cana-2105	166	63	based	base	VERB
cana-2105	166	64	on	on	ADP
cana-2105	166	65	complex	complex	ADV
cana-2105	166	66	-	-	PUNCT
cana-2105	166	67	valued	value	VERB
cana-2105	166	68	sine	sine	ADJ
cana-2105	166	69	functions	function	NOUN
cana-2105	166	70	.	.	PUNCT
cana-2105	167	1	4	4	NUM
cana-2105	167	2	generation	generation	NOUN
cana-2105	167	3	of	of	ADP
cana-2105	167	4	fractals	fractal	NOUN
cana-2105	167	5	fractals	fractal	NOUN
cana-2105	167	6	being	be	AUX
cana-2105	167	7	produced	produce	VERB
cana-2105	167	8	by	by	ADP
cana-2105	167	9	using	use	VERB
cana-2105	167	10	algorithm	algorithm	NOUN
cana-2105	167	11	1	1	NUM
cana-2105	167	12	(	(	PUNCT
cana-2105	167	13	for	for	ADP
cana-2105	167	14	julia	julia	PROPN
cana-2105	167	15	set	set	PROPN
cana-2105	167	16	)	)	PUNCT
cana-2105	167	17	and	and	CCONJ
cana-2105	167	18	algorithm	algorithm	NOUN
cana-2105	167	19	2	2	NUM
cana-2105	167	20	(	(	PUNCT
cana-2105	167	21	for	for	ADP
cana-2105	167	22	mandelbrot	mandelbrot	PROPN
cana-2105	167	23	set	set	PROPN
cana-2105	167	24	)	)	PUNCT
cana-2105	167	25	,	,	PUNCT
cana-2105	167	26	for	for	ADP
cana-2105	167	27	creating	create	VERB
cana-2105	167	28	beautiful	beautiful	ADJ
cana-2105	167	29	fractal	fractal	ADJ
cana-2105	167	30	sketches	sketch	NOUN
cana-2105	167	31	for	for	ADP
cana-2105	167	32	complex	complex	ADV
cana-2105	167	33	-	-	PUNCT
cana-2105	167	34	valued	value	VERB
cana-2105	167	35	function	function	NOUN
cana-2105	167	36	tcz	tcz	NOUN
cana-2105	167	37	=	=	SYM
cana-2105	167	38	sin(zk	sin(zk	NOUN
cana-2105	167	39	)	)	PUNCT
cana-2105	168	1	+	+	CCONJ
cana-2105	168	2	az+	az+	ADJ
cana-2105	168	3	c	c	NOUN
cana-2105	168	4	using	use	VERB
cana-2105	168	5	a	a	DET
cana-2105	168	6	four	four	NUM
cana-2105	168	7	-	-	PUNCT
cana-2105	168	8	steps	step	NOUN
cana-2105	168	9	iteration	iteration	NOUN
cana-2105	168	10	process	process	NOUN
cana-2105	168	11	enhance	enhance	VERB
cana-2105	168	12	with	with	ADP
cana-2105	168	13	s	s	NOUN
cana-2105	168	14	-	-	NOUN
cana-2105	168	15	convexity	convexity	NOUN
cana-2105	168	16	via	via	ADP
cana-2105	168	17	matlab	matlab	PROPN
cana-2105	168	18	r2021a	r2021a	PROPN
cana-2105	168	19	on	on	ADP
cana-2105	168	20	a	a	DET
cana-2105	168	21	computer	computer	NOUN
cana-2105	168	22	system	system	NOUN
cana-2105	168	23	featuring	feature	VERB
cana-2105	168	24	an	an	DET
cana-2105	168	25	amd	amd	ADJ
cana-2105	168	26	ryzen	ryzen	ADJ
cana-2105	168	27	5	5	NUM
cana-2105	168	28	7520u	7520u	NOUN
cana-2105	168	29	processor	processor	NOUN
cana-2105	168	30	with	with	ADP
cana-2105	168	31	a	a	DET
cana-2105	168	32	clock	clock	NOUN
cana-2105	168	33	speed	speed	NOUN
cana-2105	168	34	of	of	ADP
cana-2105	168	35	2.80	2.80	NUM
cana-2105	168	36	ghz	ghz	NOUN
cana-2105	168	37	,	,	PUNCT
cana-2105	168	38	8	8	NUM
cana-2105	168	39	gb	gb	NOUN
cana-2105	168	40	of	of	ADP
cana-2105	168	41	ram	ram	NOUN
cana-2105	168	42	,	,	PUNCT
cana-2105	168	43	and	and	CCONJ
cana-2105	168	44	running	run	VERB
cana-2105	168	45	the	the	DET
cana-2105	168	46	microsoft	microsoft	PROPN
cana-2105	168	47	windows	windows	PROPN
cana-2105	168	48	11	11	NUM
cana-2105	168	49	(	(	PUNCT
cana-2105	168	50	64	64	NUM
cana-2105	168	51	-	-	PUNCT
cana-2105	168	52	bit	bit	NOUN
cana-2105	168	53	)	)	PUNCT
cana-2105	168	54	operating	operating	NOUN
cana-2105	168	55	system	system	NOUN
cana-2105	168	56	.	.	PUNCT
cana-2105	169	1	we	we	PRON
cana-2105	169	2	employed	employ	VERB
cana-2105	169	3	the	the	DET
cana-2105	169	4	”	"	PUNCT
cana-2105	169	5	jet	jet	NOUN
cana-2105	169	6	”	"	PUNCT
cana-2105	169	7	colormap	colormap	NOUN
cana-2105	169	8	shown	show	VERB
cana-2105	169	9	in	in	ADP
cana-2105	169	10	figure	figure	NOUN
cana-2105	169	11	1	1	NUM
cana-2105	169	12	,	,	PUNCT
cana-2105	169	13	a	a	DET
cana-2105	169	14	widely	widely	ADV
cana-2105	169	15	adopted	adopt	VERB
cana-2105	169	16	standard	standard	NOUN
cana-2105	169	17	colormap	colormap	VERB
cana-2105	169	18	,	,	PUNCT
cana-2105	169	19	to	to	PART
cana-2105	169	20	assign	assign	VERB
cana-2105	169	21	colors	color	NOUN
cana-2105	169	22	to	to	ADP
cana-2105	169	23	the	the	DET
cana-2105	169	24	data	data	NOUN
cana-2105	169	25	points	point	NOUN
cana-2105	169	26	to	to	PART
cana-2105	169	27	enhance	enhance	VERB
cana-2105	169	28	the	the	DET
cana-2105	169	29	visual	visual	ADJ
cana-2105	169	30	representation	representation	NOUN
cana-2105	169	31	.	.	PUNCT
cana-2105	170	1	our	our	PRON
cana-2105	170	2	four	four	NUM
cana-2105	170	3	-	-	PUNCT
cana-2105	170	4	step	step	NOUN
cana-2105	170	5	iteration	iteration	NOUN
cana-2105	170	6	with	with	ADP
cana-2105	170	7	given	give	VERB
cana-2105	170	8	complex	complex	ADV
cana-2105	170	9	-	-	PUNCT
cana-2105	170	10	valued	value	VERB
cana-2105	170	11	function	function	NOUN
cana-2105	170	12	involves	involve	VERB
cana-2105	170	13	13	13	NUM
cana-2105	170	14	parameters	parameter	NOUN
cana-2105	170	15	,	,	PUNCT
cana-2105	170	16	it	it	PRON
cana-2105	170	17	can	can	AUX
cana-2105	170	18	be	be	AUX
cana-2105	170	19	challenging	challenge	VERB
cana-2105	170	20	to	to	PART
cana-2105	170	21	discuss	discuss	VERB
cana-2105	170	22	the	the	DET
cana-2105	170	23	julia	julia	PROPN
cana-2105	170	24	and	and	CCONJ
cana-2105	170	25	mandelbrot	mandelbrot	PROPN
cana-2105	170	26	sets	set	VERB
cana-2105	170	27	comprehensively	comprehensively	ADV
cana-2105	170	28	by	by	ADP
cana-2105	170	29	changing	change	VERB
cana-2105	170	30	all	all	PRON
cana-2105	170	31	of	of	ADP
cana-2105	170	32	these	these	DET
cana-2105	170	33	parameters	parameter	NOUN
cana-2105	170	34	.	.	PUNCT
cana-2105	171	1	however	however	ADV
cana-2105	171	2	,	,	PUNCT
cana-2105	171	3	we	we	PRON
cana-2105	171	4	only	only	ADV
cana-2105	171	5	discuss	discuss	VERB
cana-2105	171	6	the	the	DET
cana-2105	171	7	behavior	behavior	NOUN
cana-2105	171	8	of	of	ADP
cana-2105	171	9	a	a	DET
cana-2105	171	10	fractals	fractal	NOUN
cana-2105	171	11	by	by	ADP
cana-2105	171	12	varying	vary	VERB
cana-2105	171	13	some	some	DET
cana-2105	171	14	parameters	parameter	NOUN
cana-2105	171	15	values	value	NOUN
cana-2105	171	16	.	.	PUNCT
cana-2105	172	1	communications	communication	NOUN
cana-2105	172	2	on	on	ADP
cana-2105	172	3	applied	apply	VERB
cana-2105	172	4	nonlinear	nonlinear	ADJ
cana-2105	172	5	analysis	analysis	NOUN
cana-2105	172	6	issn	issn	NOUN
cana-2105	172	7	:	:	PUNCT
cana-2105	172	8	1074	1074	NUM
cana-2105	172	9	-	-	PUNCT
cana-2105	172	10	133x	133x	NUM
cana-2105	172	11	vol	vol	NOUN
cana-2105	172	12	32	32	NUM
cana-2105	172	13	no	no	NOUN
cana-2105	172	14	.	.	PUNCT
cana-2105	173	1	1s	1s	NUM
cana-2105	173	2	(	(	PUNCT
cana-2105	173	3	2025	2025	NUM
cana-2105	173	4	)	)	PUNCT
cana-2105	173	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	173	6	70	70	NUM
cana-2105	173	7	figure	figure	NOUN
cana-2105	173	8	1	1	NUM
cana-2105	173	9	:	:	PUNCT
cana-2105	173	10	a	a	DET
cana-2105	173	11	colormap	colormap	NOUN
cana-2105	173	12	is	be	AUX
cana-2105	173	13	used	use	VERB
cana-2105	173	14	to	to	PART
cana-2105	173	15	create	create	VERB
cana-2105	173	16	julia	julia	PROPN
cana-2105	173	17	and	and	CCONJ
cana-2105	173	18	mandelbrot	mandelbrot	PROPN
cana-2105	173	19	sets	set	NOUN
cana-2105	173	20	.	.	PUNCT
cana-2105	174	1	algorithm	algorithm	NOUN
cana-2105	174	2	1	1	NUM
cana-2105	174	3	:	:	PUNCT
cana-2105	174	4	creating	create	VERB
cana-2105	174	5	julia	julia	PROPN
cana-2105	174	6	set	set	VERB
cana-2105	174	7	input	input	NOUN
cana-2105	174	8	:	:	PUNCT
cana-2105	174	9	tc(z	tc(z	X
cana-2105	174	10	)	)	PUNCT
cana-2105	174	11	=	=	SYM
cana-2105	174	12	sin(zk	sin(zk	X
cana-2105	174	13	)	)	PUNCT
cana-2105	175	1	+	+	CCONJ
cana-2105	175	2	az	az	PROPN
cana-2105	175	3	+	+	CCONJ
cana-2105	175	4	c	c	PROPN
cana-2105	175	5	for	for	ADP
cana-2105	175	6	all	all	DET
cana-2105	175	7	z	z	NOUN
cana-2105	175	8	∈	∈	PROPN
cana-2105	175	9	c	c	NOUN
cana-2105	175	10	,	,	PUNCT
cana-2105	175	11	k	k	PROPN
cana-2105	175	12	∈	∈	PROPN
cana-2105	175	13	n	n	PRON
cana-2105	175	14	\	\	NOUN
cana-2105	175	15	{	{	PUNCT
cana-2105	175	16	1	1	NUM
cana-2105	175	17	}	}	PUNCT
cana-2105	175	18	,	,	PUNCT
cana-2105	175	19	a	a	PRON
cana-2105	175	20	,	,	PUNCT
cana-2105	175	21	c	c	PROPN
cana-2105	175	22	∈	∈	PROPN
cana-2105	175	23	c	c	NOUN
cana-2105	175	24	:	:	PUNCT
cana-2105	175	25	a	a	DET
cana-2105	175	26	̸=	̸=	PROPN
cana-2105	175	27	0	0	NUM
cana-2105	175	28	complex	complex	ADJ
cana-2105	175	29	constants	constant	NOUN
cana-2105	175	30	;	;	PUNCT
cana-2105	175	31	b	b	X
cana-2105	175	32	⊂	⊂	PROPN
cana-2105	175	33	c	c	PROPN
cana-2105	175	34	area	area	NOUN
cana-2105	175	35	;	;	PUNCT
cana-2105	175	36	k	k	PROPN
cana-2105	175	37	the	the	DET
cana-2105	175	38	maximum	maximum	ADJ
cana-2105	175	39	number	number	NOUN
cana-2105	175	40	of	of	ADP
cana-2105	175	41	iterations	iteration	NOUN
cana-2105	175	42	;	;	PUNCT
cana-2105	175	43	s	s	X
cana-2105	175	44	,	,	PUNCT
cana-2105	175	45	α	α	X
cana-2105	175	46	,	,	PUNCT
cana-2105	175	47	β	β	X
cana-2105	175	48	,	,	PUNCT
cana-2105	175	49	γ	γ	PROPN
cana-2105	175	50	,	,	PUNCT
cana-2105	175	51	δ	δ	PROPN
cana-2105	175	52	,	,	PUNCT
cana-2105	175	53	|ω1|	|ω1|	PROPN
cana-2105	175	54	,	,	PUNCT
cana-2105	175	55	|ω2|	|ω2|	NOUN
cana-2105	175	56	,	,	PUNCT
cana-2105	175	57	|ω3|	|ω3|	NOUN
cana-2105	175	58	,	,	PUNCT
cana-2105	175	59	|ω4|	|ω4|	NOUN
cana-2105	175	60	∈	∈	PROPN
cana-2105	175	61	(	(	PUNCT
cana-2105	175	62	0	0	NUM
cana-2105	175	63	,	,	PUNCT
cana-2105	175	64	1	1	NUM
cana-2105	175	65	]	]	PUNCT
cana-2105	175	66	parameters	parameter	NOUN
cana-2105	175	67	for	for	ADP
cana-2105	175	68	the	the	DET
cana-2105	175	69	approximation	approximation	NOUN
cana-2105	175	70	of	of	ADP
cana-2105	175	71	four	four	NUM
cana-2105	175	72	-	-	PUNCT
cana-2105	175	73	steps	step	NOUN
cana-2105	175	74	iterative	iterative	NOUN
cana-2105	175	75	method	method	NOUN
cana-2105	175	76	with	with	ADP
cana-2105	175	77	s	s	NOUN
cana-2105	175	78	-	-	NOUN
cana-2105	175	79	convexity	convexity	NOUN
cana-2105	175	80	and	and	CCONJ
cana-2105	175	81	colourmap	colourmap	NOUN
cana-2105	176	1	[	[	X
cana-2105	176	2	0	0	NUM
cana-2105	176	3	..	..	SYM
cana-2105	176	4	f	f	X
cana-2105	176	5	]	]	PUNCT
cana-2105	176	6	colour	colour	NOUN
cana-2105	176	7	map	map	NOUN
cana-2105	176	8	with	with	ADP
cana-2105	176	9	f	f	PROPN
cana-2105	176	10	+	+	CCONJ
cana-2105	176	11	1	1	NUM
cana-2105	176	12	colours	colour	NOUN
cana-2105	176	13	.	.	PUNCT
cana-2105	177	1	output	output	NOUN
cana-2105	177	2	:	:	PUNCT
cana-2105	177	3	julia	julia	PROPN
cana-2105	177	4	set	set	VERB
cana-2105	177	5	for	for	ADP
cana-2105	177	6	area	area	NOUN
cana-2105	177	7	b	b	PROPN
cana-2105	177	8	1	1	NUM
cana-2105	177	9	for	for	ADP
cana-2105	177	10	z0	z0	PROPN
cana-2105	177	11	∈	∈	PROPN
cana-2105	177	12	a	a	DET
cana-2105	177	13	do	do	NOUN
cana-2105	177	14	2	2	NUM
cana-2105	177	15	r	r	NOUN
cana-2105	177	16	=	=	SYM
cana-2105	177	17	max	max	PROPN
cana-2105	177	18	{	{	PUNCT
cana-2105	177	19	|c|	|c|	PROPN
cana-2105	177	20	,	,	PUNCT
cana-2105	177	21	(	(	PUNCT
cana-2105	177	22	2(1+|a|	2(1+|a|	X
cana-2105	177	23	)	)	PUNCT
cana-2105	177	24	sα|ω1|	sα|ω1|	PROPN
cana-2105	177	25	)	)	PUNCT
cana-2105	177	26	1	1	NUM
cana-2105	177	27	k−1	k−1	PROPN
cana-2105	177	28	,	,	PUNCT
cana-2105	177	29	(	(	PUNCT
cana-2105	177	30	2(1+|a|	2(1+|a|	X
cana-2105	177	31	)	)	PUNCT
cana-2105	177	32	sβ|ω2|	sβ|ω2|	NOUN
cana-2105	177	33	)	)	PUNCT
cana-2105	177	34	1	1	NUM
cana-2105	177	35	k−1	k−1	PROPN
cana-2105	177	36	,	,	PUNCT
cana-2105	177	37	(	(	PUNCT
cana-2105	177	38	2(1+|a|	2(1+|a|	X
cana-2105	177	39	)	)	PUNCT
cana-2105	177	40	sγ|ω3|	sγ|ω3|	NUM
cana-2105	177	41	)	)	PUNCT
cana-2105	177	42	1	1	NUM
cana-2105	177	43	k−1	k−1	PROPN
cana-2105	177	44	,	,	PUNCT
cana-2105	177	45	(	(	PUNCT
cana-2105	177	46	2(1+|a|	2(1+|a|	X
cana-2105	177	47	)	)	PUNCT
cana-2105	177	48	sδ|ω4|	sδ|ω4|	PROPN
cana-2105	177	49	)	)	PUNCT
cana-2105	177	50	1	1	NUM
cana-2105	177	51	k−1	k−1	PROPN
cana-2105	177	52	}	}	PUNCT
cana-2105	177	53	3	3	NUM
cana-2105	177	54	n	n	NOUN
cana-2105	177	55	=	=	SYM
cana-2105	177	56	0	0	SYM
cana-2105	177	57	4	4	NUM
cana-2105	177	58	z0	z0	NOUN
cana-2105	177	59	=	=	SYM
cana-2105	177	60	0	0	NUM
cana-2105	177	61	5	5	NUM
cana-2105	177	62	while	while	SCONJ
cana-2105	177	63	n	n	ADP
cana-2105	177	64	≤	≤	X
cana-2105	178	1	k	k	X
cana-2105	178	2	do	do	VERB
cana-2105	178	3	6	6	NUM
cana-2105	178	4	un	un	NOUN
cana-2105	178	5	=	=	SYM
cana-2105	178	6	(	(	PUNCT
cana-2105	178	7	1−	1−	NUM
cana-2105	178	8	δ)szn	δ)szn	PROPN
cana-2105	178	9	+	+	CCONJ
cana-2105	178	10	δstczn	δstczn	VERB
cana-2105	178	11	7	7	NUM
cana-2105	178	12	vn	vn	NOUN
cana-2105	178	13	=	=	SYM
cana-2105	178	14	(	(	PUNCT
cana-2105	178	15	1−	1−	NUM
cana-2105	178	16	γ)szn	γ)szn	NOUN
cana-2105	178	17	+	+	CCONJ
cana-2105	178	18	γstcun	γstcun	NOUN
cana-2105	178	19	8	8	NUM
cana-2105	178	20	wn	wn	NOUN
cana-2105	178	21	=	=	SYM
cana-2105	178	22	(	(	PUNCT
cana-2105	178	23	1−	1−	NUM
cana-2105	178	24	β)szn	β)szn	NOUN
cana-2105	178	25	+	+	CCONJ
cana-2105	178	26	βstcvn	βstcvn	ADJ
cana-2105	178	27	9	9	NUM
cana-2105	178	28	zn+1	zn+1	NOUN
cana-2105	178	29	=	=	SYM
cana-2105	178	30	(	(	PUNCT
cana-2105	178	31	1−	1−	NUM
cana-2105	178	32	α)szn	α)szn	NUM
cana-2105	178	33	+	+	CCONJ
cana-2105	178	34	αstcwn	αstcwn	NOUN
cana-2105	178	35	10	10	NUM
cana-2105	178	36	if	if	SCONJ
cana-2105	178	37	|zn+1|	|zn+1|	NOUN
cana-2105	178	38	>	>	X
cana-2105	178	39	r	r	NOUN
cana-2105	178	40	then	then	ADV
cana-2105	178	41	11	11	NUM
cana-2105	178	42	break	break	NOUN
cana-2105	178	43	12	12	NUM
cana-2105	178	44	n	n	NOUN
cana-2105	178	45	=	=	PUNCT
cana-2105	178	46	n+	n+	ADP
cana-2105	178	47	1	1	NUM
cana-2105	178	48	13	13	NUM
cana-2105	178	49	i	i	NOUN
cana-2105	178	50	=	=	PUNCT
cana-2105	178	51	⌊f	⌊f	NOUN
cana-2105	178	52	n	n	CCONJ
cana-2105	178	53	k	k	PROPN
cana-2105	178	54	⌋	⌋	NOUN
cana-2105	178	55	14	14	NUM
cana-2105	178	56	color	color	NOUN
cana-2105	178	57	z0	z0	NOUN
cana-2105	178	58	with	with	ADP
cana-2105	178	59	color	color	NOUN
cana-2105	178	60	map	map	NOUN
cana-2105	179	1	[	[	X
cana-2105	179	2	i	i	X
cana-2105	179	3	]	]	X
cana-2105	179	4	communications	communication	NOUN
cana-2105	179	5	on	on	ADP
cana-2105	179	6	applied	apply	VERB
cana-2105	179	7	nonlinear	nonlinear	ADJ
cana-2105	179	8	analysis	analysis	NOUN
cana-2105	179	9	issn	issn	NOUN
cana-2105	179	10	:	:	PUNCT
cana-2105	179	11	1074	1074	NUM
cana-2105	179	12	-	-	PUNCT
cana-2105	179	13	133x	133x	NUM
cana-2105	179	14	vol	vol	NOUN
cana-2105	179	15	32	32	NUM
cana-2105	179	16	no	no	NOUN
cana-2105	179	17	.	.	PUNCT
cana-2105	180	1	1s	1s	NUM
cana-2105	180	2	(	(	PUNCT
cana-2105	180	3	2025	2025	NUM
cana-2105	180	4	)	)	PUNCT
cana-2105	180	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	180	6	71	71	NUM
cana-2105	180	7	algorithm	algorithm	NOUN
cana-2105	180	8	2	2	NUM
cana-2105	180	9	:	:	PUNCT
cana-2105	180	10	creating	create	VERB
cana-2105	180	11	mandelbrot	mandelbrot	NOUN
cana-2105	180	12	set	set	VERB
cana-2105	180	13	input	input	NOUN
cana-2105	180	14	:	:	PUNCT
cana-2105	180	15	tc(z	tc(z	X
cana-2105	180	16	)	)	PUNCT
cana-2105	180	17	=	=	SYM
cana-2105	180	18	sin(zk	sin(zk	X
cana-2105	180	19	)	)	PUNCT
cana-2105	181	1	+	+	CCONJ
cana-2105	181	2	az	az	PROPN
cana-2105	181	3	+	+	CCONJ
cana-2105	181	4	c	c	PROPN
cana-2105	181	5	for	for	ADP
cana-2105	181	6	all	all	DET
cana-2105	181	7	z	z	NOUN
cana-2105	181	8	∈	∈	PROPN
cana-2105	181	9	c	c	NOUN
cana-2105	181	10	,	,	PUNCT
cana-2105	181	11	k	k	PROPN
cana-2105	181	12	∈	∈	PROPN
cana-2105	181	13	n	n	PRON
cana-2105	181	14	\	\	NOUN
cana-2105	181	15	{	{	PUNCT
cana-2105	181	16	1	1	NUM
cana-2105	181	17	}	}	PUNCT
cana-2105	181	18	,	,	PUNCT
cana-2105	181	19	a	a	PRON
cana-2105	181	20	,	,	PUNCT
cana-2105	181	21	c	c	PROPN
cana-2105	181	22	∈	∈	PROPN
cana-2105	181	23	c	c	NOUN
cana-2105	181	24	:	:	PUNCT
cana-2105	181	25	a	a	DET
cana-2105	181	26	̸=	̸=	PROPN
cana-2105	181	27	0	0	NUM
cana-2105	181	28	complex	complex	ADJ
cana-2105	181	29	constants	constant	NOUN
cana-2105	181	30	;	;	PUNCT
cana-2105	181	31	b	b	X
cana-2105	181	32	⊂	⊂	PROPN
cana-2105	181	33	c	c	PROPN
cana-2105	181	34	area	area	NOUN
cana-2105	181	35	;	;	PUNCT
cana-2105	181	36	k	k	PROPN
cana-2105	181	37	the	the	DET
cana-2105	181	38	maximum	maximum	ADJ
cana-2105	181	39	number	number	NOUN
cana-2105	181	40	of	of	ADP
cana-2105	181	41	iterations	iteration	NOUN
cana-2105	181	42	;	;	PUNCT
cana-2105	181	43	s	s	X
cana-2105	181	44	,	,	PUNCT
cana-2105	181	45	α	α	X
cana-2105	181	46	,	,	PUNCT
cana-2105	181	47	β	β	X
cana-2105	181	48	,	,	PUNCT
cana-2105	181	49	γ	γ	PROPN
cana-2105	181	50	,	,	PUNCT
cana-2105	181	51	δ	δ	PROPN
cana-2105	181	52	,	,	PUNCT
cana-2105	181	53	|ω1|	|ω1|	PROPN
cana-2105	181	54	,	,	PUNCT
cana-2105	181	55	|ω2|	|ω2|	NOUN
cana-2105	181	56	,	,	PUNCT
cana-2105	181	57	|ω3|	|ω3|	NOUN
cana-2105	181	58	,	,	PUNCT
cana-2105	181	59	|ω4|	|ω4|	NOUN
cana-2105	181	60	∈	∈	PROPN
cana-2105	181	61	(	(	PUNCT
cana-2105	181	62	0	0	NUM
cana-2105	181	63	,	,	PUNCT
cana-2105	181	64	1	1	NUM
cana-2105	181	65	]	]	PUNCT
cana-2105	181	66	parameters	parameter	NOUN
cana-2105	181	67	for	for	ADP
cana-2105	181	68	the	the	DET
cana-2105	181	69	approximation	approximation	NOUN
cana-2105	181	70	of	of	ADP
cana-2105	181	71	four	four	NUM
cana-2105	181	72	-	-	PUNCT
cana-2105	181	73	steps	step	NOUN
cana-2105	181	74	iterative	iterative	NOUN
cana-2105	181	75	method	method	NOUN
cana-2105	181	76	with	with	ADP
cana-2105	181	77	s	s	NOUN
cana-2105	181	78	-	-	NOUN
cana-2105	181	79	convexity	convexity	NOUN
cana-2105	181	80	;	;	PUNCT
cana-2105	181	81	κ	κ	NOUN
cana-2105	181	82	-	-	ADJ
cana-2105	181	83	critical	critical	ADJ
cana-2105	181	84	point	point	NOUN
cana-2105	181	85	of	of	ADP
cana-2105	181	86	t	t	NOUN
cana-2105	181	87	,	,	PUNCT
cana-2105	181	88	and	and	CCONJ
cana-2105	181	89	colourmap	colourmap	NOUN
cana-2105	182	1	[	[	X
cana-2105	182	2	0	0	NUM
cana-2105	182	3	..	..	SYM
cana-2105	182	4	f	f	X
cana-2105	182	5	]	]	PUNCT
cana-2105	182	6	colour	colour	NOUN
cana-2105	182	7	map	map	NOUN
cana-2105	182	8	with	with	ADP
cana-2105	182	9	f	f	PROPN
cana-2105	182	10	+	+	CCONJ
cana-2105	182	11	1	1	NUM
cana-2105	182	12	colours	colour	NOUN
cana-2105	182	13	.	.	PUNCT
cana-2105	183	1	output	output	NOUN
cana-2105	183	2	:	:	PUNCT
cana-2105	183	3	mandelbrot	mandelbrot	PROPN
cana-2105	183	4	set	set	VERB
cana-2105	183	5	for	for	ADP
cana-2105	183	6	area	area	NOUN
cana-2105	183	7	b	b	PROPN
cana-2105	183	8	1	1	NUM
cana-2105	183	9	for	for	ADP
cana-2105	183	10	c	c	PROPN
cana-2105	183	11	∈	∈	PROPN
cana-2105	183	12	a	a	DET
cana-2105	183	13	do	do	NOUN
cana-2105	183	14	2	2	NUM
cana-2105	183	15	r	r	NOUN
cana-2105	183	16	=	=	SYM
cana-2105	183	17	max	max	PROPN
cana-2105	183	18	{	{	PUNCT
cana-2105	183	19	|c|	|c|	PROPN
cana-2105	183	20	,	,	PUNCT
cana-2105	183	21	(	(	PUNCT
cana-2105	183	22	2(1+|a|	2(1+|a|	X
cana-2105	183	23	)	)	PUNCT
cana-2105	183	24	sα|ω1|	sα|ω1|	PROPN
cana-2105	183	25	)	)	PUNCT
cana-2105	183	26	1	1	NUM
cana-2105	183	27	k−1	k−1	PROPN
cana-2105	183	28	,	,	PUNCT
cana-2105	183	29	(	(	PUNCT
cana-2105	183	30	2(1+|a|	2(1+|a|	X
cana-2105	183	31	)	)	PUNCT
cana-2105	183	32	sβ|ω2|	sβ|ω2|	NOUN
cana-2105	183	33	)	)	PUNCT
cana-2105	183	34	1	1	NUM
cana-2105	183	35	k−1	k−1	PROPN
cana-2105	183	36	,	,	PUNCT
cana-2105	183	37	(	(	PUNCT
cana-2105	183	38	2(1+|a|	2(1+|a|	X
cana-2105	183	39	)	)	PUNCT
cana-2105	183	40	sγ|ω3|	sγ|ω3|	NUM
cana-2105	183	41	)	)	PUNCT
cana-2105	183	42	1	1	NUM
cana-2105	183	43	k−1	k−1	PROPN
cana-2105	183	44	,	,	PUNCT
cana-2105	183	45	(	(	PUNCT
cana-2105	183	46	2(1+|a|	2(1+|a|	X
cana-2105	183	47	)	)	PUNCT
cana-2105	183	48	sδ|ω4|	sδ|ω4|	PROPN
cana-2105	183	49	)	)	PUNCT
cana-2105	183	50	1	1	NUM
cana-2105	183	51	k−1	k−1	PROPN
cana-2105	183	52	}	}	PUNCT
cana-2105	183	53	3	3	NUM
cana-2105	183	54	n	n	NOUN
cana-2105	183	55	=	=	SYM
cana-2105	183	56	0	0	NUM
cana-2105	183	57	4	4	NUM
cana-2105	183	58	z	z	NOUN
cana-2105	183	59	=	=	SYM
cana-2105	183	60	κ	κ	NOUN
cana-2105	183	61	5	5	NUM
cana-2105	183	62	while	while	SCONJ
cana-2105	183	63	n	n	ADP
cana-2105	183	64	≤	≤	X
cana-2105	183	65	k	k	X
cana-2105	183	66	do	do	VERB
cana-2105	183	67	6	6	NUM
cana-2105	183	68	un	un	NOUN
cana-2105	183	69	=	=	SYM
cana-2105	183	70	(	(	PUNCT
cana-2105	183	71	1−	1−	NUM
cana-2105	183	72	δ)szn	δ)szn	PROPN
cana-2105	183	73	+	+	CCONJ
cana-2105	183	74	δstczn	δstczn	VERB
cana-2105	183	75	7	7	NUM
cana-2105	183	76	vn	vn	NOUN
cana-2105	183	77	=	=	SYM
cana-2105	183	78	(	(	PUNCT
cana-2105	183	79	1−	1−	NUM
cana-2105	183	80	γ)szn	γ)szn	NOUN
cana-2105	183	81	+	+	CCONJ
cana-2105	183	82	γstcun	γstcun	NOUN
cana-2105	183	83	8	8	NUM
cana-2105	183	84	wn	wn	NOUN
cana-2105	183	85	=	=	SYM
cana-2105	183	86	(	(	PUNCT
cana-2105	183	87	1−	1−	NUM
cana-2105	183	88	β)szn	β)szn	NOUN
cana-2105	183	89	+	+	CCONJ
cana-2105	183	90	βstcvn	βstcvn	ADJ
cana-2105	183	91	9	9	NUM
cana-2105	183	92	zn+1	zn+1	NOUN
cana-2105	183	93	=	=	SYM
cana-2105	183	94	(	(	PUNCT
cana-2105	183	95	1−	1−	NUM
cana-2105	183	96	α)szn	α)szn	NUM
cana-2105	183	97	+	+	CCONJ
cana-2105	183	98	αstcwn	αstcwn	NOUN
cana-2105	183	99	10	10	NUM
cana-2105	183	100	if	if	SCONJ
cana-2105	183	101	|zn+1|	|zn+1|	NOUN
cana-2105	183	102	>	>	X
cana-2105	183	103	r	r	NOUN
cana-2105	183	104	then	then	ADV
cana-2105	183	105	11	11	NUM
cana-2105	183	106	break	break	NOUN
cana-2105	183	107	12	12	NUM
cana-2105	183	108	n	n	NOUN
cana-2105	183	109	=	=	PUNCT
cana-2105	183	110	n+	n+	ADP
cana-2105	183	111	1	1	NUM
cana-2105	183	112	13	13	NUM
cana-2105	183	113	i	i	NOUN
cana-2105	183	114	=	=	PUNCT
cana-2105	183	115	⌊f	⌊f	NOUN
cana-2105	183	116	n	n	CCONJ
cana-2105	183	117	k	k	PROPN
cana-2105	183	118	⌋	⌋	NOUN
cana-2105	183	119	14	14	NUM
cana-2105	183	120	color	color	NOUN
cana-2105	183	121	c	c	NOUN
cana-2105	183	122	with	with	ADP
cana-2105	183	123	color	color	NOUN
cana-2105	183	124	map	map	NOUN
cana-2105	184	1	[	[	X
cana-2105	184	2	i	i	X
cana-2105	184	3	]	]	PUNCT
cana-2105	184	4	4.1	4.1	NUM
cana-2105	184	5	julia	julia	PROPN
cana-2105	184	6	set	set	VERB
cana-2105	184	7	in	in	ADP
cana-2105	184	8	this	this	DET
cana-2105	184	9	subsection	subsection	NOUN
cana-2105	184	10	we	we	PRON
cana-2105	184	11	create	create	VERB
cana-2105	184	12	the	the	DET
cana-2105	184	13	julia	julia	PROPN
cana-2105	184	14	set	set	VERB
cana-2105	184	15	by	by	ADP
cana-2105	184	16	using	use	VERB
cana-2105	184	17	the	the	DET
cana-2105	184	18	algorithm	algorithm	NOUN
cana-2105	184	19	1	1	NUM
cana-2105	184	20	varying	vary	VERB
cana-2105	184	21	the	the	DET
cana-2105	184	22	parameters	parameter	NOUN
cana-2105	184	23	one	one	NUM
cana-2105	184	24	by	by	ADP
cana-2105	184	25	one	one	NUM
cana-2105	184	26	.	.	PUNCT
cana-2105	185	1	we	we	PRON
cana-2105	185	2	take	take	VERB
cana-2105	185	3	a	a	DET
cana-2105	185	4	maximum	maximum	ADJ
cana-2105	185	5	iteration	iteration	NOUN
cana-2105	185	6	limit	limit	NOUN
cana-2105	185	7	of	of	ADP
cana-2105	185	8	k	k	PROPN
cana-2105	185	9	=	=	SYM
cana-2105	185	10	30	30	NUM
cana-2105	185	11	and	and	CCONJ
cana-2105	185	12	b	b	X
cana-2105	185	13	=	=	SYM
cana-2105	186	1	[	[	X
cana-2105	186	2	−4.5	−4.5	PROPN
cana-2105	186	3	,	,	PUNCT
cana-2105	186	4	4.5	4.5	NUM
cana-2105	186	5	]	]	SYM
cana-2105	186	6	×	×	NOUN
cana-2105	187	1	[	[	X
cana-2105	187	2	−4.5	−4.5	PROPN
cana-2105	187	3	,	,	PUNCT
cana-2105	187	4	4.5	4.5	NUM
cana-2105	187	5	]	]	PUNCT
cana-2105	187	6	as	as	ADP
cana-2105	187	7	the	the	DET
cana-2105	187	8	area	area	NOUN
cana-2105	187	9	for	for	ADP
cana-2105	187	10	julia	julia	PROPN
cana-2105	187	11	set	set	PROPN
cana-2105	187	12	.	.	PUNCT
cana-2105	188	1	initially	initially	ADV
cana-2105	188	2	,	,	PUNCT
cana-2105	188	3	we	we	PRON
cana-2105	188	4	fix	fix	VERB
cana-2105	188	5	the	the	DET
cana-2105	188	6	parameters	parameter	NOUN
cana-2105	188	7	a	a	DET
cana-2105	188	8	=	=	SYM
cana-2105	188	9	1.2001	1.2001	NUM
cana-2105	188	10	,	,	PUNCT
cana-2105	188	11	c	c	NOUN
cana-2105	188	12	=	=	SYM
cana-2105	188	13	0.501	0.501	NUM
cana-2105	188	14	,	,	PUNCT
cana-2105	188	15	s	s	PART
cana-2105	188	16	=	=	NOUN
cana-2105	188	17	0.6767	0.6767	NUM
cana-2105	188	18	,	,	PUNCT
cana-2105	188	19	α	α	NOUN
cana-2105	188	20	=	=	NOUN
cana-2105	188	21	0.005	0.005	NUM
cana-2105	188	22	,	,	PUNCT
cana-2105	188	23	β	β	X
cana-2105	188	24	=	=	SYM
cana-2105	188	25	0.003	0.003	NUM
cana-2105	188	26	,	,	PUNCT
cana-2105	188	27	γ	γ	X
cana-2105	188	28	=	=	SYM
cana-2105	188	29	0.002	0.002	NUM
cana-2105	188	30	,	,	PUNCT
cana-2105	188	31	δ	δ	PROPN
cana-2105	188	32	=	=	SYM
cana-2105	188	33	0.001	0.001	NUM
cana-2105	188	34	,	,	PUNCT
cana-2105	188	35	ω1	ω1	PROPN
cana-2105	188	36	=	=	SYM
cana-2105	188	37	0.110	0.110	NUM
cana-2105	188	38	,	,	PUNCT
cana-2105	188	39	ω2	ω2	NOUN
cana-2105	188	40	=	=	SYM
cana-2105	188	41	0.112	0.112	NUM
cana-2105	188	42	,	,	PUNCT
cana-2105	188	43	ω3	ω3	NOUN
cana-2105	188	44	=	=	SYM
cana-2105	188	45	0.114	0.114	NUM
cana-2105	188	46	,	,	PUNCT
cana-2105	188	47	ω4	ω4	NUM
cana-2105	188	48	=	=	PUNCT
cana-2105	188	49	0.115	0.115	NUM
cana-2105	188	50	,	,	PUNCT
cana-2105	188	51	k	k	PROPN
cana-2105	188	52	=	=	SYM
cana-2105	188	53	2	2	X
cana-2105	188	54	.	.	X
cana-2105	188	55	4.1.1	4.1.1	PROPN
cana-2105	188	56	julia	julia	PROPN
cana-2105	188	57	set	set	PROPN
cana-2105	188	58	for	for	ADP
cana-2105	188	59	the	the	DET
cana-2105	188	60	function	function	NOUN
cana-2105	188	61	tcz	tcz	NOUN
cana-2105	188	62	=	=	SYM
cana-2105	188	63	sin(zk	sin(zk	NOUN
cana-2105	188	64	)	)	PUNCT
cana-2105	189	1	+	+	CCONJ
cana-2105	189	2	az	az	PROPN
cana-2105	189	3	+	+	CCONJ
cana-2105	189	4	c	c	NOUN
cana-2105	189	5	varying	vary	VERB
cana-2105	189	6	the	the	DET
cana-2105	189	7	parameter	parameter	NOUN
cana-2105	189	8	a	a	PRON
cana-2105	189	9	upon	upon	SCONJ
cana-2105	189	10	examining	examine	VERB
cana-2105	189	11	figure	figure	NOUN
cana-2105	189	12	2	2	NUM
cana-2105	189	13	,	,	PUNCT
cana-2105	189	14	we	we	PRON
cana-2105	189	15	observe	observe	VERB
cana-2105	189	16	intriguing	intriguing	ADJ
cana-2105	189	17	representations	representation	NOUN
cana-2105	189	18	of	of	ADP
cana-2105	189	19	julia	julia	PROPN
cana-2105	189	20	sets	set	NOUN
cana-2105	189	21	with	with	ADP
cana-2105	189	22	a	a	DET
cana-2105	189	23	degree	degree	NOUN
cana-2105	189	24	of	of	ADP
cana-2105	189	25	two	two	NUM
cana-2105	189	26	while	while	SCONJ
cana-2105	189	27	varying	vary	VERB
cana-2105	189	28	a	a	DET
cana-2105	189	29	parameter	parameter	NOUN
cana-2105	189	30	a	a	DET
cana-2105	189	31	∈	∈	PROPN
cana-2105	189	32	c.	c.	NOUN
cana-2105	189	33	for	for	ADP
cana-2105	189	34	real	real	ADJ
cana-2105	189	35	number	number	NOUN
cana-2105	189	36	a	a	PRON
cana-2105	189	37	,	,	PUNCT
cana-2105	189	38	each	each	DET
cana-2105	189	39	julia	julia	PROPN
cana-2105	189	40	set	set	VERB
cana-2105	189	41	exhibits	exhibit	NOUN
cana-2105	189	42	symmetry	symmetry	NOUN
cana-2105	189	43	about	about	ADP
cana-2105	189	44	the	the	DET
cana-2105	189	45	real	real	ADJ
cana-2105	189	46	axis	axis	NOUN
cana-2105	189	47	.	.	PUNCT
cana-2105	190	1	as	as	ADP
cana-2105	190	2	the	the	DET
cana-2105	190	3	value	value	NOUN
cana-2105	190	4	of	of	ADP
cana-2105	190	5	a	a	DET
cana-2105	190	6	increases	increase	NOUN
cana-2105	190	7	,	,	PUNCT
cana-2105	190	8	the	the	DET
cana-2105	190	9	intensity	intensity	NOUN
cana-2105	190	10	of	of	ADP
cana-2105	190	11	brown	brown	ADJ
cana-2105	190	12	color	color	NOUN
cana-2105	190	13	decreases	decrease	VERB
cana-2105	190	14	,	,	PUNCT
cana-2105	190	15	and	and	CCONJ
cana-2105	190	16	the	the	DET
cana-2105	190	17	intensity	intensity	NOUN
cana-2105	190	18	of	of	ADP
cana-2105	190	19	sky	sky	NOUN
cana-2105	190	20	blue	blue	ADJ
cana-2105	190	21	color	color	NOUN
cana-2105	190	22	increases	increase	VERB
cana-2105	190	23	along	along	ADP
cana-2105	190	24	the	the	DET
cana-2105	190	25	axes	axis	NOUN
cana-2105	190	26	,	,	PUNCT
cana-2105	190	27	accompanied	accompany	VERB
cana-2105	190	28	by	by	ADP
cana-2105	190	29	a	a	DET
cana-2105	190	30	rise	rise	NOUN
cana-2105	190	31	in	in	ADP
cana-2105	190	32	the	the	DET
cana-2105	190	33	number	number	NOUN
cana-2105	190	34	of	of	ADP
cana-2105	190	35	branches	branch	NOUN
cana-2105	190	36	or	or	CCONJ
cana-2105	190	37	lashes	lash	NOUN
cana-2105	190	38	.	.	PUNCT
cana-2105	191	1	on	on	ADP
cana-2105	191	2	the	the	DET
cana-2105	191	3	other	other	ADJ
cana-2105	191	4	hand	hand	NOUN
cana-2105	191	5	,	,	PUNCT
cana-2105	191	6	when	when	SCONJ
cana-2105	191	7	a	a	PRON
cana-2105	191	8	is	be	AUX
cana-2105	191	9	a	a	DET
cana-2105	191	10	complex	complex	ADJ
cana-2105	191	11	number	number	NOUN
cana-2105	191	12	,	,	PUNCT
cana-2105	191	13	each	each	DET
cana-2105	191	14	julia	julia	PROPN
cana-2105	191	15	set	set	PROPN
cana-2105	191	16	loses	lose	VERB
cana-2105	191	17	its	its	PRON
cana-2105	191	18	symmetry	symmetry	NOUN
cana-2105	191	19	,	,	PUNCT
cana-2105	191	20	and	and	CCONJ
cana-2105	191	21	the	the	DET
cana-2105	191	22	shape	shape	NOUN
cana-2105	191	23	and	and	CCONJ
cana-2105	191	24	size	size	NOUN
cana-2105	191	25	remain	remain	VERB
cana-2105	191	26	almost	almost	ADV
cana-2105	191	27	constant	constant	ADJ
cana-2105	191	28	for	for	ADP
cana-2105	191	29	all	all	DET
cana-2105	191	30	complex	complex	ADJ
cana-2105	191	31	numbers	number	NOUN
cana-2105	191	32	of	of	ADP
cana-2105	191	33	a	a	PRON
cana-2105	191	34	,	,	PUNCT
cana-2105	191	35	which	which	PRON
cana-2105	191	36	we	we	PRON
cana-2105	191	37	are	be	AUX
cana-2105	191	38	taking	take	VERB
cana-2105	191	39	for	for	ADP
cana-2105	191	40	investigation	investigation	NOUN
cana-2105	191	41	.	.	PUNCT
cana-2105	192	1	communications	communication	NOUN
cana-2105	192	2	on	on	ADP
cana-2105	192	3	applied	apply	VERB
cana-2105	192	4	nonlinear	nonlinear	ADJ
cana-2105	192	5	analysis	analysis	NOUN
cana-2105	192	6	issn	issn	NOUN
cana-2105	192	7	:	:	PUNCT
cana-2105	192	8	1074	1074	NUM
cana-2105	192	9	-	-	PUNCT
cana-2105	192	10	133x	133x	NUM
cana-2105	192	11	vol	vol	NOUN
cana-2105	192	12	32	32	NUM
cana-2105	192	13	no	no	NOUN
cana-2105	192	14	.	.	PUNCT
cana-2105	193	1	1s	1s	NUM
cana-2105	193	2	(	(	PUNCT
cana-2105	193	3	2025	2025	NUM
cana-2105	193	4	)	)	PUNCT
cana-2105	193	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	193	6	72	72	NUM
cana-2105	193	7	(	(	PUNCT
cana-2105	193	8	a	a	NOUN
cana-2105	193	9	)	)	PUNCT
cana-2105	193	10	a	a	DET
cana-2105	193	11	=	=	X
cana-2105	193	12	−0.03	−0.03	ADP
cana-2105	193	13	(	(	PUNCT
cana-2105	193	14	b	b	NOUN
cana-2105	193	15	)	)	PUNCT
cana-2105	194	1	a	a	DET
cana-2105	194	2	=	=	SYM
cana-2105	194	3	0.5	0.5	NUM
cana-2105	194	4	(	(	PUNCT
cana-2105	194	5	c	c	NOUN
cana-2105	194	6	)	)	PUNCT
cana-2105	194	7	a	a	DET
cana-2105	194	8	=	=	SYM
cana-2105	194	9	1.2001	1.2001	NUM
cana-2105	194	10	(	(	PUNCT
cana-2105	194	11	d	d	NOUN
cana-2105	194	12	)	)	PUNCT
cana-2105	194	13	a	a	PRON
cana-2105	194	14	=	=	X
cana-2105	194	15	i	i	INTJ
cana-2105	194	16	(	(	PUNCT
cana-2105	194	17	e	e	NOUN
cana-2105	194	18	)	)	PUNCT
cana-2105	194	19	a	a	PRON
cana-2105	194	20	=	=	SYM
cana-2105	194	21	0.5−	0.5−	NUM
cana-2105	194	22	0.4i	0.4i	NOUN
cana-2105	194	23	(	(	PUNCT
cana-2105	194	24	f	f	X
cana-2105	194	25	)	)	PUNCT
cana-2105	194	26	a	a	PRON
cana-2105	194	27	=	=	SYM
cana-2105	194	28	1	1	NUM
cana-2105	194	29	+	+	NUM
cana-2105	194	30	1.5i	1.5i	NUM
cana-2105	194	31	figure	figure	NOUN
cana-2105	194	32	2	2	NUM
cana-2105	194	33	:	:	PUNCT
cana-2105	194	34	the	the	DET
cana-2105	194	35	impact	impact	NOUN
cana-2105	194	36	on	on	ADP
cana-2105	194	37	julia	julia	PROPN
cana-2105	194	38	sets	set	NOUN
cana-2105	194	39	for	for	ADP
cana-2105	194	40	varying	vary	VERB
cana-2105	194	41	the	the	DET
cana-2105	194	42	parameter	parameter	NOUN
cana-2105	194	43	a	a	DET
cana-2105	194	44	4.1.2	4.1.2	NUM
cana-2105	194	45	julia	julia	PROPN
cana-2105	194	46	set	set	VERB
cana-2105	194	47	for	for	ADP
cana-2105	194	48	the	the	DET
cana-2105	194	49	function	function	NOUN
cana-2105	194	50	tcz	tcz	NOUN
cana-2105	194	51	=	=	PUNCT
cana-2105	194	52	sin(zk)+az+	sin(zk)+az+	PUNCT
cana-2105	194	53	c	c	NOUN
cana-2105	194	54	varying	vary	VERB
cana-2105	194	55	the	the	DET
cana-2105	194	56	parameter	parameter	NOUN
cana-2105	195	1	c	c	NOUN
cana-2105	195	2	we	we	PRON
cana-2105	195	3	observe	observe	VERB
cana-2105	195	4	captivating	captivating	ADJ
cana-2105	195	5	depictions	depiction	NOUN
cana-2105	195	6	of	of	ADP
cana-2105	195	7	julia	julia	PROPN
cana-2105	195	8	sets	set	NOUN
cana-2105	195	9	with	with	ADP
cana-2105	195	10	a	a	DET
cana-2105	195	11	degree	degree	NOUN
cana-2105	195	12	of	of	ADP
cana-2105	195	13	two	two	NUM
cana-2105	195	14	,	,	PUNCT
cana-2105	195	15	varying	vary	VERB
cana-2105	195	16	a	a	DET
cana-2105	195	17	parameter	parameter	NOUN
cana-2105	195	18	a	a	PRON
cana-2105	195	19	as	as	SCONJ
cana-2105	195	20	illustrated	illustrate	VERB
cana-2105	195	21	in	in	ADP
cana-2105	195	22	figure	figure	NOUN
cana-2105	195	23	3	3	NUM
cana-2105	195	24	.	.	PUNCT
cana-2105	195	25	when	when	SCONJ
cana-2105	195	26	a	a	PRON
cana-2105	195	27	is	be	AUX
cana-2105	195	28	a	a	DET
cana-2105	195	29	real	real	ADJ
cana-2105	195	30	number	number	NOUN
cana-2105	195	31	,	,	PUNCT
cana-2105	195	32	each	each	DET
cana-2105	195	33	julia	julia	PROPN
cana-2105	195	34	set	set	VERB
cana-2105	195	35	displays	display	NOUN
cana-2105	195	36	symmetry	symmetry	VERB
cana-2105	195	37	about	about	ADP
cana-2105	195	38	the	the	DET
cana-2105	195	39	real	real	ADJ
cana-2105	195	40	axis	axis	NOUN
cana-2105	195	41	.	.	PUNCT
cana-2105	196	1	with	with	ADP
cana-2105	196	2	an	an	DET
cana-2105	196	3	increase	increase	NOUN
cana-2105	196	4	in	in	ADP
cana-2105	196	5	the	the	DET
cana-2105	196	6	value	value	NOUN
cana-2105	196	7	of	of	ADP
cana-2105	196	8	a	a	PRON
cana-2105	196	9	,	,	PUNCT
cana-2105	196	10	there	there	PRON
cana-2105	196	11	is	be	VERB
cana-2105	196	12	an	an	DET
cana-2105	196	13	augmentation	augmentation	NOUN
cana-2105	196	14	in	in	ADP
cana-2105	196	15	the	the	DET
cana-2105	196	16	intensity	intensity	NOUN
cana-2105	196	17	of	of	ADP
cana-2105	196	18	brown	brown	ADJ
cana-2105	196	19	color	color	NOUN
cana-2105	196	20	,	,	PUNCT
cana-2105	196	21	accompanied	accompany	VERB
cana-2105	196	22	by	by	ADP
cana-2105	196	23	a	a	DET
cana-2105	196	24	decrease	decrease	NOUN
cana-2105	196	25	in	in	ADP
cana-2105	196	26	the	the	DET
cana-2105	196	27	intensity	intensity	NOUN
cana-2105	196	28	of	of	ADP
cana-2105	196	29	sky	sky	NOUN
cana-2105	196	30	blue	blue	NOUN
cana-2105	196	31	.	.	PUNCT
cana-2105	197	1	simultaneously	simultaneously	ADV
cana-2105	197	2	,	,	PUNCT
cana-2105	197	3	there	there	PRON
cana-2105	197	4	is	be	VERB
cana-2105	197	5	a	a	DET
cana-2105	197	6	reduction	reduction	NOUN
cana-2105	197	7	in	in	ADP
cana-2105	197	8	the	the	DET
cana-2105	197	9	number	number	NOUN
cana-2105	197	10	of	of	ADP
cana-2105	197	11	branches	branch	NOUN
cana-2105	197	12	or	or	CCONJ
cana-2105	197	13	lashes	lash	NOUN
cana-2105	197	14	,	,	PUNCT
cana-2105	197	15	and	and	CCONJ
cana-2105	197	16	the	the	DET
cana-2105	197	17	size	size	NOUN
cana-2105	197	18	of	of	ADP
cana-2105	197	19	the	the	DET
cana-2105	197	20	set	set	NOUN
cana-2105	197	21	increases	increase	NOUN
cana-2105	197	22	.	.	PUNCT
cana-2105	198	1	conversely	conversely	ADV
cana-2105	198	2	,	,	PUNCT
cana-2105	198	3	when	when	SCONJ
cana-2105	198	4	a	a	PRON
cana-2105	198	5	is	be	AUX
cana-2105	198	6	a	a	DET
cana-2105	198	7	complex	complex	ADJ
cana-2105	198	8	number	number	NOUN
cana-2105	198	9	,	,	PUNCT
cana-2105	198	10	each	each	DET
cana-2105	198	11	julia	julia	PROPN
cana-2105	198	12	set	set	PROPN
cana-2105	198	13	loses	lose	VERB
cana-2105	198	14	its	its	PRON
cana-2105	198	15	symmetry	symmetry	NOUN
cana-2105	198	16	,	,	PUNCT
cana-2105	198	17	and	and	CCONJ
cana-2105	198	18	lashes	lash	NOUN
cana-2105	198	19	are	be	AUX
cana-2105	198	20	formed	form	VERB
cana-2105	198	21	more	more	ADV
cana-2105	198	22	arbitrarily	arbitrarily	ADV
cana-2105	198	23	.	.	PUNCT
cana-2105	199	1	the	the	DET
cana-2105	199	2	mesmerizing	mesmerizing	ADJ
cana-2105	199	3	julia	julia	PROPN
cana-2105	199	4	sets	set	NOUN
cana-2105	199	5	mainly	mainly	ADV
cana-2105	199	6	manifest	manifest	VERB
cana-2105	199	7	when	when	SCONJ
cana-2105	199	8	the	the	DET
cana-2105	199	9	parameter	parameter	NOUN
cana-2105	199	10	a	a	PRON
cana-2105	199	11	is	be	AUX
cana-2105	199	12	a	a	DET
cana-2105	199	13	real	real	ADJ
cana-2105	199	14	number	number	NOUN
cana-2105	199	15	.	.	PUNCT
cana-2105	200	1	communications	communication	NOUN
cana-2105	200	2	on	on	ADP
cana-2105	200	3	applied	apply	VERB
cana-2105	200	4	nonlinear	nonlinear	ADJ
cana-2105	200	5	analysis	analysis	NOUN
cana-2105	200	6	issn	issn	NOUN
cana-2105	200	7	:	:	PUNCT
cana-2105	200	8	1074	1074	NUM
cana-2105	200	9	-	-	PUNCT
cana-2105	200	10	133x	133x	NUM
cana-2105	200	11	vol	vol	NOUN
cana-2105	200	12	32	32	NUM
cana-2105	200	13	no	no	NOUN
cana-2105	200	14	.	.	PUNCT
cana-2105	201	1	1s	1s	NUM
cana-2105	201	2	(	(	PUNCT
cana-2105	201	3	2025	2025	NUM
cana-2105	201	4	)	)	PUNCT
cana-2105	201	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	201	6	73	73	NUM
cana-2105	201	7	(	(	PUNCT
cana-2105	201	8	a	a	NOUN
cana-2105	201	9	)	)	PUNCT
cana-2105	201	10	c	c	NOUN
cana-2105	201	11	=	=	SYM
cana-2105	202	1	−0.5	−0.5	PROPN
cana-2105	202	2	(	(	PUNCT
cana-2105	202	3	b	b	NOUN
cana-2105	202	4	)	)	PUNCT
cana-2105	202	5	c	c	NOUN
cana-2105	202	6	=	=	SYM
cana-2105	202	7	0.5	0.5	NUM
cana-2105	202	8	(	(	PUNCT
cana-2105	202	9	c	c	NOUN
cana-2105	202	10	)	)	PUNCT
cana-2105	202	11	c	c	NOUN
cana-2105	203	1	=	=	SYM
cana-2105	203	2	2.02	2.02	NUM
cana-2105	203	3	(	(	PUNCT
cana-2105	203	4	d	d	NOUN
cana-2105	203	5	)	)	PUNCT
cana-2105	203	6	c	c	NOUN
cana-2105	204	1	=	=	SYM
cana-2105	204	2	i	i	NOUN
cana-2105	204	3	(	(	PUNCT
cana-2105	204	4	e	e	NOUN
cana-2105	204	5	)	)	PUNCT
cana-2105	204	6	c	c	NOUN
cana-2105	204	7	=	=	SYM
cana-2105	205	1	−0.744	−0.744	NOUN
cana-2105	206	1	+	+	NUM
cana-2105	206	2	0.148i	0.148i	NUM
cana-2105	206	3	(	(	PUNCT
cana-2105	206	4	f	f	X
cana-2105	206	5	)	)	PUNCT
cana-2105	206	6	c	c	NOUN
cana-2105	207	1	=	=	SYM
cana-2105	207	2	−0.293−	−0.293−	PROPN
cana-2105	207	3	0.629i	0.629i	ADJ
cana-2105	207	4	figure	figure	NOUN
cana-2105	207	5	3	3	NUM
cana-2105	207	6	:	:	PUNCT
cana-2105	207	7	the	the	DET
cana-2105	207	8	impact	impact	NOUN
cana-2105	207	9	on	on	ADP
cana-2105	207	10	julia	julia	PROPN
cana-2105	207	11	sets	set	NOUN
cana-2105	207	12	for	for	ADP
cana-2105	207	13	varying	vary	VERB
cana-2105	207	14	the	the	DET
cana-2105	207	15	parameter	parameter	NOUN
cana-2105	207	16	c	c	PROPN
cana-2105	207	17	4.1.3	4.1.3	NUM
cana-2105	207	18	julia	julia	PROPN
cana-2105	207	19	set	set	VERB
cana-2105	207	20	for	for	ADP
cana-2105	207	21	the	the	DET
cana-2105	207	22	function	function	NOUN
cana-2105	207	23	tcz	tcz	NOUN
cana-2105	207	24	=	=	SYM
cana-2105	207	25	sin(zk	sin(zk	NOUN
cana-2105	207	26	)	)	PUNCT
cana-2105	208	1	+	+	CCONJ
cana-2105	208	2	az	az	PROPN
cana-2105	208	3	+	+	CCONJ
cana-2105	208	4	c	c	NOUN
cana-2105	208	5	varying	vary	VERB
cana-2105	208	6	the	the	DET
cana-2105	208	7	convexity	convexity	NOUN
cana-2105	208	8	parameter	parameter	NOUN
cana-2105	208	9	s	s	PRON
cana-2105	208	10	we	we	PRON
cana-2105	208	11	observe	observe	VERB
cana-2105	208	12	stunning	stunning	ADJ
cana-2105	208	13	representations	representation	NOUN
cana-2105	208	14	of	of	ADP
cana-2105	208	15	julia	julia	PROPN
cana-2105	208	16	sets	set	NOUN
cana-2105	208	17	with	with	ADP
cana-2105	208	18	a	a	DET
cana-2105	208	19	degree	degree	NOUN
cana-2105	208	20	of	of	ADP
cana-2105	208	21	two	two	NUM
cana-2105	208	22	,	,	PUNCT
cana-2105	208	23	varying	vary	VERB
cana-2105	208	24	a	a	DET
cana-2105	208	25	parameter	parameter	NOUN
cana-2105	208	26	s	s	NOUN
cana-2105	208	27	as	as	SCONJ
cana-2105	208	28	shown	show	VERB
cana-2105	208	29	in	in	ADP
cana-2105	208	30	figure	figure	NOUN
cana-2105	208	31	4	4	NUM
cana-2105	208	32	.	.	PUNCT
cana-2105	208	33	when	when	SCONJ
cana-2105	208	34	the	the	DET
cana-2105	208	35	value	value	NOUN
cana-2105	208	36	of	of	ADP
cana-2105	208	37	s	s	NOUN
cana-2105	208	38	is	be	AUX
cana-2105	208	39	small	small	ADJ
cana-2105	208	40	,	,	PUNCT
cana-2105	208	41	approaching	approach	VERB
cana-2105	208	42	zero	zero	NUM
cana-2105	208	43	,	,	PUNCT
cana-2105	208	44	most	most	ADJ
cana-2105	208	45	points	point	NOUN
cana-2105	208	46	in	in	ADP
cana-2105	208	47	the	the	DET
cana-2105	208	48	considered	consider	VERB
cana-2105	208	49	area	area	NOUN
cana-2105	208	50	escape	escape	VERB
cana-2105	208	51	to	to	ADP
cana-2105	208	52	infinity	infinity	NOUN
cana-2105	208	53	,	,	PUNCT
cana-2105	208	54	resulting	result	VERB
cana-2105	208	55	in	in	ADP
cana-2105	208	56	a	a	DET
cana-2105	208	57	minor	minor	ADJ
cana-2105	208	58	,	,	PUNCT
cana-2105	208	59	undeclared	undeclared	ADJ
cana-2105	208	60	julia	julia	PROPN
cana-2105	208	61	set	set	VERB
cana-2105	208	62	with	with	ADP
cana-2105	208	63	a	a	DET
cana-2105	208	64	predominant	predominant	ADJ
cana-2105	208	65	sky	sky	NOUN
cana-2105	208	66	blue	blue	ADJ
cana-2105	208	67	color	color	NOUN
cana-2105	208	68	.	.	PUNCT
cana-2105	209	1	as	as	ADP
cana-2105	209	2	s	s	PART
cana-2105	209	3	increases	increase	NOUN
cana-2105	209	4	,	,	PUNCT
cana-2105	209	5	the	the	DET
cana-2105	209	6	size	size	NOUN
cana-2105	209	7	of	of	ADP
cana-2105	209	8	the	the	DET
cana-2105	209	9	julia	julia	PROPN
cana-2105	209	10	set	set	PROPN
cana-2105	209	11	also	also	ADV
cana-2105	209	12	increases	increase	VERB
cana-2105	209	13	,	,	PUNCT
cana-2105	209	14	accompanied	accompany	VERB
cana-2105	209	15	by	by	ADP
cana-2105	209	16	an	an	DET
cana-2105	209	17	intensification	intensification	NOUN
cana-2105	209	18	of	of	ADP
cana-2105	209	19	the	the	DET
cana-2105	209	20	brown	brown	ADJ
cana-2105	209	21	and	and	CCONJ
cana-2105	209	22	yellow	yellow	ADJ
cana-2105	209	23	color	color	NOUN
cana-2105	209	24	and	and	CCONJ
cana-2105	209	25	a	a	DET
cana-2105	209	26	reduction	reduction	NOUN
cana-2105	209	27	in	in	ADP
cana-2105	209	28	the	the	DET
cana-2105	209	29	intensity	intensity	NOUN
cana-2105	209	30	of	of	ADP
cana-2105	209	31	the	the	DET
cana-2105	209	32	sky	sky	NOUN
cana-2105	209	33	-	-	PUNCT
cana-2105	209	34	blue	blue	ADJ
cana-2105	209	35	hue	hue	NOUN
cana-2105	209	36	.	.	PUNCT
cana-2105	210	1	additionally	additionally	ADV
cana-2105	210	2	,	,	PUNCT
cana-2105	210	3	the	the	DET
cana-2105	210	4	boundary	boundary	NOUN
cana-2105	210	5	exhibits	exhibit	VERB
cana-2105	210	6	numerous	numerous	ADJ
cana-2105	210	7	lashes	lash	NOUN
cana-2105	210	8	.	.	PUNCT
cana-2105	211	1	when	when	SCONJ
cana-2105	211	2	s	s	X
cana-2105	211	3	approaches	approach	VERB
cana-2105	211	4	1	1	NUM
cana-2105	211	5	,	,	PUNCT
cana-2105	211	6	the	the	DET
cana-2105	211	7	julia	julia	PROPN
cana-2105	211	8	set	set	PROPN
cana-2105	211	9	is	be	AUX
cana-2105	211	10	predominantly	predominantly	ADV
cana-2105	211	11	filled	fill	VERB
cana-2105	211	12	with	with	ADP
cana-2105	211	13	brown	brown	ADJ
cana-2105	211	14	color	color	NOUN
cana-2105	211	15	.	.	PUNCT
cana-2105	212	1	interestingly	interestingly	ADV
cana-2105	212	2	,	,	PUNCT
cana-2105	212	3	for	for	ADP
cana-2105	212	4	all	all	DET
cana-2105	212	5	the	the	DET
cana-2105	212	6	values	value	NOUN
cana-2105	212	7	of	of	ADP
cana-2105	212	8	s	s	PRON
cana-2105	212	9	considered	consider	VERB
cana-2105	212	10	in	in	ADP
cana-2105	212	11	our	our	PRON
cana-2105	212	12	observations	observation	NOUN
cana-2105	212	13	,	,	PUNCT
cana-2105	212	14	each	each	DET
cana-2105	212	15	julia	julia	PROPN
cana-2105	212	16	set	set	PROPN
cana-2105	212	17	maintains	maintain	VERB
cana-2105	212	18	symmetry	symmetry	NOUN
cana-2105	212	19	with	with	ADP
cana-2105	212	20	respect	respect	NOUN
cana-2105	212	21	to	to	ADP
cana-2105	212	22	the	the	DET
cana-2105	212	23	real	real	ADJ
cana-2105	212	24	axis	axis	NOUN
cana-2105	212	25	.	.	PUNCT
cana-2105	213	1	communications	communication	NOUN
cana-2105	213	2	on	on	ADP
cana-2105	213	3	applied	apply	VERB
cana-2105	213	4	nonlinear	nonlinear	ADJ
cana-2105	213	5	analysis	analysis	NOUN
cana-2105	213	6	issn	issn	NOUN
cana-2105	213	7	:	:	PUNCT
cana-2105	213	8	1074	1074	NUM
cana-2105	213	9	-	-	PUNCT
cana-2105	213	10	133x	133x	NUM
cana-2105	213	11	vol	vol	NOUN
cana-2105	213	12	32	32	NUM
cana-2105	213	13	no	no	NOUN
cana-2105	213	14	.	.	PUNCT
cana-2105	214	1	1s	1s	NUM
cana-2105	214	2	(	(	PUNCT
cana-2105	214	3	2025	2025	NUM
cana-2105	214	4	)	)	PUNCT
cana-2105	214	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	214	6	74	74	NUM
cana-2105	214	7	(	(	PUNCT
cana-2105	214	8	a	a	NOUN
cana-2105	214	9	)	)	PUNCT
cana-2105	214	10	s	s	PART
cana-2105	214	11	=	=	NOUN
cana-2105	214	12	0.01	0.01	NUM
cana-2105	214	13	(	(	PUNCT
cana-2105	214	14	b	b	NOUN
cana-2105	214	15	)	)	PUNCT
cana-2105	214	16	s	s	PART
cana-2105	214	17	=	=	NOUN
cana-2105	214	18	0.2	0.2	NUM
cana-2105	214	19	(	(	PUNCT
cana-2105	214	20	c	c	NOUN
cana-2105	214	21	)	)	PUNCT
cana-2105	214	22	s	s	PART
cana-2105	215	1	=	=	SYM
cana-2105	215	2	0.3573	0.3573	NUM
cana-2105	215	3	(	(	PUNCT
cana-2105	215	4	d	d	NOUN
cana-2105	215	5	)	)	PUNCT
cana-2105	215	6	s	s	PART
cana-2105	215	7	=	=	SYM
cana-2105	215	8	0.505	0.505	NUM
cana-2105	215	9	(	(	PUNCT
cana-2105	215	10	e	e	NOUN
cana-2105	215	11	)	)	PUNCT
cana-2105	215	12	s	s	PART
cana-2105	215	13	=	=	SYM
cana-2105	215	14	753	753	NUM
cana-2105	215	15	(	(	PUNCT
cana-2105	215	16	f	f	X
cana-2105	215	17	)	)	PUNCT
cana-2105	215	18	s	s	PART
cana-2105	215	19	=	=	SYM
cana-2105	215	20	0.912	0.912	NUM
cana-2105	215	21	figure	figure	NOUN
cana-2105	215	22	4	4	NUM
cana-2105	215	23	:	:	PUNCT
cana-2105	215	24	the	the	DET
cana-2105	215	25	impact	impact	NOUN
cana-2105	215	26	on	on	ADP
cana-2105	215	27	julia	julia	PROPN
cana-2105	215	28	sets	set	NOUN
cana-2105	215	29	for	for	ADP
cana-2105	215	30	varying	vary	VERB
cana-2105	215	31	the	the	DET
cana-2105	215	32	convexity	convexity	NOUN
cana-2105	215	33	parameter	parameter	NOUN
cana-2105	215	34	s	s	PROPN
cana-2105	215	35	4.1.4	4.1.4	PROPN
cana-2105	215	36	julia	julia	PROPN
cana-2105	215	37	set	set	VERB
cana-2105	215	38	for	for	ADP
cana-2105	215	39	the	the	DET
cana-2105	215	40	function	function	NOUN
cana-2105	215	41	tcz	tcz	NOUN
cana-2105	215	42	=	=	SYM
cana-2105	215	43	sin(zk	sin(zk	NOUN
cana-2105	215	44	)	)	PUNCT
cana-2105	216	1	+	+	CCONJ
cana-2105	216	2	az	az	PROPN
cana-2105	216	3	+	+	CCONJ
cana-2105	216	4	c	c	NOUN
cana-2105	216	5	varying	vary	VERB
cana-2105	216	6	the	the	DET
cana-2105	216	7	parameter	parameter	NOUN
cana-2105	216	8	α	α	PRON
cana-2105	217	1	we	we	PRON
cana-2105	217	2	observe	observe	VERB
cana-2105	217	3	captivating	captivating	ADJ
cana-2105	217	4	depictions	depiction	NOUN
cana-2105	217	5	of	of	ADP
cana-2105	217	6	julia	julia	PROPN
cana-2105	217	7	sets	set	NOUN
cana-2105	217	8	with	with	ADP
cana-2105	217	9	a	a	DET
cana-2105	217	10	degree	degree	NOUN
cana-2105	217	11	of	of	ADP
cana-2105	217	12	two	two	NUM
cana-2105	217	13	while	while	SCONJ
cana-2105	217	14	varying	vary	VERB
cana-2105	217	15	a	a	DET
cana-2105	217	16	parameter	parameter	NOUN
cana-2105	217	17	α	α	NOUN
cana-2105	217	18	as	as	SCONJ
cana-2105	217	19	illustrated	illustrate	VERB
cana-2105	217	20	in	in	ADP
cana-2105	217	21	figure	figure	NOUN
cana-2105	217	22	5	5	NUM
cana-2105	217	23	.	.	PUNCT
cana-2105	217	24	when	when	SCONJ
cana-2105	217	25	the	the	DET
cana-2105	217	26	value	value	NOUN
cana-2105	217	27	of	of	ADP
cana-2105	217	28	α	α	PROPN
cana-2105	217	29	is	be	AUX
cana-2105	217	30	close	close	ADJ
cana-2105	217	31	to	to	ADP
cana-2105	217	32	zero	zero	NUM
cana-2105	217	33	,	,	PUNCT
cana-2105	217	34	indicating	indicate	VERB
cana-2105	217	35	a	a	DET
cana-2105	217	36	minimal	minimal	ADJ
cana-2105	217	37	value	value	NOUN
cana-2105	217	38	,	,	PUNCT
cana-2105	217	39	the	the	DET
cana-2105	217	40	intensity	intensity	NOUN
cana-2105	217	41	of	of	ADP
cana-2105	217	42	the	the	DET
cana-2105	217	43	brown	brown	ADJ
cana-2105	217	44	color	color	NOUN
cana-2105	217	45	is	be	AUX
cana-2105	217	46	high	high	ADJ
cana-2105	217	47	.	.	PUNCT
cana-2105	218	1	each	each	DET
cana-2105	218	2	lash	lash	NOUN
cana-2105	218	3	is	be	AUX
cana-2105	218	4	fully	fully	ADV
cana-2105	218	5	developed	develop	VERB
cana-2105	218	6	,	,	PUNCT
cana-2105	218	7	featuring	feature	VERB
cana-2105	218	8	tiny	tiny	ADJ
cana-2105	218	9	lashes	lash	NOUN
cana-2105	218	10	at	at	ADP
cana-2105	218	11	the	the	DET
cana-2105	218	12	tip	tip	NOUN
cana-2105	218	13	,	,	PUNCT
cana-2105	218	14	and	and	CCONJ
cana-2105	218	15	lashes	lash	NOUN
cana-2105	218	16	look	look	VERB
cana-2105	218	17	like	like	ADP
cana-2105	218	18	cactus	cactus	NOUN
cana-2105	218	19	leaves	leave	NOUN
cana-2105	218	20	.	.	PUNCT
cana-2105	219	1	in	in	ADP
cana-2105	219	2	this	this	DET
cana-2105	219	3	scenario	scenario	NOUN
cana-2105	219	4	,	,	PUNCT
cana-2105	219	5	there	there	PRON
cana-2105	219	6	are	be	VERB
cana-2105	219	7	more	more	ADJ
cana-2105	219	8	non	non	ADJ
cana-2105	219	9	-	-	ADJ
cana-2105	219	10	escaping	escaping	ADJ
cana-2105	219	11	points	point	NOUN
cana-2105	219	12	within	within	ADP
cana-2105	219	13	the	the	DET
cana-2105	219	14	considered	considered	ADJ
cana-2105	219	15	area	area	NOUN
cana-2105	219	16	.	.	PUNCT
cana-2105	220	1	as	as	ADP
cana-2105	220	2	α	α	NOUN
cana-2105	220	3	increases	increase	NOUN
cana-2105	220	4	,	,	PUNCT
cana-2105	220	5	the	the	DET
cana-2105	220	6	number	number	NOUN
cana-2105	220	7	of	of	ADP
cana-2105	220	8	escaping	escape	VERB
cana-2105	220	9	points	point	NOUN
cana-2105	220	10	also	also	ADV
cana-2105	220	11	increases	increase	VERB
cana-2105	220	12	,	,	PUNCT
cana-2105	220	13	resulting	result	VERB
cana-2105	220	14	in	in	ADP
cana-2105	220	15	a	a	DET
cana-2105	220	16	decrease	decrease	NOUN
cana-2105	220	17	in	in	ADP
cana-2105	220	18	the	the	DET
cana-2105	220	19	size	size	NOUN
cana-2105	220	20	of	of	ADP
cana-2105	220	21	julia	julia	PROPN
cana-2105	220	22	sets	set	NOUN
cana-2105	220	23	.	.	PUNCT
cana-2105	221	1	simultaneously	simultaneously	ADV
cana-2105	221	2	,	,	PUNCT
cana-2105	221	3	the	the	DET
cana-2105	221	4	intensity	intensity	NOUN
cana-2105	221	5	of	of	ADP
cana-2105	221	6	brown	brown	ADJ
cana-2105	221	7	color	color	NOUN
cana-2105	221	8	decreases	decrease	VERB
cana-2105	221	9	,	,	PUNCT
cana-2105	221	10	and	and	CCONJ
cana-2105	221	11	the	the	DET
cana-2105	221	12	intensity	intensity	NOUN
cana-2105	221	13	of	of	ADP
cana-2105	221	14	the	the	DET
cana-2105	221	15	sky	sky	NOUN
cana-2105	221	16	blue	blue	ADJ
cana-2105	221	17	hue	hue	NOUN
cana-2105	221	18	increases	increase	NOUN
cana-2105	221	19	.	.	PUNCT
cana-2105	222	1	for	for	ADP
cana-2105	222	2	values	value	NOUN
cana-2105	222	3	of	of	ADP
cana-2105	222	4	α	α	PRON
cana-2105	222	5	approaching	approach	VERB
cana-2105	222	6	1	1	NUM
cana-2105	222	7	,	,	PUNCT
cana-2105	222	8	the	the	DET
cana-2105	222	9	brown	brown	ADJ
cana-2105	222	10	color	color	NOUN
cana-2105	222	11	is	be	AUX
cana-2105	222	12	completely	completely	ADV
cana-2105	222	13	removed	remove	VERB
cana-2105	222	14	,	,	PUNCT
cana-2105	222	15	causing	cause	VERB
cana-2105	222	16	the	the	DET
cana-2105	222	17	julia	julia	PROPN
cana-2105	222	18	set	set	VERB
cana-2105	222	19	to	to	PART
cana-2105	222	20	appear	appear	VERB
cana-2105	222	21	weakened	weaken	VERB
cana-2105	222	22	,	,	PUNCT
cana-2105	222	23	making	make	VERB
cana-2105	222	24	the	the	DET
cana-2105	222	25	details	detail	NOUN
cana-2105	222	26	less	less	ADV
cana-2105	222	27	clearly	clearly	ADV
cana-2105	222	28	visible	visible	ADJ
cana-2105	222	29	.	.	PUNCT
cana-2105	223	1	notably	notably	ADV
cana-2105	223	2	,	,	PUNCT
cana-2105	223	3	for	for	ADP
cana-2105	223	4	each	each	DET
cana-2105	223	5	value	value	NOUN
cana-2105	223	6	of	of	ADP
cana-2105	223	7	α	α	NOUN
cana-2105	223	8	,	,	PUNCT
cana-2105	223	9	the	the	DET
cana-2105	223	10	julia	julia	PROPN
cana-2105	223	11	sets	set	VERB
cana-2105	223	12	exhibit	exhibit	NOUN
cana-2105	223	13	symmetry	symmetry	NOUN
cana-2105	223	14	about	about	ADP
cana-2105	223	15	the	the	DET
cana-2105	223	16	real	real	ADJ
cana-2105	223	17	axis	axis	NOUN
cana-2105	223	18	.	.	PUNCT
cana-2105	224	1	communications	communication	NOUN
cana-2105	224	2	on	on	ADP
cana-2105	224	3	applied	apply	VERB
cana-2105	224	4	nonlinear	nonlinear	ADJ
cana-2105	224	5	analysis	analysis	NOUN
cana-2105	224	6	issn	issn	NOUN
cana-2105	224	7	:	:	PUNCT
cana-2105	224	8	1074	1074	NUM
cana-2105	224	9	-	-	PUNCT
cana-2105	224	10	133x	133x	NUM
cana-2105	224	11	vol	vol	NOUN
cana-2105	224	12	32	32	NUM
cana-2105	224	13	no	no	NOUN
cana-2105	224	14	.	.	PUNCT
cana-2105	225	1	1s	1s	NUM
cana-2105	225	2	(	(	PUNCT
cana-2105	225	3	2025	2025	NUM
cana-2105	225	4	)	)	PUNCT
cana-2105	225	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	226	1	75	75	NUM
cana-2105	226	2	(	(	PUNCT
cana-2105	226	3	a	a	NOUN
cana-2105	226	4	)	)	PUNCT
cana-2105	226	5	α	α	NOUN
cana-2105	226	6	=	=	SYM
cana-2105	226	7	0.0001	0.0001	NUM
cana-2105	226	8	(	(	PUNCT
cana-2105	226	9	b	b	NOUN
cana-2105	226	10	)	)	PUNCT
cana-2105	226	11	α	α	NOUN
cana-2105	226	12	=	=	SYM
cana-2105	226	13	0.1	0.1	NUM
cana-2105	226	14	(	(	PUNCT
cana-2105	226	15	c	c	NOUN
cana-2105	226	16	)	)	PUNCT
cana-2105	226	17	α	α	NOUN
cana-2105	226	18	=	=	SYM
cana-2105	226	19	0.301	0.301	NUM
cana-2105	226	20	(	(	PUNCT
cana-2105	226	21	d	d	NOUN
cana-2105	226	22	)	)	PUNCT
cana-2105	226	23	α	α	NOUN
cana-2105	226	24	=	=	NOUN
cana-2105	226	25	0.491	0.491	NUM
cana-2105	226	26	(	(	PUNCT
cana-2105	226	27	e	e	NOUN
cana-2105	226	28	)	)	PUNCT
cana-2105	226	29	α	α	NOUN
cana-2105	226	30	=	=	SYM
cana-2105	226	31	0.752	0.752	NUM
cana-2105	226	32	(	(	PUNCT
cana-2105	226	33	f	f	X
cana-2105	226	34	)	)	PUNCT
cana-2105	226	35	α	α	NOUN
cana-2105	226	36	=	=	SYM
cana-2105	226	37	1	1	NUM
cana-2105	226	38	figure	figure	NOUN
cana-2105	226	39	5	5	NUM
cana-2105	226	40	:	:	PUNCT
cana-2105	226	41	the	the	DET
cana-2105	226	42	impact	impact	NOUN
cana-2105	226	43	on	on	ADP
cana-2105	226	44	julia	julia	PROPN
cana-2105	226	45	sets	set	NOUN
cana-2105	226	46	for	for	ADP
cana-2105	226	47	varying	vary	VERB
cana-2105	226	48	the	the	DET
cana-2105	226	49	parameter	parameter	NOUN
cana-2105	226	50	α	α	PROPN
cana-2105	226	51	4.1.5	4.1.5	PROPN
cana-2105	227	1	julia	julia	PROPN
cana-2105	228	1	set	set	VERB
cana-2105	228	2	for	for	ADP
cana-2105	228	3	the	the	DET
cana-2105	228	4	function	function	NOUN
cana-2105	228	5	tcz	tcz	NOUN
cana-2105	228	6	=	=	SYM
cana-2105	228	7	sin(zk	sin(zk	NOUN
cana-2105	228	8	)	)	PUNCT
cana-2105	229	1	+	+	CCONJ
cana-2105	229	2	az	az	PROPN
cana-2105	229	3	+	+	CCONJ
cana-2105	229	4	c	c	NOUN
cana-2105	229	5	varying	vary	VERB
cana-2105	229	6	the	the	DET
cana-2105	229	7	parameter	parameter	NOUN
cana-2105	229	8	β	β	NOUN
cana-2105	230	1	we	we	PRON
cana-2105	230	2	observe	observe	VERB
cana-2105	230	3	captivating	captivating	ADJ
cana-2105	230	4	depictions	depiction	NOUN
cana-2105	230	5	of	of	ADP
cana-2105	230	6	julia	julia	PROPN
cana-2105	230	7	sets	set	NOUN
cana-2105	230	8	with	with	ADP
cana-2105	230	9	a	a	DET
cana-2105	230	10	degree	degree	NOUN
cana-2105	230	11	of	of	ADP
cana-2105	230	12	two	two	NUM
cana-2105	230	13	,	,	PUNCT
cana-2105	230	14	varying	vary	VERB
cana-2105	230	15	a	a	DET
cana-2105	230	16	parameter	parameter	NOUN
cana-2105	230	17	β	β	X
cana-2105	230	18	as	as	SCONJ
cana-2105	230	19	shown	show	VERB
cana-2105	230	20	in	in	ADP
cana-2105	230	21	figure	figure	NOUN
cana-2105	230	22	6	6	NUM
cana-2105	230	23	.	.	PUNCT
cana-2105	231	1	for	for	ADP
cana-2105	231	2	each	each	DET
cana-2105	231	3	value	value	NOUN
cana-2105	231	4	of	of	ADP
cana-2105	231	5	β	β	PRON
cana-2105	231	6	,	,	PUNCT
cana-2105	231	7	the	the	DET
cana-2105	231	8	julia	julia	PROPN
cana-2105	231	9	sets	set	NOUN
cana-2105	231	10	maintain	maintain	VERB
cana-2105	231	11	symmetry	symmetry	NOUN
cana-2105	231	12	about	about	ADP
cana-2105	231	13	the	the	DET
cana-2105	231	14	real	real	ADJ
cana-2105	231	15	axis	axis	NOUN
cana-2105	231	16	.	.	PUNCT
cana-2105	232	1	when	when	SCONJ
cana-2105	232	2	the	the	DET
cana-2105	232	3	value	value	NOUN
cana-2105	232	4	of	of	ADP
cana-2105	232	5	β	β	PROPN
cana-2105	232	6	approaches	approach	NOUN
cana-2105	232	7	zero	zero	NUM
cana-2105	232	8	,	,	PUNCT
cana-2105	232	9	the	the	DET
cana-2105	232	10	brown	brown	ADJ
cana-2105	232	11	color	color	NOUN
cana-2105	232	12	intensity	intensity	NOUN
cana-2105	232	13	is	be	AUX
cana-2105	232	14	high	high	ADJ
cana-2105	232	15	,	,	PUNCT
cana-2105	232	16	and	and	CCONJ
cana-2105	232	17	each	each	DET
cana-2105	232	18	lash	lash	NOUN
cana-2105	232	19	is	be	AUX
cana-2105	232	20	fully	fully	ADV
cana-2105	232	21	developed	develop	VERB
cana-2105	232	22	with	with	ADP
cana-2105	232	23	tiny	tiny	ADJ
cana-2105	232	24	lashes	lash	NOUN
cana-2105	232	25	at	at	ADP
cana-2105	232	26	the	the	DET
cana-2105	232	27	tip	tip	NOUN
cana-2105	232	28	,	,	PUNCT
cana-2105	232	29	resembling	resemble	VERB
cana-2105	232	30	cactus	cactus	NOUN
cana-2105	232	31	leaves	leave	NOUN
cana-2105	232	32	and	and	CCONJ
cana-2105	232	33	forming	form	VERB
cana-2105	232	34	intricate	intricate	ADJ
cana-2105	232	35	julia	julia	PROPN
cana-2105	232	36	sets	set	NOUN
cana-2105	232	37	.	.	PUNCT
cana-2105	233	1	in	in	ADP
cana-2105	233	2	this	this	DET
cana-2105	233	3	scenario	scenario	NOUN
cana-2105	233	4	,	,	PUNCT
cana-2105	233	5	there	there	PRON
cana-2105	233	6	are	be	VERB
cana-2105	233	7	more	more	ADJ
cana-2105	233	8	non	non	ADJ
cana-2105	233	9	-	-	ADJ
cana-2105	233	10	escaping	escaping	ADJ
cana-2105	233	11	points	point	NOUN
cana-2105	233	12	within	within	ADP
cana-2105	233	13	the	the	DET
cana-2105	233	14	considered	considered	ADJ
cana-2105	233	15	area	area	NOUN
cana-2105	233	16	.	.	PUNCT
cana-2105	234	1	with	with	ADP
cana-2105	234	2	increasing	increase	VERB
cana-2105	234	3	values	value	NOUN
cana-2105	234	4	of	of	ADP
cana-2105	234	5	β	β	X
cana-2105	234	6	,	,	PUNCT
cana-2105	234	7	the	the	DET
cana-2105	234	8	number	number	NOUN
cana-2105	234	9	of	of	ADP
cana-2105	234	10	escaping	escape	VERB
cana-2105	234	11	points	point	NOUN
cana-2105	234	12	also	also	ADV
cana-2105	234	13	rises	rise	VERB
cana-2105	234	14	,	,	PUNCT
cana-2105	234	15	reducing	reduce	VERB
cana-2105	234	16	the	the	DET
cana-2105	234	17	size	size	NOUN
cana-2105	234	18	of	of	ADP
cana-2105	234	19	julia	julia	PROPN
cana-2105	234	20	sets	set	NOUN
cana-2105	234	21	.	.	PUNCT
cana-2105	235	1	concurrently	concurrently	ADV
cana-2105	235	2	,	,	PUNCT
cana-2105	235	3	the	the	DET
cana-2105	235	4	intensity	intensity	NOUN
cana-2105	235	5	of	of	ADP
cana-2105	235	6	the	the	DET
cana-2105	235	7	brown	brown	ADJ
cana-2105	235	8	color	color	NOUN
cana-2105	235	9	diminishes	diminish	VERB
cana-2105	235	10	ultimately	ultimately	ADV
cana-2105	235	11	after	after	ADP
cana-2105	235	12	β	β	X
cana-2105	235	13	≥	≥	NUM
cana-2105	235	14	0.312	0.312	NUM
cana-2105	235	15	,	,	PUNCT
cana-2105	235	16	leaving	leave	VERB
cana-2105	235	17	only	only	ADV
cana-2105	235	18	the	the	DET
cana-2105	235	19	sky	sky	NOUN
cana-2105	235	20	blue	blue	ADJ
cana-2105	235	21	hue	hue	NOUN
cana-2105	235	22	.	.	PUNCT
cana-2105	236	1	this	this	PRON
cana-2105	236	2	causes	cause	VERB
cana-2105	236	3	the	the	DET
cana-2105	236	4	julia	julia	PROPN
cana-2105	236	5	set	set	VERB
cana-2105	236	6	to	to	PART
cana-2105	236	7	appear	appear	VERB
cana-2105	236	8	weakened	weaken	VERB
cana-2105	236	9	,	,	PUNCT
cana-2105	236	10	resulting	result	VERB
cana-2105	236	11	in	in	ADP
cana-2105	236	12	less	less	ADV
cana-2105	236	13	clear	clear	ADJ
cana-2105	236	14	visibility	visibility	NOUN
cana-2105	236	15	of	of	ADP
cana-2105	236	16	details	detail	NOUN
cana-2105	236	17	.	.	PUNCT
cana-2105	237	1	communications	communication	NOUN
cana-2105	237	2	on	on	ADP
cana-2105	237	3	applied	apply	VERB
cana-2105	237	4	nonlinear	nonlinear	ADJ
cana-2105	237	5	analysis	analysis	NOUN
cana-2105	237	6	issn	issn	NOUN
cana-2105	237	7	:	:	PUNCT
cana-2105	237	8	1074	1074	NUM
cana-2105	237	9	-	-	PUNCT
cana-2105	237	10	133x	133x	NUM
cana-2105	237	11	vol	vol	NOUN
cana-2105	237	12	32	32	NUM
cana-2105	237	13	no	no	NOUN
cana-2105	237	14	.	.	PUNCT
cana-2105	238	1	1s	1s	NUM
cana-2105	238	2	(	(	PUNCT
cana-2105	238	3	2025	2025	NUM
cana-2105	238	4	)	)	PUNCT
cana-2105	238	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	238	6	76	76	NUM
cana-2105	238	7	(	(	PUNCT
cana-2105	238	8	a	a	NOUN
cana-2105	238	9	)	)	PUNCT
cana-2105	238	10	β	β	NOUN
cana-2105	238	11	=	=	PUNCT
cana-2105	238	12	0.0001	0.0001	NUM
cana-2105	238	13	(	(	PUNCT
cana-2105	238	14	b	b	NOUN
cana-2105	238	15	)	)	PUNCT
cana-2105	238	16	β	β	NOUN
cana-2105	239	1	=	=	PUNCT
cana-2105	239	2	0.01	0.01	NUM
cana-2105	239	3	(	(	PUNCT
cana-2105	239	4	c	c	NOUN
cana-2105	239	5	)	)	PUNCT
cana-2105	239	6	β	β	NOUN
cana-2105	239	7	=	=	NOUN
cana-2105	239	8	0.312	0.312	NUM
cana-2105	239	9	(	(	PUNCT
cana-2105	239	10	d	d	NOUN
cana-2105	239	11	)	)	PUNCT
cana-2105	239	12	β	β	NOUN
cana-2105	239	13	=	=	SYM
cana-2105	239	14	0.5241	0.5241	NUM
cana-2105	239	15	(	(	PUNCT
cana-2105	239	16	e	e	NOUN
cana-2105	239	17	)	)	PUNCT
cana-2105	239	18	β	β	X
cana-2105	239	19	=	=	SYM
cana-2105	239	20	0.7482	0.7482	NUM
cana-2105	239	21	(	(	PUNCT
cana-2105	239	22	f	f	X
cana-2105	239	23	)	)	PUNCT
cana-2105	239	24	β	β	NOUN
cana-2105	239	25	=	=	SYM
cana-2105	239	26	1	1	NUM
cana-2105	239	27	figure	figure	NOUN
cana-2105	239	28	6	6	NUM
cana-2105	239	29	:	:	PUNCT
cana-2105	239	30	the	the	DET
cana-2105	239	31	impact	impact	NOUN
cana-2105	239	32	on	on	ADP
cana-2105	239	33	julia	julia	PROPN
cana-2105	239	34	sets	set	NOUN
cana-2105	239	35	for	for	ADP
cana-2105	239	36	varying	vary	VERB
cana-2105	239	37	the	the	DET
cana-2105	239	38	parameter	parameter	NOUN
cana-2105	239	39	β	β	PROPN
cana-2105	239	40	4.1.6	4.1.6	PROPN
cana-2105	239	41	julia	julia	PROPN
cana-2105	239	42	set	set	PROPN
cana-2105	239	43	for	for	ADP
cana-2105	239	44	the	the	DET
cana-2105	239	45	function	function	NOUN
cana-2105	239	46	tcz	tcz	NOUN
cana-2105	239	47	=	=	SYM
cana-2105	239	48	sin(zk	sin(zk	NOUN
cana-2105	239	49	)	)	PUNCT
cana-2105	240	1	+	+	CCONJ
cana-2105	240	2	az	az	PROPN
cana-2105	240	3	+	+	CCONJ
cana-2105	240	4	c	c	NOUN
cana-2105	240	5	varying	vary	VERB
cana-2105	240	6	the	the	DET
cana-2105	240	7	parameter	parameter	NOUN
cana-2105	240	8	β	β	NOUN
cana-2105	241	1	we	we	PRON
cana-2105	241	2	observe	observe	VERB
cana-2105	241	3	fascinating	fascinating	ADJ
cana-2105	241	4	depictions	depiction	NOUN
cana-2105	241	5	of	of	ADP
cana-2105	241	6	julia	julia	PROPN
cana-2105	241	7	sets	set	NOUN
cana-2105	241	8	with	with	ADP
cana-2105	241	9	a	a	DET
cana-2105	241	10	degree	degree	NOUN
cana-2105	241	11	of	of	ADP
cana-2105	241	12	two	two	NUM
cana-2105	241	13	,	,	PUNCT
cana-2105	241	14	varying	vary	VERB
cana-2105	241	15	a	a	DET
cana-2105	241	16	parameter	parameter	NOUN
cana-2105	241	17	β	β	X
cana-2105	241	18	as	as	SCONJ
cana-2105	241	19	shown	show	VERB
cana-2105	241	20	in	in	ADP
cana-2105	241	21	figure	figure	NOUN
cana-2105	241	22	7	7	NUM
cana-2105	241	23	.	.	PUNCT
cana-2105	242	1	for	for	ADP
cana-2105	242	2	each	each	DET
cana-2105	242	3	value	value	NOUN
cana-2105	242	4	of	of	ADP
cana-2105	242	5	β	β	PRON
cana-2105	242	6	,	,	PUNCT
cana-2105	242	7	the	the	DET
cana-2105	242	8	julia	julia	PROPN
cana-2105	242	9	sets	set	NOUN
cana-2105	242	10	maintain	maintain	VERB
cana-2105	242	11	symmetry	symmetry	NOUN
cana-2105	242	12	about	about	ADP
cana-2105	242	13	the	the	DET
cana-2105	242	14	real	real	ADJ
cana-2105	242	15	axis	axis	NOUN
cana-2105	242	16	.	.	PUNCT
cana-2105	243	1	when	when	SCONJ
cana-2105	243	2	the	the	DET
cana-2105	243	3	value	value	NOUN
cana-2105	243	4	of	of	ADP
cana-2105	243	5	β	β	PROPN
cana-2105	243	6	approaches	approach	NOUN
cana-2105	243	7	zero	zero	NUM
cana-2105	243	8	,	,	PUNCT
cana-2105	243	9	the	the	DET
cana-2105	243	10	brown	brown	ADJ
cana-2105	243	11	color	color	NOUN
cana-2105	243	12	intensity	intensity	NOUN
cana-2105	243	13	is	be	AUX
cana-2105	243	14	high	high	ADJ
cana-2105	243	15	,	,	PUNCT
cana-2105	243	16	and	and	CCONJ
cana-2105	243	17	each	each	DET
cana-2105	243	18	lash	lash	NOUN
cana-2105	243	19	is	be	AUX
cana-2105	243	20	fully	fully	ADV
cana-2105	243	21	formed	form	VERB
cana-2105	243	22	with	with	ADP
cana-2105	243	23	tiny	tiny	ADJ
cana-2105	243	24	lashes	lash	NOUN
cana-2105	243	25	at	at	ADP
cana-2105	243	26	the	the	DET
cana-2105	243	27	end	end	NOUN
cana-2105	243	28	,	,	PUNCT
cana-2105	243	29	resembling	resemble	VERB
cana-2105	243	30	cactus	cactus	NOUN
cana-2105	243	31	leaves	leave	NOUN
cana-2105	243	32	and	and	CCONJ
cana-2105	243	33	intricate	intricate	ADJ
cana-2105	243	34	julia	julia	PROPN
cana-2105	243	35	sets	set	NOUN
cana-2105	243	36	.	.	PUNCT
cana-2105	244	1	in	in	ADP
cana-2105	244	2	this	this	DET
cana-2105	244	3	procedure	procedure	NOUN
cana-2105	244	4	,	,	PUNCT
cana-2105	244	5	there	there	PRON
cana-2105	244	6	are	be	VERB
cana-2105	244	7	more	more	ADJ
cana-2105	244	8	non	non	ADJ
cana-2105	244	9	-	-	ADJ
cana-2105	244	10	escaping	escaping	ADJ
cana-2105	244	11	points	point	NOUN
cana-2105	244	12	within	within	ADP
cana-2105	244	13	the	the	DET
cana-2105	244	14	considered	considered	ADJ
cana-2105	244	15	area	area	NOUN
cana-2105	244	16	.	.	PUNCT
cana-2105	245	1	with	with	ADP
cana-2105	245	2	increasing	increase	VERB
cana-2105	245	3	values	value	NOUN
cana-2105	245	4	of	of	ADP
cana-2105	245	5	β	β	X
cana-2105	245	6	,	,	PUNCT
cana-2105	245	7	the	the	DET
cana-2105	245	8	number	number	NOUN
cana-2105	245	9	of	of	ADP
cana-2105	245	10	escaping	escape	VERB
cana-2105	245	11	points	point	NOUN
cana-2105	245	12	also	also	ADV
cana-2105	245	13	rises	rise	VERB
cana-2105	245	14	,	,	PUNCT
cana-2105	245	15	reducing	reduce	VERB
cana-2105	245	16	the	the	DET
cana-2105	245	17	size	size	NOUN
cana-2105	245	18	of	of	ADP
cana-2105	245	19	julia	julia	PROPN
cana-2105	245	20	sets	set	NOUN
cana-2105	245	21	.	.	PUNCT
cana-2105	246	1	concurrently	concurrently	ADV
cana-2105	246	2	,	,	PUNCT
cana-2105	246	3	the	the	DET
cana-2105	246	4	intensity	intensity	NOUN
cana-2105	246	5	of	of	ADP
cana-2105	246	6	the	the	DET
cana-2105	246	7	brown	brown	ADJ
cana-2105	246	8	color	color	NOUN
cana-2105	246	9	diminishes	diminish	VERB
cana-2105	246	10	ultimately	ultimately	ADV
cana-2105	246	11	after	after	ADP
cana-2105	246	12	β	β	X
cana-2105	246	13	≥	≥	NUM
cana-2105	246	14	0.312	0.312	NUM
cana-2105	246	15	;	;	PUNCT
cana-2105	246	16	only	only	ADV
cana-2105	246	17	the	the	DET
cana-2105	246	18	sky	sky	NOUN
cana-2105	246	19	blue	blue	ADJ
cana-2105	246	20	hue	hue	NOUN
cana-2105	246	21	is	be	AUX
cana-2105	246	22	present	present	ADJ
cana-2105	246	23	,	,	PUNCT
cana-2105	246	24	and	and	CCONJ
cana-2105	246	25	the	the	DET
cana-2105	246	26	julia	julia	PROPN
cana-2105	246	27	set	set	PROPN
cana-2105	246	28	appears	appear	VERB
cana-2105	246	29	weakened	weaken	VERB
cana-2105	246	30	,	,	PUNCT
cana-2105	246	31	resulting	result	VERB
cana-2105	246	32	in	in	ADP
cana-2105	246	33	less	less	ADV
cana-2105	246	34	clear	clear	ADJ
cana-2105	246	35	visibility	visibility	NOUN
cana-2105	246	36	of	of	ADP
cana-2105	246	37	details	detail	NOUN
cana-2105	246	38	.	.	PUNCT
cana-2105	247	1	communications	communication	NOUN
cana-2105	247	2	on	on	ADP
cana-2105	247	3	applied	apply	VERB
cana-2105	247	4	nonlinear	nonlinear	ADJ
cana-2105	247	5	analysis	analysis	NOUN
cana-2105	247	6	issn	issn	NOUN
cana-2105	247	7	:	:	PUNCT
cana-2105	247	8	1074	1074	NUM
cana-2105	247	9	-	-	PUNCT
cana-2105	247	10	133x	133x	NUM
cana-2105	247	11	vol	vol	NOUN
cana-2105	247	12	32	32	NUM
cana-2105	247	13	no	no	NOUN
cana-2105	247	14	.	.	PUNCT
cana-2105	248	1	1s	1s	NUM
cana-2105	248	2	(	(	PUNCT
cana-2105	248	3	2025	2025	NUM
cana-2105	248	4	)	)	PUNCT
cana-2105	248	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	248	6	77	77	NUM
cana-2105	248	7	(	(	PUNCT
cana-2105	248	8	a	a	NOUN
cana-2105	248	9	)	)	PUNCT
cana-2105	248	10	β	β	NOUN
cana-2105	248	11	=	=	PUNCT
cana-2105	248	12	0.0001	0.0001	NUM
cana-2105	248	13	(	(	PUNCT
cana-2105	248	14	b	b	NOUN
cana-2105	248	15	)	)	PUNCT
cana-2105	248	16	β	β	NOUN
cana-2105	249	1	=	=	PUNCT
cana-2105	249	2	0.01	0.01	NUM
cana-2105	249	3	(	(	PUNCT
cana-2105	249	4	c	c	NOUN
cana-2105	249	5	)	)	PUNCT
cana-2105	249	6	β	β	NOUN
cana-2105	249	7	=	=	NOUN
cana-2105	249	8	0.312	0.312	NUM
cana-2105	249	9	(	(	PUNCT
cana-2105	249	10	d	d	NOUN
cana-2105	249	11	)	)	PUNCT
cana-2105	249	12	β	β	NOUN
cana-2105	249	13	=	=	SYM
cana-2105	249	14	0.5241	0.5241	NUM
cana-2105	249	15	(	(	PUNCT
cana-2105	249	16	e	e	NOUN
cana-2105	249	17	)	)	PUNCT
cana-2105	249	18	β	β	X
cana-2105	249	19	=	=	SYM
cana-2105	249	20	0.7482	0.7482	NUM
cana-2105	249	21	(	(	PUNCT
cana-2105	249	22	f	f	X
cana-2105	249	23	)	)	PUNCT
cana-2105	249	24	β	β	NOUN
cana-2105	249	25	=	=	SYM
cana-2105	249	26	1	1	NUM
cana-2105	249	27	figure	figure	NOUN
cana-2105	249	28	7	7	NUM
cana-2105	249	29	:	:	PUNCT
cana-2105	249	30	the	the	DET
cana-2105	249	31	impact	impact	NOUN
cana-2105	249	32	on	on	ADP
cana-2105	249	33	julia	julia	PROPN
cana-2105	249	34	sets	set	NOUN
cana-2105	249	35	for	for	ADP
cana-2105	249	36	varying	vary	VERB
cana-2105	249	37	the	the	DET
cana-2105	249	38	parameter	parameter	NOUN
cana-2105	249	39	β	β	PROPN
cana-2105	249	40	4.1.7	4.1.7	PROPN
cana-2105	249	41	julia	julia	PROPN
cana-2105	249	42	set	set	VERB
cana-2105	249	43	for	for	ADP
cana-2105	249	44	the	the	DET
cana-2105	249	45	function	function	NOUN
cana-2105	249	46	tcz	tcz	NOUN
cana-2105	249	47	=	=	SYM
cana-2105	249	48	sin(zk	sin(zk	NOUN
cana-2105	249	49	)	)	PUNCT
cana-2105	250	1	+	+	CCONJ
cana-2105	250	2	az	az	PROPN
cana-2105	250	3	+	+	CCONJ
cana-2105	250	4	c	c	NOUN
cana-2105	250	5	varying	vary	VERB
cana-2105	250	6	the	the	DET
cana-2105	250	7	parameter	parameter	NOUN
cana-2105	250	8	γ	γ	X
cana-2105	250	9	we	we	PRON
cana-2105	250	10	observe	observe	VERB
cana-2105	250	11	captivating	captivating	ADJ
cana-2105	250	12	depictions	depiction	NOUN
cana-2105	250	13	of	of	ADP
cana-2105	250	14	julia	julia	PROPN
cana-2105	250	15	sets	set	NOUN
cana-2105	250	16	with	with	ADP
cana-2105	250	17	a	a	DET
cana-2105	250	18	degree	degree	NOUN
cana-2105	250	19	of	of	ADP
cana-2105	250	20	two	two	NUM
cana-2105	250	21	while	while	SCONJ
cana-2105	250	22	manipulating	manipulate	VERB
cana-2105	250	23	a	a	DET
cana-2105	250	24	parameter	parameter	NOUN
cana-2105	250	25	γ	γ	NOUN
cana-2105	250	26	as	as	SCONJ
cana-2105	250	27	depicted	depict	VERB
cana-2105	250	28	in	in	ADP
cana-2105	250	29	figure	figure	NOUN
cana-2105	250	30	8	8	NUM
cana-2105	250	31	.	.	PUNCT
cana-2105	251	1	notably	notably	ADV
cana-2105	251	2	,	,	PUNCT
cana-2105	251	3	for	for	ADP
cana-2105	251	4	each	each	DET
cana-2105	251	5	value	value	NOUN
cana-2105	251	6	of	of	ADP
cana-2105	251	7	γ	γ	PROPN
cana-2105	251	8	,	,	PUNCT
cana-2105	251	9	the	the	DET
cana-2105	251	10	julia	julia	PROPN
cana-2105	251	11	sets	set	VERB
cana-2105	251	12	exhibit	exhibit	NOUN
cana-2105	251	13	symmetry	symmetry	NOUN
cana-2105	251	14	with	with	ADP
cana-2105	251	15	respect	respect	NOUN
cana-2105	251	16	to	to	ADP
cana-2105	251	17	the	the	DET
cana-2105	251	18	real	real	ADJ
cana-2105	251	19	axis	axis	NOUN
cana-2105	251	20	.	.	PUNCT
cana-2105	252	1	when	when	SCONJ
cana-2105	252	2	γ	γ	X
cana-2105	252	3	is	be	AUX
cana-2105	252	4	close	close	ADJ
cana-2105	252	5	to	to	ADP
cana-2105	252	6	zero	zero	NUM
cana-2105	252	7	,	,	PUNCT
cana-2105	252	8	a	a	DET
cana-2105	252	9	striking	strike	VERB
cana-2105	252	10	julia	julia	NOUN
cana-2105	252	11	set	set	PROPN
cana-2105	252	12	is	be	AUX
cana-2105	252	13	formed	form	VERB
cana-2105	252	14	with	with	ADP
cana-2105	252	15	a	a	DET
cana-2105	252	16	high	high	ADJ
cana-2105	252	17	-	-	PUNCT
cana-2105	252	18	intensity	intensity	NOUN
cana-2105	252	19	brown	brown	ADJ
cana-2105	252	20	color	color	NOUN
cana-2105	252	21	.	.	PUNCT
cana-2105	253	1	numerous	numerous	ADJ
cana-2105	253	2	lashes	lash	NOUN
cana-2105	253	3	are	be	AUX
cana-2105	253	4	present	present	ADJ
cana-2105	253	5	,	,	PUNCT
cana-2105	253	6	each	each	PRON
cana-2105	253	7	exhibiting	exhibit	VERB
cana-2105	253	8	a	a	DET
cana-2105	253	9	shape	shape	NOUN
cana-2105	253	10	reminiscent	reminiscent	ADJ
cana-2105	253	11	of	of	ADP
cana-2105	253	12	cactus	cactus	NOUN
cana-2105	253	13	leaves	leave	NOUN
cana-2105	253	14	.	.	PUNCT
cana-2105	254	1	this	this	DET
cana-2105	254	2	configuration	configuration	NOUN
cana-2105	254	3	results	result	VERB
cana-2105	254	4	in	in	ADP
cana-2105	254	5	a	a	DET
cana-2105	254	6	visually	visually	ADV
cana-2105	254	7	appealing	appealing	ADJ
cana-2105	254	8	julia	julia	PROPN
cana-2105	254	9	set	set	VERB
cana-2105	254	10	with	with	ADP
cana-2105	254	11	intricate	intricate	ADJ
cana-2105	254	12	details	detail	NOUN
cana-2105	254	13	.	.	PUNCT
cana-2105	255	1	as	as	ADP
cana-2105	255	2	the	the	DET
cana-2105	255	3	value	value	NOUN
cana-2105	255	4	of	of	ADP
cana-2105	255	5	γ	γ	NOUN
cana-2105	255	6	increases	increase	NOUN
cana-2105	255	7	,	,	PUNCT
cana-2105	255	8	there	there	PRON
cana-2105	255	9	is	be	VERB
cana-2105	255	10	a	a	DET
cana-2105	255	11	reduction	reduction	NOUN
cana-2105	255	12	in	in	ADP
cana-2105	255	13	the	the	DET
cana-2105	255	14	size	size	NOUN
cana-2105	255	15	of	of	ADP
cana-2105	255	16	julia	julia	PROPN
cana-2105	255	17	sets	set	NOUN
cana-2105	255	18	,	,	PUNCT
cana-2105	255	19	accompanied	accompany	VERB
cana-2105	255	20	by	by	ADP
cana-2105	255	21	a	a	DET
cana-2105	255	22	decrease	decrease	NOUN
cana-2105	255	23	in	in	ADP
cana-2105	255	24	the	the	DET
cana-2105	255	25	number	number	NOUN
cana-2105	255	26	of	of	ADP
cana-2105	255	27	lashes	lash	NOUN
cana-2105	255	28	and	and	CCONJ
cana-2105	255	29	a	a	DET
cana-2105	255	30	diminishing	diminishing	NOUN
cana-2105	255	31	intensity	intensity	NOUN
cana-2105	255	32	of	of	ADP
cana-2105	255	33	brown	brown	ADJ
cana-2105	255	34	color	color	NOUN
cana-2105	255	35	.	.	PUNCT
cana-2105	256	1	after	after	SCONJ
cana-2105	256	2	γ	γ	X
cana-2105	256	3	exceeds	exceed	VERB
cana-2105	256	4	0.2	0.2	NUM
cana-2105	256	5	,	,	PUNCT
cana-2105	256	6	the	the	DET
cana-2105	256	7	brown	brown	ADJ
cana-2105	256	8	color	color	NOUN
cana-2105	256	9	completely	completely	ADV
cana-2105	256	10	disappears	disappear	VERB
cana-2105	256	11	,	,	PUNCT
cana-2105	256	12	and	and	CCONJ
cana-2105	256	13	only	only	ADV
cana-2105	256	14	the	the	DET
cana-2105	256	15	sky	sky	NOUN
cana-2105	256	16	blue	blue	ADJ
cana-2105	256	17	color	color	NOUN
cana-2105	256	18	remains	remain	VERB
cana-2105	256	19	in	in	ADP
cana-2105	256	20	the	the	DET
cana-2105	256	21	julia	julia	PROPN
cana-2105	256	22	sets	set	NOUN
cana-2105	256	23	.	.	PUNCT
cana-2105	257	1	these	these	DET
cana-2105	257	2	sets	set	NOUN
cana-2105	257	3	require	require	VERB
cana-2105	257	4	more	more	ADJ
cana-2105	257	5	prominence	prominence	NOUN
cana-2105	257	6	,	,	PUNCT
cana-2105	257	7	making	make	VERB
cana-2105	257	8	perceiving	perceive	VERB
cana-2105	257	9	the	the	DET
cana-2105	257	10	finer	fine	ADJ
cana-2105	257	11	details	detail	NOUN
cana-2105	257	12	difficult	difficult	ADJ
cana-2105	257	13	.	.	PUNCT
cana-2105	258	1	this	this	DET
cana-2105	258	2	transition	transition	NOUN
cana-2105	258	3	suggests	suggest	VERB
cana-2105	258	4	that	that	SCONJ
cana-2105	258	5	as	as	SCONJ
cana-2105	258	6	γ	γ	PROPN
cana-2105	258	7	approaches	approach	VERB
cana-2105	258	8	one	one	NUM
cana-2105	258	9	,	,	PUNCT
cana-2105	258	10	the	the	DET
cana-2105	258	11	number	number	NOUN
cana-2105	258	12	of	of	ADP
cana-2105	258	13	escaping	escape	VERB
cana-2105	258	14	points	point	NOUN
cana-2105	258	15	increases	increase	NOUN
cana-2105	258	16	,	,	PUNCT
cana-2105	258	17	significantly	significantly	ADV
cana-2105	258	18	altering	alter	VERB
cana-2105	258	19	the	the	DET
cana-2105	258	20	julia	julia	PROPN
cana-2105	258	21	sets	set	NOUN
cana-2105	258	22	’	'	PUNCT
cana-2105	258	23	visual	visual	ADJ
cana-2105	258	24	characteristics	characteristic	NOUN
cana-2105	258	25	.	.	PUNCT
cana-2105	259	1	communications	communication	NOUN
cana-2105	259	2	on	on	ADP
cana-2105	259	3	applied	apply	VERB
cana-2105	259	4	nonlinear	nonlinear	ADJ
cana-2105	259	5	analysis	analysis	NOUN
cana-2105	259	6	issn	issn	NOUN
cana-2105	259	7	:	:	PUNCT
cana-2105	259	8	1074	1074	NUM
cana-2105	259	9	-	-	PUNCT
cana-2105	259	10	133x	133x	NUM
cana-2105	259	11	vol	vol	NOUN
cana-2105	259	12	32	32	NUM
cana-2105	259	13	no	no	NOUN
cana-2105	259	14	.	.	PUNCT
cana-2105	260	1	1s	1s	NUM
cana-2105	260	2	(	(	PUNCT
cana-2105	260	3	2025	2025	NUM
cana-2105	260	4	)	)	PUNCT
cana-2105	260	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	260	6	78	78	NUM
cana-2105	260	7	(	(	PUNCT
cana-2105	260	8	a	a	NOUN
cana-2105	260	9	)	)	PUNCT
cana-2105	260	10	γ	γ	NOUN
cana-2105	260	11	=	=	SYM
cana-2105	260	12	0.0001	0.0001	NUM
cana-2105	260	13	(	(	PUNCT
cana-2105	260	14	b	b	NOUN
cana-2105	260	15	)	)	PUNCT
cana-2105	260	16	γ	γ	NOUN
cana-2105	260	17	=	=	SYM
cana-2105	260	18	0.02	0.02	NUM
cana-2105	260	19	(	(	PUNCT
cana-2105	260	20	c	c	NOUN
cana-2105	260	21	)	)	PUNCT
cana-2105	260	22	γ	γ	NOUN
cana-2105	260	23	=	=	SYM
cana-2105	260	24	0.035	0.035	NUM
cana-2105	260	25	(	(	PUNCT
cana-2105	260	26	d	d	NOUN
cana-2105	260	27	)	)	PUNCT
cana-2105	260	28	γ	γ	PROPN
cana-2105	260	29	=	=	SYM
cana-2105	260	30	0.421	0.421	NUM
cana-2105	260	31	(	(	PUNCT
cana-2105	260	32	e	e	NOUN
cana-2105	260	33	)	)	PUNCT
cana-2105	260	34	γ	γ	NOUN
cana-2105	260	35	=	=	SYM
cana-2105	260	36	0.751	0.751	NUM
cana-2105	260	37	(	(	PUNCT
cana-2105	260	38	f	f	X
cana-2105	260	39	)	)	PUNCT
cana-2105	260	40	γ	γ	NOUN
cana-2105	260	41	=	=	SYM
cana-2105	260	42	0.965	0.965	NUM
cana-2105	260	43	figure	figure	NOUN
cana-2105	260	44	8	8	NUM
cana-2105	260	45	:	:	PUNCT
cana-2105	260	46	the	the	DET
cana-2105	260	47	impact	impact	NOUN
cana-2105	260	48	on	on	ADP
cana-2105	260	49	julia	julia	PROPN
cana-2105	260	50	sets	set	NOUN
cana-2105	260	51	for	for	ADP
cana-2105	260	52	varying	vary	VERB
cana-2105	260	53	the	the	DET
cana-2105	260	54	parameter	parameter	NOUN
cana-2105	260	55	γ	γ	PROPN
cana-2105	260	56	4.1.8	4.1.8	PROPN
cana-2105	260	57	julia	julia	PROPN
cana-2105	260	58	set	set	VERB
cana-2105	260	59	for	for	ADP
cana-2105	260	60	the	the	DET
cana-2105	260	61	function	function	NOUN
cana-2105	260	62	tcz	tcz	NOUN
cana-2105	260	63	=	=	PUNCT
cana-2105	260	64	sin(zk)+az+	sin(zk)+az+	PUNCT
cana-2105	260	65	c	c	NOUN
cana-2105	260	66	varying	vary	VERB
cana-2105	260	67	the	the	DET
cana-2105	260	68	parameter	parameter	NOUN
cana-2105	260	69	δ	δ	PROPN
cana-2105	261	1	we	we	PRON
cana-2105	261	2	observe	observe	VERB
cana-2105	261	3	enchanting	enchanting	ADJ
cana-2105	261	4	illustrations	illustration	NOUN
cana-2105	261	5	of	of	ADP
cana-2105	261	6	quadratic	quadratic	ADJ
cana-2105	261	7	julia	julia	PROPN
cana-2105	261	8	sets	set	NOUN
cana-2105	261	9	while	while	SCONJ
cana-2105	261	10	altering	alter	VERB
cana-2105	261	11	a	a	DET
cana-2105	261	12	parameter	parameter	NOUN
cana-2105	261	13	δ	δ	PROPN
cana-2105	261	14	as	as	SCONJ
cana-2105	261	15	illustrated	illustrate	VERB
cana-2105	261	16	in	in	ADP
cana-2105	261	17	figure	figure	NOUN
cana-2105	261	18	9	9	NUM
cana-2105	261	19	.	.	PUNCT
cana-2105	261	20	notably	notably	ADV
cana-2105	261	21	,	,	PUNCT
cana-2105	261	22	for	for	ADP
cana-2105	261	23	each	each	DET
cana-2105	261	24	value	value	NOUN
cana-2105	261	25	of	of	ADP
cana-2105	261	26	δ	δ	PROPN
cana-2105	261	27	,	,	PUNCT
cana-2105	261	28	the	the	DET
cana-2105	261	29	julia	julia	PROPN
cana-2105	261	30	sets	set	VERB
cana-2105	261	31	preserve	preserve	VERB
cana-2105	261	32	symmetry	symmetry	NOUN
cana-2105	261	33	regarding	regard	VERB
cana-2105	261	34	the	the	DET
cana-2105	261	35	real	real	ADJ
cana-2105	261	36	axis	axis	NOUN
cana-2105	261	37	.	.	PUNCT
cana-2105	262	1	when	when	SCONJ
cana-2105	262	2	δ	δ	PROPN
cana-2105	262	3	approaches	approach	VERB
cana-2105	262	4	zero	zero	NUM
cana-2105	262	5	,	,	PUNCT
cana-2105	262	6	an	an	DET
cana-2105	262	7	impressive	impressive	ADJ
cana-2105	262	8	julia	julia	NOUN
cana-2105	262	9	set	set	NOUN
cana-2105	262	10	emerges	emerge	NOUN
cana-2105	262	11	,	,	PUNCT
cana-2105	262	12	characterized	characterize	VERB
cana-2105	262	13	by	by	ADP
cana-2105	262	14	a	a	DET
cana-2105	262	15	rich	rich	ADJ
cana-2105	262	16	,	,	PUNCT
cana-2105	262	17	high	high	ADJ
cana-2105	262	18	-	-	PUNCT
cana-2105	262	19	intensity	intensity	NOUN
cana-2105	262	20	brown	brown	ADJ
cana-2105	262	21	color	color	NOUN
cana-2105	262	22	.	.	PUNCT
cana-2105	263	1	the	the	DET
cana-2105	263	2	set	set	NOUN
cana-2105	263	3	features	feature	VERB
cana-2105	263	4	numerous	numerous	ADJ
cana-2105	263	5	lashes	lash	NOUN
cana-2105	263	6	,	,	PUNCT
cana-2105	263	7	each	each	PRON
cana-2105	263	8	resembling	resemble	VERB
cana-2105	263	9	the	the	DET
cana-2105	263	10	shape	shape	NOUN
cana-2105	263	11	of	of	ADP
cana-2105	263	12	cactus	cactus	NOUN
cana-2105	263	13	leaves	leave	NOUN
cana-2105	263	14	,	,	PUNCT
cana-2105	263	15	resulting	result	VERB
cana-2105	263	16	in	in	ADP
cana-2105	263	17	a	a	DET
cana-2105	263	18	visually	visually	ADV
cana-2105	263	19	appealing	appealing	ADJ
cana-2105	263	20	and	and	CCONJ
cana-2105	263	21	intricately	intricately	ADV
cana-2105	263	22	detailed	detailed	ADJ
cana-2105	263	23	julia	julia	PROPN
cana-2105	263	24	set	set	PROPN
cana-2105	263	25	.	.	PUNCT
cana-2105	264	1	many	many	ADJ
cana-2105	264	2	tiny	tiny	ADJ
cana-2105	264	3	lashes	lash	NOUN
cana-2105	264	4	are	be	AUX
cana-2105	264	5	present	present	ADJ
cana-2105	264	6	at	at	ADP
cana-2105	264	7	the	the	DET
cana-2105	264	8	tip	tip	NOUN
cana-2105	264	9	of	of	ADP
cana-2105	264	10	each	each	DET
cana-2105	264	11	central	central	ADJ
cana-2105	264	12	lash	lash	NOUN
cana-2105	264	13	.	.	PUNCT
cana-2105	265	1	as	as	ADP
cana-2105	265	2	the	the	DET
cana-2105	265	3	value	value	NOUN
cana-2105	265	4	of	of	ADP
cana-2105	265	5	δ	δ	PROPN
cana-2105	265	6	increases	increase	NOUN
cana-2105	265	7	,	,	PUNCT
cana-2105	265	8	there	there	PRON
cana-2105	265	9	is	be	VERB
cana-2105	265	10	a	a	DET
cana-2105	265	11	noticeable	noticeable	ADJ
cana-2105	265	12	reduction	reduction	NOUN
cana-2105	265	13	in	in	ADP
cana-2105	265	14	the	the	DET
cana-2105	265	15	size	size	NOUN
cana-2105	265	16	of	of	ADP
cana-2105	265	17	the	the	DET
cana-2105	265	18	julia	julia	PROPN
cana-2105	265	19	sets	set	NOUN
cana-2105	265	20	,	,	PUNCT
cana-2105	265	21	accompanied	accompany	VERB
cana-2105	265	22	by	by	ADP
cana-2105	265	23	a	a	DET
cana-2105	265	24	decrease	decrease	NOUN
cana-2105	265	25	in	in	ADP
cana-2105	265	26	the	the	DET
cana-2105	265	27	number	number	NOUN
cana-2105	265	28	and	and	CCONJ
cana-2105	265	29	size	size	NOUN
cana-2105	265	30	of	of	ADP
cana-2105	265	31	lashes	lash	NOUN
cana-2105	265	32	and	and	CCONJ
cana-2105	265	33	a	a	DET
cana-2105	265	34	gradual	gradual	ADJ
cana-2105	265	35	reduction	reduction	NOUN
cana-2105	265	36	in	in	ADP
cana-2105	265	37	the	the	DET
cana-2105	265	38	intensity	intensity	NOUN
cana-2105	265	39	of	of	ADP
cana-2105	265	40	the	the	DET
cana-2105	265	41	brown	brown	ADJ
cana-2105	265	42	color	color	NOUN
cana-2105	265	43	.	.	PUNCT
cana-2105	266	1	when	when	SCONJ
cana-2105	266	2	δ	δ	X
cana-2105	266	3	>	>	X
cana-2105	266	4	0.1	0.1	NUM
cana-2105	266	5	,	,	PUNCT
cana-2105	266	6	the	the	DET
cana-2105	266	7	brown	brown	ADJ
cana-2105	266	8	color	color	NOUN
cana-2105	266	9	completely	completely	ADV
cana-2105	266	10	vanishes	vanish	VERB
cana-2105	266	11	,	,	PUNCT
cana-2105	266	12	leaving	leave	VERB
cana-2105	266	13	julia	julia	PROPN
cana-2105	266	14	’s	’s	PART
cana-2105	266	15	sets	set	NOUN
cana-2105	266	16	dominated	dominate	VERB
cana-2105	266	17	by	by	ADP
cana-2105	266	18	a	a	DET
cana-2105	266	19	sky	sky	NOUN
cana-2105	266	20	blue	blue	ADJ
cana-2105	266	21	color	color	NOUN
cana-2105	266	22	behind	behind	ADV
cana-2105	266	23	.	.	PUNCT
cana-2105	267	1	however	however	ADV
cana-2105	267	2	,	,	PUNCT
cana-2105	267	3	these	these	DET
cana-2105	267	4	sets	set	NOUN
cana-2105	267	5	require	require	VERB
cana-2105	267	6	heightened	heightened	ADJ
cana-2105	267	7	prominence	prominence	NOUN
cana-2105	267	8	,	,	PUNCT
cana-2105	267	9	and	and	CCONJ
cana-2105	267	10	discerning	discern	VERB
cana-2105	267	11	finer	fine	ADJ
cana-2105	267	12	details	detail	NOUN
cana-2105	267	13	becomes	become	VERB
cana-2105	267	14	challenging	challenging	ADJ
cana-2105	267	15	.	.	PUNCT
cana-2105	268	1	this	this	DET
cana-2105	268	2	shift	shift	NOUN
cana-2105	268	3	implies	imply	VERB
cana-2105	268	4	that	that	SCONJ
cana-2105	268	5	as	as	SCONJ
cana-2105	268	6	δ	δ	PROPN
cana-2105	268	7	approaches	approach	VERB
cana-2105	268	8	one	one	NUM
cana-2105	268	9	,	,	PUNCT
cana-2105	268	10	the	the	DET
cana-2105	268	11	number	number	NOUN
cana-2105	268	12	of	of	ADP
cana-2105	268	13	points	point	NOUN
cana-2105	268	14	escaping	escape	VERB
cana-2105	268	15	to	to	PART
cana-2105	268	16	infinity	infinity	VERB
cana-2105	268	17	increases	increase	NOUN
cana-2105	268	18	,	,	PUNCT
cana-2105	268	19	leading	lead	VERB
cana-2105	268	20	to	to	ADP
cana-2105	268	21	a	a	DET
cana-2105	268	22	significant	significant	ADJ
cana-2105	268	23	transformation	transformation	NOUN
cana-2105	268	24	in	in	ADP
cana-2105	268	25	the	the	DET
cana-2105	268	26	visual	visual	ADJ
cana-2105	268	27	characteristics	characteristic	NOUN
cana-2105	268	28	of	of	ADP
cana-2105	268	29	the	the	DET
cana-2105	268	30	julia	julia	PROPN
cana-2105	268	31	sets	set	NOUN
cana-2105	268	32	.	.	PUNCT
cana-2105	269	1	communications	communication	NOUN
cana-2105	269	2	on	on	ADP
cana-2105	269	3	applied	apply	VERB
cana-2105	269	4	nonlinear	nonlinear	ADJ
cana-2105	269	5	analysis	analysis	NOUN
cana-2105	269	6	issn	issn	NOUN
cana-2105	269	7	:	:	PUNCT
cana-2105	269	8	1074	1074	NUM
cana-2105	269	9	-	-	PUNCT
cana-2105	269	10	133x	133x	NUM
cana-2105	269	11	vol	vol	NOUN
cana-2105	269	12	32	32	NUM
cana-2105	269	13	no	no	NOUN
cana-2105	269	14	.	.	PUNCT
cana-2105	270	1	1s	1s	NUM
cana-2105	270	2	(	(	PUNCT
cana-2105	270	3	2025	2025	NUM
cana-2105	270	4	)	)	PUNCT
cana-2105	270	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	270	6	79	79	NUM
cana-2105	270	7	(	(	PUNCT
cana-2105	270	8	a	a	NOUN
cana-2105	270	9	)	)	PUNCT
cana-2105	270	10	δ	δ	NOUN
cana-2105	270	11	=	=	PUNCT
cana-2105	271	1	0.00001	0.00001	NUM
cana-2105	271	2	(	(	PUNCT
cana-2105	271	3	b	b	NOUN
cana-2105	271	4	)	)	PUNCT
cana-2105	271	5	δ	δ	NOUN
cana-2105	271	6	=	=	PUNCT
cana-2105	271	7	0.002	0.002	NUM
cana-2105	271	8	(	(	PUNCT
cana-2105	271	9	c	c	NOUN
cana-2105	271	10	)	)	PUNCT
cana-2105	271	11	δ	δ	NOUN
cana-2105	271	12	=	=	PUNCT
cana-2105	271	13	0.124	0.124	NUM
cana-2105	271	14	(	(	PUNCT
cana-2105	271	15	d	d	NOUN
cana-2105	271	16	)	)	PUNCT
cana-2105	271	17	δ	δ	X
cana-2105	271	18	=	=	PUNCT
cana-2105	271	19	0.432	0.432	NUM
cana-2105	271	20	(	(	PUNCT
cana-2105	271	21	e	e	NOUN
cana-2105	271	22	)	)	PUNCT
cana-2105	271	23	δ	δ	X
cana-2105	272	1	=	=	PUNCT
cana-2105	272	2	0.684	0.684	NUM
cana-2105	272	3	(	(	PUNCT
cana-2105	272	4	f	f	X
cana-2105	272	5	)	)	PUNCT
cana-2105	272	6	γ	γ	NOUN
cana-2105	272	7	=	=	SYM
cana-2105	272	8	0.912	0.912	NUM
cana-2105	272	9	figure	figure	NOUN
cana-2105	272	10	9	9	NUM
cana-2105	272	11	:	:	PUNCT
cana-2105	272	12	the	the	DET
cana-2105	272	13	impact	impact	NOUN
cana-2105	272	14	on	on	ADP
cana-2105	272	15	julia	julia	PROPN
cana-2105	272	16	sets	set	NOUN
cana-2105	272	17	for	for	ADP
cana-2105	272	18	varying	vary	VERB
cana-2105	272	19	the	the	DET
cana-2105	272	20	parameter	parameter	NOUN
cana-2105	272	21	δ	δ	PROPN
cana-2105	272	22	4.1.9	4.1.9	NUM
cana-2105	272	23	julia	julia	PROPN
cana-2105	272	24	set	set	VERB
cana-2105	272	25	for	for	ADP
cana-2105	272	26	the	the	DET
cana-2105	272	27	function	function	NOUN
cana-2105	272	28	tcz	tcz	NOUN
cana-2105	272	29	=	=	SYM
cana-2105	272	30	sin(zk	sin(zk	NOUN
cana-2105	272	31	)	)	PUNCT
cana-2105	273	1	+	+	CCONJ
cana-2105	273	2	az	az	PROPN
cana-2105	273	3	+	+	CCONJ
cana-2105	273	4	c	c	X
cana-2105	273	5	varying	vary	VERB
cana-2105	273	6	the	the	DET
cana-2105	273	7	k	k	NOUN
cana-2105	273	8	we	we	PRON
cana-2105	273	9	generate	generate	VERB
cana-2105	273	10	captivating	captivate	VERB
cana-2105	273	11	fractal	fractal	ADJ
cana-2105	273	12	patterns	pattern	NOUN
cana-2105	273	13	,	,	PUNCT
cana-2105	273	14	as	as	SCONJ
cana-2105	273	15	illustrated	illustrate	VERB
cana-2105	273	16	in	in	ADP
cana-2105	273	17	figure	figure	NOUN
cana-2105	273	18	10	10	NUM
cana-2105	273	19	,	,	PUNCT
cana-2105	273	20	by	by	ADP
cana-2105	273	21	varying	vary	VERB
cana-2105	273	22	the	the	DET
cana-2105	273	23	parameter	parameter	NOUN
cana-2105	273	24	k.	k.	PROPN
cana-2105	273	25	for	for	ADP
cana-2105	273	26	k	k	PROPN
cana-2105	273	27	=	=	SYM
cana-2105	273	28	2	2	NUM
cana-2105	273	29	,	,	PUNCT
cana-2105	273	30	the	the	DET
cana-2105	273	31	resulting	result	VERB
cana-2105	273	32	julia	julia	NOUN
cana-2105	273	33	set	set	VERB
cana-2105	273	34	displays	display	VERB
cana-2105	273	35	four	four	NUM
cana-2105	273	36	distinct	distinct	ADJ
cana-2105	273	37	lashes	lash	NOUN
cana-2105	273	38	formed	form	VERB
cana-2105	273	39	by	by	ADP
cana-2105	273	40	blending	blend	VERB
cana-2105	273	41	sky	sky	NOUN
cana-2105	273	42	blue	blue	NOUN
cana-2105	273	43	,	,	PUNCT
cana-2105	273	44	light	light	NOUN
cana-2105	273	45	yellow	yellow	ADJ
cana-2105	273	46	,	,	PUNCT
cana-2105	273	47	and	and	CCONJ
cana-2105	273	48	brown	brown	ADJ
cana-2105	273	49	colors	color	NOUN
cana-2105	273	50	along	along	ADP
cana-2105	273	51	the	the	DET
cana-2105	273	52	real	real	ADJ
cana-2105	273	53	and	and	CCONJ
cana-2105	273	54	imaginary	imaginary	ADJ
cana-2105	273	55	axes	axis	NOUN
cana-2105	273	56	.	.	PUNCT
cana-2105	274	1	additionally	additionally	ADV
cana-2105	274	2	,	,	PUNCT
cana-2105	274	3	numerous	numerous	ADJ
cana-2105	274	4	cactus	cactus	ADJ
cana-2105	274	5	leaf	leaf	NOUN
cana-2105	274	6	-	-	PUNCT
cana-2105	274	7	like	like	ADJ
cana-2105	274	8	lashes	lash	NOUN
cana-2105	274	9	with	with	ADP
cana-2105	274	10	a	a	DET
cana-2105	274	11	brown	brown	ADJ
cana-2105	274	12	hue	hue	NOUN
cana-2105	274	13	are	be	AUX
cana-2105	274	14	present	present	ADJ
cana-2105	274	15	within	within	ADP
cana-2105	274	16	the	the	DET
cana-2105	274	17	julia	julia	PROPN
cana-2105	274	18	set	set	PROPN
cana-2105	274	19	.	.	PUNCT
cana-2105	275	1	when	when	SCONJ
cana-2105	275	2	k	k	PROPN
cana-2105	275	3	=	=	SYM
cana-2105	275	4	3	3	NUM
cana-2105	275	5	,	,	PUNCT
cana-2105	275	6	the	the	DET
cana-2105	275	7	outer	outer	ADJ
cana-2105	275	8	part	part	NOUN
cana-2105	275	9	of	of	ADP
cana-2105	275	10	the	the	DET
cana-2105	275	11	julia	julia	PROPN
cana-2105	275	12	set	set	NOUN
cana-2105	275	13	exhibits	exhibit	VERB
cana-2105	275	14	six	six	NUM
cana-2105	275	15	lashes	lash	NOUN
cana-2105	275	16	with	with	ADP
cana-2105	275	17	a	a	DET
cana-2105	275	18	sky	sky	NOUN
cana-2105	275	19	blue	blue	ADJ
cana-2105	275	20	color	color	NOUN
cana-2105	275	21	,	,	PUNCT
cana-2105	275	22	while	while	SCONJ
cana-2105	275	23	the	the	DET
cana-2105	275	24	inner	inner	ADJ
cana-2105	275	25	region	region	NOUN
cana-2105	275	26	features	feature	VERB
cana-2105	275	27	numerous	numerous	ADJ
cana-2105	275	28	lashes	lash	NOUN
cana-2105	275	29	with	with	ADP
cana-2105	275	30	a	a	DET
cana-2105	275	31	brown	brown	ADJ
cana-2105	275	32	hue	hue	NOUN
cana-2105	275	33	.	.	PUNCT
cana-2105	276	1	as	as	ADP
cana-2105	276	2	the	the	DET
cana-2105	276	3	value	value	NOUN
cana-2105	276	4	of	of	ADP
cana-2105	276	5	the	the	DET
cana-2105	276	6	parameter	parameter	NOUN
cana-2105	276	7	k	k	PROPN
cana-2105	276	8	increases	increase	NOUN
cana-2105	276	9	,	,	PUNCT
cana-2105	276	10	the	the	DET
cana-2105	276	11	size	size	NOUN
cana-2105	276	12	of	of	ADP
cana-2105	276	13	the	the	DET
cana-2105	276	14	julia	julia	PROPN
cana-2105	276	15	set	set	PROPN
cana-2105	276	16	decreases	decrease	VERB
cana-2105	276	17	,	,	PUNCT
cana-2105	276	18	and	and	CCONJ
cana-2105	276	19	the	the	DET
cana-2105	276	20	set	set	NOUN
cana-2105	276	21	adopts	adopt	VERB
cana-2105	276	22	a	a	DET
cana-2105	276	23	more	more	ADV
cana-2105	276	24	circular	circular	ADJ
cana-2105	276	25	shape	shape	NOUN
cana-2105	276	26	.	.	PUNCT
cana-2105	277	1	each	each	DET
cana-2105	277	2	julia	julia	PROPN
cana-2105	277	3	set	set	PROPN
cana-2105	277	4	,	,	PUNCT
cana-2105	277	5	regardless	regardless	ADV
cana-2105	277	6	of	of	ADP
cana-2105	277	7	the	the	DET
cana-2105	277	8	value	value	NOUN
cana-2105	277	9	of	of	ADP
cana-2105	277	10	k	k	PROPN
cana-2105	277	11	,	,	PUNCT
cana-2105	277	12	showcases	showcase	VERB
cana-2105	277	13	2k	2k	NUM
cana-2105	277	14	outer	outer	ADJ
cana-2105	277	15	lashes	lash	NOUN
cana-2105	277	16	,	,	PUNCT
cana-2105	277	17	with	with	ADP
cana-2105	277	18	smaller	small	ADJ
cana-2105	277	19	lashes	lash	NOUN
cana-2105	277	20	forming	form	VERB
cana-2105	277	21	in	in	ADP
cana-2105	277	22	the	the	DET
cana-2105	277	23	central	central	ADJ
cana-2105	277	24	region	region	NOUN
cana-2105	277	25	.	.	PUNCT
cana-2105	278	1	the	the	DET
cana-2105	278	2	julia	julia	PROPN
cana-2105	278	3	set	set	PROPN
cana-2105	278	4	is	be	AUX
cana-2105	278	5	more	more	ADV
cana-2105	278	6	aesthetically	aesthetically	ADV
cana-2105	278	7	pleasing	pleasing	ADJ
cana-2105	278	8	when	when	SCONJ
cana-2105	278	9	the	the	DET
cana-2105	278	10	parameter	parameter	NOUN
cana-2105	278	11	k	k	PROPN
cana-2105	278	12	is	be	AUX
cana-2105	278	13	lower	low	ADJ
cana-2105	278	14	.	.	PUNCT
cana-2105	279	1	communications	communication	NOUN
cana-2105	279	2	on	on	ADP
cana-2105	279	3	applied	apply	VERB
cana-2105	279	4	nonlinear	nonlinear	ADJ
cana-2105	279	5	analysis	analysis	NOUN
cana-2105	279	6	issn	issn	NOUN
cana-2105	279	7	:	:	PUNCT
cana-2105	279	8	1074	1074	NUM
cana-2105	279	9	-	-	PUNCT
cana-2105	279	10	133x	133x	NUM
cana-2105	279	11	vol	vol	NOUN
cana-2105	279	12	32	32	NUM
cana-2105	279	13	no	no	NOUN
cana-2105	279	14	.	.	PUNCT
cana-2105	280	1	1s	1s	NUM
cana-2105	280	2	(	(	PUNCT
cana-2105	280	3	2025	2025	NUM
cana-2105	280	4	)	)	PUNCT
cana-2105	280	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	280	6	80	80	NUM
cana-2105	280	7	(	(	PUNCT
cana-2105	280	8	a	a	NOUN
cana-2105	280	9	)	)	PUNCT
cana-2105	280	10	k	k	NOUN
cana-2105	281	1	=	=	SYM
cana-2105	281	2	2	2	NUM
cana-2105	281	3	(	(	PUNCT
cana-2105	281	4	b	b	NOUN
cana-2105	281	5	)	)	PUNCT
cana-2105	281	6	k	k	NOUN
cana-2105	281	7	=	=	SYM
cana-2105	281	8	3	3	NUM
cana-2105	281	9	(	(	PUNCT
cana-2105	281	10	c	c	NOUN
cana-2105	281	11	)	)	PUNCT
cana-2105	281	12	k	k	NOUN
cana-2105	282	1	=	=	SYM
cana-2105	282	2	4	4	NUM
cana-2105	282	3	(	(	PUNCT
cana-2105	282	4	d	d	NOUN
cana-2105	282	5	)	)	PUNCT
cana-2105	282	6	k	k	NOUN
cana-2105	283	1	=	=	SYM
cana-2105	283	2	5	5	NUM
cana-2105	283	3	(	(	PUNCT
cana-2105	283	4	e	e	NOUN
cana-2105	283	5	)	)	PUNCT
cana-2105	283	6	k	k	NOUN
cana-2105	284	1	=	=	SYM
cana-2105	284	2	10	10	NUM
cana-2105	284	3	(	(	PUNCT
cana-2105	284	4	f	f	X
cana-2105	284	5	)	)	PUNCT
cana-2105	284	6	k	k	NOUN
cana-2105	285	1	=	=	SYM
cana-2105	285	2	15	15	NUM
cana-2105	285	3	figure	figure	NOUN
cana-2105	285	4	10	10	NUM
cana-2105	285	5	:	:	PUNCT
cana-2105	285	6	the	the	DET
cana-2105	285	7	impact	impact	NOUN
cana-2105	285	8	on	on	ADP
cana-2105	285	9	julia	julia	PROPN
cana-2105	285	10	sets	set	NOUN
cana-2105	285	11	for	for	ADP
cana-2105	285	12	varying	vary	VERB
cana-2105	285	13	k	k	PROPN
cana-2105	285	14	4.2	4.2	NUM
cana-2105	285	15	mandelbrot	mandelbrot	NOUN
cana-2105	285	16	set	set	VERB
cana-2105	285	17	in	in	ADP
cana-2105	285	18	this	this	DET
cana-2105	285	19	segment	segment	NOUN
cana-2105	285	20	,	,	PUNCT
cana-2105	285	21	we	we	PRON
cana-2105	285	22	generate	generate	VERB
cana-2105	285	23	mandelbrot	mandelbrot	NOUN
cana-2105	285	24	sets	set	NOUN
cana-2105	285	25	using	use	VERB
cana-2105	285	26	algorithm	algorithm	NOUN
cana-2105	285	27	2	2	NUM
cana-2105	285	28	.	.	PUNCT
cana-2105	286	1	we	we	PRON
cana-2105	286	2	systematically	systematically	ADV
cana-2105	286	3	vary	vary	VERB
cana-2105	286	4	each	each	DET
cana-2105	286	5	parameter	parameter	NOUN
cana-2105	286	6	individually	individually	ADV
cana-2105	286	7	while	while	SCONJ
cana-2105	286	8	keeping	keep	VERB
cana-2105	286	9	the	the	DET
cana-2105	286	10	remaining	remain	VERB
cana-2105	286	11	parameters	parameter	NOUN
cana-2105	286	12	fixed	fix	VERB
cana-2105	286	13	,	,	PUNCT
cana-2105	286	14	discussing	discuss	VERB
cana-2105	286	15	the	the	DET
cana-2105	286	16	resulting	result	VERB
cana-2105	286	17	properties	property	NOUN
cana-2105	286	18	.	.	PUNCT
cana-2105	287	1	we	we	PRON
cana-2105	287	2	set	set	VERB
cana-2105	287	3	the	the	DET
cana-2105	287	4	maximum	maximum	ADJ
cana-2105	287	5	iteration	iteration	NOUN
cana-2105	287	6	limit	limit	NOUN
cana-2105	287	7	to	to	ADP
cana-2105	287	8	k	k	PROPN
cana-2105	287	9	=	=	SYM
cana-2105	287	10	30	30	NUM
cana-2105	287	11	,	,	PUNCT
cana-2105	287	12	and	and	CCONJ
cana-2105	287	13	define	define	VERB
cana-2105	287	14	the	the	DET
cana-2105	287	15	area	area	NOUN
cana-2105	287	16	for	for	ADP
cana-2105	287	17	the	the	DET
cana-2105	287	18	mandelbrot	mandelbrot	NOUN
cana-2105	287	19	set	set	VERB
cana-2105	287	20	as	as	ADP
cana-2105	287	21	b	b	PROPN
cana-2105	287	22	=	=	SYM
cana-2105	287	23	[	[	X
cana-2105	287	24	−3.5	−3.5	PROPN
cana-2105	287	25	,	,	PUNCT
cana-2105	287	26	3.5	3.5	NUM
cana-2105	287	27	]	]	SYM
cana-2105	287	28	×	×	NOUN
cana-2105	288	1	[	[	X
cana-2105	288	2	−3.5	−3.5	PROPN
cana-2105	288	3	,	,	PUNCT
cana-2105	288	4	3.5	3.5	NUM
cana-2105	288	5	]	]	PUNCT
cana-2105	288	6	.	.	PUNCT
cana-2105	289	1	initially	initially	ADV
cana-2105	289	2	,	,	PUNCT
cana-2105	289	3	we	we	PRON
cana-2105	289	4	set	set	VERB
cana-2105	289	5	the	the	DET
cana-2105	289	6	parameters	parameter	NOUN
cana-2105	289	7	to	to	ADP
cana-2105	289	8	specific	specific	ADJ
cana-2105	289	9	values	value	NOUN
cana-2105	289	10	:	:	PUNCT
cana-2105	289	11	a	a	DET
cana-2105	289	12	=	=	PUNCT
cana-2105	289	13	−0.51	−0.51	NOUN
cana-2105	289	14	,	,	PUNCT
cana-2105	289	15	s	s	PART
cana-2105	289	16	=	=	SYM
cana-2105	289	17	0.5001	0.5001	NUM
cana-2105	289	18	,	,	PUNCT
cana-2105	289	19	α	α	X
cana-2105	289	20	=	=	SYM
cana-2105	289	21	0.0078	0.0078	NUM
cana-2105	289	22	,	,	PUNCT
cana-2105	289	23	β	β	X
cana-2105	289	24	=	=	SYM
cana-2105	289	25	0.0056	0.0056	NUM
cana-2105	289	26	,	,	PUNCT
cana-2105	289	27	γ	γ	X
cana-2105	289	28	=	=	SYM
cana-2105	289	29	0.0046	0.0046	NUM
cana-2105	289	30	,	,	PUNCT
cana-2105	289	31	δ	δ	X
cana-2105	289	32	=	=	PUNCT
cana-2105	289	33	0.00	0.00	NUM
cana-2105	289	34	,	,	PUNCT
cana-2105	289	35	ω1	ω1	PROPN
cana-2105	289	36	=	=	SYM
cana-2105	289	37	0.8383	0.8383	NUM
cana-2105	289	38	,	,	PUNCT
cana-2105	289	39	ω2	ω2	NOUN
cana-2105	289	40	=	=	SYM
cana-2105	289	41	0.119	0.119	NUM
cana-2105	289	42	,	,	PUNCT
cana-2105	289	43	ω3	ω3	NOUN
cana-2105	289	44	=	=	SYM
cana-2105	289	45	0.7474	0.7474	NUM
cana-2105	289	46	,	,	PUNCT
cana-2105	289	47	ω4	ω4	NUM
cana-2105	289	48	=	=	PUNCT
cana-2105	289	49	0.6556	0.6556	NUM
cana-2105	289	50	,	,	PUNCT
cana-2105	289	51	and	and	CCONJ
cana-2105	289	52	k	k	X
cana-2105	289	53	=	=	NOUN
cana-2105	289	54	2	2	X
cana-2105	289	55	.	.	X
cana-2105	289	56	4.2.1	4.2.1	NUM
cana-2105	289	57	mandelbrot	mandelbrot	NOUN
cana-2105	289	58	set	set	VERB
cana-2105	289	59	for	for	ADP
cana-2105	289	60	the	the	DET
cana-2105	289	61	function	function	NOUN
cana-2105	289	62	tcz	tcz	NOUN
cana-2105	289	63	=	=	SYM
cana-2105	289	64	sin(zk	sin(zk	NOUN
cana-2105	289	65	)	)	PUNCT
cana-2105	290	1	+	+	CCONJ
cana-2105	290	2	az	az	PROPN
cana-2105	290	3	+	+	CCONJ
cana-2105	290	4	c	c	NOUN
cana-2105	290	5	varying	vary	VERB
cana-2105	290	6	the	the	DET
cana-2105	290	7	parameter	parameter	NOUN
cana-2105	290	8	a	a	PRON
cana-2105	290	9	we	we	PRON
cana-2105	290	10	generate	generate	VERB
cana-2105	290	11	captivating	captivate	VERB
cana-2105	290	12	fractal	fractal	ADJ
cana-2105	290	13	patterns	pattern	NOUN
cana-2105	290	14	,	,	PUNCT
cana-2105	290	15	as	as	SCONJ
cana-2105	290	16	depicted	depict	VERB
cana-2105	290	17	in	in	ADP
cana-2105	290	18	figure	figure	NOUN
cana-2105	290	19	11	11	NUM
cana-2105	290	20	,	,	PUNCT
cana-2105	290	21	by	by	ADP
cana-2105	290	22	manipulating	manipulate	VERB
cana-2105	290	23	the	the	DET
cana-2105	290	24	parameter	parameter	NOUN
cana-2105	290	25	a.	a.	NOUN
cana-2105	290	26	when	when	SCONJ
cana-2105	290	27	a	a	PRON
cana-2105	290	28	is	be	AUX
cana-2105	290	29	a	a	DET
cana-2105	290	30	real	real	ADJ
cana-2105	290	31	number	number	NOUN
cana-2105	290	32	,	,	PUNCT
cana-2105	290	33	specifically	specifically	ADV
cana-2105	290	34	a	a	DET
cana-2105	290	35	=	=	SYM
cana-2105	290	36	−0.51	−0.51	NOUN
cana-2105	290	37	,	,	PUNCT
cana-2105	290	38	a	a	DET
cana-2105	290	39	prominent	prominent	ADJ
cana-2105	290	40	cardioid	cardioid	NOUN
cana-2105	290	41	shape	shape	NOUN
cana-2105	290	42	dominates	dominate	VERB
cana-2105	290	43	the	the	DET
cana-2105	290	44	center	center	NOUN
cana-2105	290	45	of	of	ADP
cana-2105	290	46	the	the	DET
cana-2105	290	47	mandelbrot	mandelbrot	NOUN
cana-2105	290	48	set	set	VERB
cana-2105	290	49	.	.	PUNCT
cana-2105	291	1	the	the	DET
cana-2105	291	2	size	size	NOUN
cana-2105	291	3	of	of	ADP
cana-2105	291	4	this	this	DET
cana-2105	291	5	cardioid	cardioid	NOUN
cana-2105	291	6	diminishes	diminish	VERB
cana-2105	291	7	continuously	continuously	ADV
cana-2105	291	8	along	along	ADP
cana-2105	291	9	the	the	DET
cana-2105	291	10	real	real	ADJ
cana-2105	291	11	axis	axis	NOUN
cana-2105	291	12	,	,	PUNCT
cana-2105	291	13	creating	create	VERB
cana-2105	291	14	a	a	DET
cana-2105	291	15	sequence	sequence	NOUN
cana-2105	291	16	of	of	ADP
cana-2105	291	17	progressively	progressively	ADV
cana-2105	291	18	smaller	small	ADJ
cana-2105	291	19	cardioids	cardioid	NOUN
cana-2105	291	20	.	.	PUNCT
cana-2105	292	1	as	as	ADP
cana-2105	292	2	a	a	DET
cana-2105	292	3	increases	increase	NOUN
cana-2105	292	4	,	,	PUNCT
cana-2105	292	5	the	the	DET
cana-2105	292	6	size	size	NOUN
cana-2105	292	7	of	of	ADP
cana-2105	292	8	the	the	DET
cana-2105	292	9	mandelbrot	mandelbrot	NOUN
cana-2105	292	10	set	set	VERB
cana-2105	292	11	decreases	decrease	NOUN
cana-2105	292	12	,	,	PUNCT
cana-2105	292	13	accompanied	accompany	VERB
cana-2105	292	14	by	by	ADP
cana-2105	292	15	a	a	DET
cana-2105	292	16	reduction	reduction	NOUN
cana-2105	292	17	in	in	ADP
cana-2105	292	18	the	the	DET
cana-2105	292	19	intensity	intensity	NOUN
cana-2105	292	20	of	of	ADP
cana-2105	292	21	the	the	DET
cana-2105	292	22	brown	brown	ADJ
cana-2105	292	23	color	color	NOUN
cana-2105	292	24	.	.	PUNCT
cana-2105	293	1	this	this	DET
cana-2105	293	2	decrease	decrease	NOUN
cana-2105	293	3	in	in	ADP
cana-2105	293	4	intensity	intensity	NOUN
cana-2105	293	5	signifies	signify	VERB
cana-2105	293	6	that	that	SCONJ
cana-2105	293	7	an	an	DET
cana-2105	293	8	increasing	increase	VERB
cana-2105	293	9	number	number	NOUN
cana-2105	293	10	of	of	ADP
cana-2105	293	11	points	point	NOUN
cana-2105	293	12	within	within	ADP
cana-2105	293	13	the	the	DET
cana-2105	293	14	considered	considered	ADJ
cana-2105	293	15	area	area	NOUN
cana-2105	293	16	escape	escape	VERB
cana-2105	293	17	to	to	PART
cana-2105	293	18	infinity	infinity	NOUN
cana-2105	293	19	as	as	ADP
cana-2105	293	20	a	a	DET
cana-2105	293	21	increases	increase	NOUN
cana-2105	293	22	.	.	PUNCT
cana-2105	294	1	each	each	DET
cana-2105	294	2	mandelbrot	mandelbrot	PROPN
cana-2105	294	3	set	set	VERB
cana-2105	294	4	,	,	PUNCT
cana-2105	294	5	corresponding	correspond	VERB
cana-2105	294	6	to	to	ADP
cana-2105	294	7	a	a	DET
cana-2105	294	8	real	real	ADJ
cana-2105	294	9	number	number	NOUN
cana-2105	294	10	a	a	NOUN
cana-2105	294	11	,	,	PUNCT
cana-2105	294	12	maintains	maintain	VERB
cana-2105	294	13	symmetry	symmetry	NOUN
cana-2105	294	14	about	about	ADP
cana-2105	294	15	the	the	DET
cana-2105	294	16	real	real	ADJ
cana-2105	294	17	axis	axis	NOUN
cana-2105	294	18	.	.	PUNCT
cana-2105	295	1	communications	communication	NOUN
cana-2105	295	2	on	on	ADP
cana-2105	295	3	applied	apply	VERB
cana-2105	295	4	nonlinear	nonlinear	ADJ
cana-2105	295	5	analysis	analysis	NOUN
cana-2105	295	6	issn	issn	NOUN
cana-2105	295	7	:	:	PUNCT
cana-2105	295	8	1074	1074	NUM
cana-2105	295	9	-	-	PUNCT
cana-2105	295	10	133x	133x	NUM
cana-2105	295	11	vol	vol	NOUN
cana-2105	295	12	32	32	NUM
cana-2105	295	13	no	no	NOUN
cana-2105	295	14	.	.	PUNCT
cana-2105	296	1	1s	1s	NUM
cana-2105	296	2	(	(	PUNCT
cana-2105	296	3	2025	2025	NUM
cana-2105	296	4	)	)	PUNCT
cana-2105	296	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	296	6	81	81	NUM
cana-2105	296	7	on	on	ADP
cana-2105	296	8	the	the	DET
cana-2105	296	9	other	other	ADJ
cana-2105	296	10	hand	hand	NOUN
cana-2105	296	11	,	,	PUNCT
cana-2105	296	12	when	when	SCONJ
cana-2105	296	13	a	a	PRON
cana-2105	296	14	is	be	AUX
cana-2105	296	15	a	a	DET
cana-2105	296	16	complex	complex	ADJ
cana-2105	296	17	number	number	NOUN
cana-2105	296	18	,	,	PUNCT
cana-2105	296	19	the	the	DET
cana-2105	296	20	symmetry	symmetry	NOUN
cana-2105	296	21	of	of	ADP
cana-2105	296	22	the	the	DET
cana-2105	296	23	mandelbrot	mandelbrot	NOUN
cana-2105	296	24	sets	set	NOUN
cana-2105	296	25	becomes	become	VERB
cana-2105	296	26	less	less	ADV
cana-2105	296	27	pronounced	pronounced	ADJ
cana-2105	296	28	,	,	PUNCT
cana-2105	296	29	introducing	introduce	VERB
cana-2105	296	30	twists	twist	NOUN
cana-2105	296	31	in	in	ADP
cana-2105	296	32	the	the	DET
cana-2105	296	33	patterns	pattern	NOUN
cana-2105	296	34	.	.	PUNCT
cana-2105	297	1	the	the	DET
cana-2105	297	2	resulting	result	VERB
cana-2105	297	3	images	image	NOUN
cana-2105	297	4	display	display	VERB
cana-2105	297	5	a	a	DET
cana-2105	297	6	more	more	ADV
cana-2105	297	7	chaotic	chaotic	ADJ
cana-2105	297	8	arrangement	arrangement	NOUN
cana-2105	297	9	,	,	PUNCT
cana-2105	297	10	making	make	VERB
cana-2105	297	11	interpreting	interpret	VERB
cana-2105	297	12	the	the	DET
cana-2105	297	13	details	detail	NOUN
cana-2105	297	14	difficult	difficult	ADJ
cana-2105	297	15	.	.	PUNCT
cana-2105	298	1	(	(	PUNCT
cana-2105	298	2	a	a	X
cana-2105	298	3	)	)	PUNCT
cana-2105	298	4	a	a	DET
cana-2105	298	5	=	=	X
cana-2105	298	6	−0.51	−0.51	X
cana-2105	298	7	(	(	PUNCT
cana-2105	298	8	b	b	NOUN
cana-2105	298	9	)	)	PUNCT
cana-2105	298	10	a	a	DET
cana-2105	298	11	=	=	SYM
cana-2105	298	12	0.5123	0.5123	NUM
cana-2105	298	13	(	(	PUNCT
cana-2105	298	14	c	c	X
cana-2105	298	15	)	)	PUNCT
cana-2105	299	1	a	a	DET
cana-2105	299	2	=	=	SYM
cana-2105	299	3	2.01	2.01	NUM
cana-2105	299	4	(	(	PUNCT
cana-2105	299	5	d	d	NOUN
cana-2105	299	6	)	)	PUNCT
cana-2105	299	7	a	a	DET
cana-2105	299	8	=	=	X
cana-2105	299	9	−i	−i	ADJ
cana-2105	299	10	(	(	PUNCT
cana-2105	299	11	e	e	NOUN
cana-2105	299	12	)	)	PUNCT
cana-2105	299	13	a	a	DET
cana-2105	299	14	=	=	SYM
cana-2105	299	15	0.5	0.5	NUM
cana-2105	299	16	+	+	CCONJ
cana-2105	299	17	0.31i	0.31i	PROPN
cana-2105	299	18	(	(	PUNCT
cana-2105	299	19	f	f	X
cana-2105	299	20	)	)	PUNCT
cana-2105	299	21	a	a	DET
cana-2105	299	22	=	=	SYM
cana-2105	299	23	−1−	−1−	PROPN
cana-2105	299	24	2i	2i	NUM
cana-2105	299	25	figure	figure	NOUN
cana-2105	299	26	11	11	NUM
cana-2105	299	27	:	:	PUNCT
cana-2105	299	28	the	the	DET
cana-2105	299	29	impact	impact	NOUN
cana-2105	299	30	on	on	ADP
cana-2105	299	31	julia	julia	PROPN
cana-2105	299	32	sets	set	NOUN
cana-2105	299	33	for	for	ADP
cana-2105	299	34	varying	vary	VERB
cana-2105	299	35	a	a	DET
cana-2105	299	36	4.2.2	4.2.2	NUM
cana-2105	299	37	mandelbrot	mandelbrot	NOUN
cana-2105	299	38	set	set	VERB
cana-2105	299	39	for	for	ADP
cana-2105	299	40	the	the	DET
cana-2105	299	41	function	function	NOUN
cana-2105	299	42	tcz	tcz	NOUN
cana-2105	299	43	=	=	SYM
cana-2105	299	44	sin(zk	sin(zk	NOUN
cana-2105	299	45	)	)	PUNCT
cana-2105	299	46	+	+	CCONJ
cana-2105	299	47	az	az	PROPN
cana-2105	299	48	+	+	CCONJ
cana-2105	299	49	c	c	NOUN
cana-2105	299	50	varying	vary	VERB
cana-2105	299	51	the	the	DET
cana-2105	299	52	parameter	parameter	NOUN
cana-2105	299	53	s	s	VERB
cana-2105	299	54	we	we	PRON
cana-2105	299	55	create	create	VERB
cana-2105	299	56	mesmerizing	mesmerizing	ADJ
cana-2105	299	57	fractal	fractal	ADJ
cana-2105	299	58	patterns	pattern	NOUN
cana-2105	299	59	,	,	PUNCT
cana-2105	299	60	as	as	SCONJ
cana-2105	299	61	showcased	showcase	VERB
cana-2105	299	62	in	in	ADP
cana-2105	299	63	figure	figure	NOUN
cana-2105	299	64	12	12	NUM
cana-2105	299	65	,	,	PUNCT
cana-2105	299	66	by	by	ADP
cana-2105	299	67	varying	vary	VERB
cana-2105	299	68	the	the	DET
cana-2105	299	69	parameter	parameter	NOUN
cana-2105	299	70	s.	s.	PROPN
cana-2105	299	71	for	for	ADP
cana-2105	299	72	each	each	DET
cana-2105	299	73	value	value	NOUN
cana-2105	299	74	of	of	ADP
cana-2105	299	75	s	s	NOUN
cana-2105	299	76	yields	yield	NOUN
cana-2105	299	77	,	,	PUNCT
cana-2105	299	78	mandelbrot	mandelbrot	PROPN
cana-2105	299	79	sets	set	VERB
cana-2105	299	80	that	that	PRON
cana-2105	299	81	exhibit	exhibit	VERB
cana-2105	299	82	a	a	DET
cana-2105	299	83	symmetrical	symmetrical	NOUN
cana-2105	299	84	about	about	ADP
cana-2105	299	85	the	the	DET
cana-2105	299	86	real	real	ADJ
cana-2105	299	87	axis	axis	NOUN
cana-2105	299	88	.	.	PUNCT
cana-2105	300	1	in	in	ADP
cana-2105	300	2	instances	instance	NOUN
cana-2105	300	3	where	where	SCONJ
cana-2105	300	4	s	s	VERB
cana-2105	300	5	is	be	AUX
cana-2105	300	6	close	close	ADJ
cana-2105	300	7	to	to	ADP
cana-2105	300	8	zero	zero	NUM
cana-2105	300	9	,	,	PUNCT
cana-2105	300	10	signifying	signify	VERB
cana-2105	300	11	a	a	DET
cana-2105	300	12	small	small	ADJ
cana-2105	300	13	value	value	NOUN
cana-2105	300	14	,	,	PUNCT
cana-2105	300	15	the	the	DET
cana-2105	300	16	resulting	result	VERB
cana-2105	300	17	mandelbrot	mandelbrot	NOUN
cana-2105	300	18	sets	set	NOUN
cana-2105	300	19	are	be	AUX
cana-2105	300	20	characterized	characterize	VERB
cana-2105	300	21	by	by	ADP
cana-2105	300	22	reduced	reduced	ADJ
cana-2105	300	23	size	size	NOUN
cana-2105	300	24	,	,	PUNCT
cana-2105	300	25	indicating	indicate	VERB
cana-2105	300	26	most	most	ADJ
cana-2105	300	27	points	point	NOUN
cana-2105	300	28	within	within	ADP
cana-2105	300	29	the	the	DET
cana-2105	300	30	defined	define	VERB
cana-2105	300	31	area	area	NOUN
cana-2105	300	32	escape	escape	VERB
cana-2105	300	33	to	to	ADP
cana-2105	300	34	infinity	infinity	NOUN
cana-2105	300	35	.	.	PUNCT
cana-2105	301	1	as	as	SCONJ
cana-2105	301	2	we	we	PRON
cana-2105	301	3	increment	increment	VERB
cana-2105	301	4	the	the	DET
cana-2105	301	5	value	value	NOUN
cana-2105	301	6	of	of	ADP
cana-2105	301	7	s	s	PROPN
cana-2105	301	8	,	,	PUNCT
cana-2105	301	9	the	the	DET
cana-2105	301	10	size	size	NOUN
cana-2105	301	11	of	of	ADP
cana-2105	301	12	the	the	DET
cana-2105	301	13	mandelbrot	mandelbrot	NOUN
cana-2105	301	14	sets	set	VERB
cana-2105	301	15	gradually	gradually	ADV
cana-2105	301	16	enlarges	enlarge	VERB
cana-2105	301	17	.	.	PUNCT
cana-2105	302	1	simultaneously	simultaneously	ADV
cana-2105	302	2	,	,	PUNCT
cana-2105	302	3	there	there	PRON
cana-2105	302	4	is	be	VERB
cana-2105	302	5	a	a	DET
cana-2105	302	6	discernible	discernible	ADJ
cana-2105	302	7	augmentation	augmentation	NOUN
cana-2105	302	8	in	in	ADP
cana-2105	302	9	the	the	DET
cana-2105	302	10	intensity	intensity	NOUN
cana-2105	302	11	of	of	ADP
cana-2105	302	12	the	the	DET
cana-2105	302	13	brown	brown	ADJ
cana-2105	302	14	color	color	NOUN
cana-2105	302	15	,	,	PUNCT
cana-2105	302	16	creating	create	VERB
cana-2105	302	17	a	a	DET
cana-2105	302	18	visually	visually	ADV
cana-2105	302	19	dynamic	dynamic	ADJ
cana-2105	302	20	effect	effect	NOUN
cana-2105	302	21	.	.	PUNCT
cana-2105	303	1	eventually	eventually	ADV
cana-2105	303	2	,	,	PUNCT
cana-2105	303	3	when	when	SCONJ
cana-2105	303	4	s	s	NOUN
cana-2105	303	5	approaches	approach	VERB
cana-2105	303	6	a	a	DET
cana-2105	303	7	value	value	NOUN
cana-2105	303	8	close	close	ADV
cana-2105	303	9	to	to	ADP
cana-2105	303	10	1	1	NUM
cana-2105	303	11	,	,	PUNCT
cana-2105	303	12	the	the	DET
cana-2105	303	13	entire	entire	ADJ
cana-2105	303	14	mandelbrot	mandelbrot	NOUN
cana-2105	303	15	set	set	VERB
cana-2105	303	16	adopts	adopt	VERB
cana-2105	303	17	a	a	DET
cana-2105	303	18	uniform	uniform	ADJ
cana-2105	303	19	brown	brown	ADJ
cana-2105	303	20	hue	hue	NOUN
cana-2105	303	21	,	,	PUNCT
cana-2105	303	22	providing	provide	VERB
cana-2105	303	23	a	a	DET
cana-2105	303	24	fascinating	fascinating	ADJ
cana-2105	303	25	visual	visual	ADJ
cana-2105	303	26	outcome	outcome	NOUN
cana-2105	303	27	.	.	PUNCT
cana-2105	304	1	communications	communication	NOUN
cana-2105	304	2	on	on	ADP
cana-2105	304	3	applied	apply	VERB
cana-2105	304	4	nonlinear	nonlinear	ADJ
cana-2105	304	5	analysis	analysis	NOUN
cana-2105	304	6	issn	issn	NOUN
cana-2105	304	7	:	:	PUNCT
cana-2105	304	8	1074	1074	NUM
cana-2105	304	9	-	-	PUNCT
cana-2105	304	10	133x	133x	NUM
cana-2105	304	11	vol	vol	NOUN
cana-2105	304	12	32	32	NUM
cana-2105	304	13	no	no	NOUN
cana-2105	304	14	.	.	PUNCT
cana-2105	305	1	1s	1s	NUM
cana-2105	305	2	(	(	PUNCT
cana-2105	305	3	2025	2025	NUM
cana-2105	305	4	)	)	PUNCT
cana-2105	305	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	305	6	82	82	NUM
cana-2105	305	7	(	(	PUNCT
cana-2105	305	8	a	a	NOUN
cana-2105	305	9	)	)	PUNCT
cana-2105	305	10	s	s	PART
cana-2105	305	11	=	=	SYM
cana-2105	305	12	0.001	0.001	NUM
cana-2105	305	13	(	(	PUNCT
cana-2105	305	14	b	b	NOUN
cana-2105	305	15	)	)	PUNCT
cana-2105	305	16	s	s	PART
cana-2105	305	17	=	=	NOUN
cana-2105	305	18	0.013	0.013	NUM
cana-2105	305	19	(	(	PUNCT
cana-2105	305	20	c	c	NOUN
cana-2105	305	21	)	)	PUNCT
cana-2105	305	22	s	s	PART
cana-2105	305	23	=	=	VERB
cana-2105	305	24	0.241	0.241	NUM
cana-2105	305	25	(	(	PUNCT
cana-2105	305	26	d	d	NOUN
cana-2105	305	27	)	)	PUNCT
cana-2105	305	28	s	s	PART
cana-2105	305	29	=	=	SYM
cana-2105	305	30	0.513	0.513	NUM
cana-2105	305	31	(	(	PUNCT
cana-2105	305	32	e	e	NOUN
cana-2105	305	33	)	)	PUNCT
cana-2105	305	34	s	s	PART
cana-2105	305	35	=	=	SYM
cana-2105	305	36	0.764	0.764	NUM
cana-2105	305	37	(	(	PUNCT
cana-2105	305	38	f	f	X
cana-2105	305	39	)	)	PUNCT
cana-2105	305	40	s	s	PART
cana-2105	305	41	=	=	SYM
cana-2105	305	42	0.986	0.986	NUM
cana-2105	305	43	figure	figure	NOUN
cana-2105	305	44	12	12	NUM
cana-2105	305	45	:	:	PUNCT
cana-2105	305	46	the	the	DET
cana-2105	305	47	impact	impact	NOUN
cana-2105	305	48	on	on	ADP
cana-2105	305	49	mandelbrot	mandelbrot	NOUN
cana-2105	305	50	sets	set	NOUN
cana-2105	305	51	for	for	ADP
cana-2105	305	52	varying	vary	VERB
cana-2105	305	53	the	the	DET
cana-2105	305	54	parameter	parameter	NOUN
cana-2105	305	55	s	s	PART
cana-2105	305	56	4.2.3	4.2.3	PROPN
cana-2105	305	57	mandelbrot	mandelbrot	NOUN
cana-2105	305	58	set	set	VERB
cana-2105	305	59	for	for	ADP
cana-2105	305	60	the	the	DET
cana-2105	305	61	function	function	NOUN
cana-2105	305	62	tcz	tcz	NOUN
cana-2105	305	63	=	=	SYM
cana-2105	305	64	sin(zk	sin(zk	NOUN
cana-2105	305	65	)	)	PUNCT
cana-2105	306	1	+	+	CCONJ
cana-2105	306	2	az	az	PROPN
cana-2105	306	3	+	+	CCONJ
cana-2105	306	4	c	c	NOUN
cana-2105	306	5	varying	vary	VERB
cana-2105	306	6	the	the	DET
cana-2105	306	7	parameter	parameter	NOUN
cana-2105	306	8	α	α	PRON
cana-2105	306	9	we	we	PRON
cana-2105	306	10	generate	generate	VERB
cana-2105	306	11	captivating	captivate	VERB
cana-2105	306	12	fractal	fractal	ADJ
cana-2105	306	13	patterns	pattern	NOUN
cana-2105	306	14	,	,	PUNCT
cana-2105	306	15	as	as	SCONJ
cana-2105	306	16	depicted	depict	VERB
cana-2105	306	17	in	in	ADP
cana-2105	306	18	figure	figure	NOUN
cana-2105	306	19	13	13	NUM
cana-2105	306	20	,	,	PUNCT
cana-2105	306	21	by	by	ADP
cana-2105	306	22	adjusting	adjust	VERB
cana-2105	306	23	the	the	DET
cana-2105	306	24	parameter	parameter	NOUN
cana-2105	306	25	α	α	NOUN
cana-2105	306	26	.	.	PUNCT
cana-2105	307	1	each	each	DET
cana-2105	307	2	specific	specific	ADJ
cana-2105	307	3	value	value	NOUN
cana-2105	307	4	of	of	ADP
cana-2105	307	5	α	α	PROPN
cana-2105	307	6	produces	produce	VERB
cana-2105	307	7	mandelbrot	mandelbrot	NOUN
cana-2105	307	8	sets	set	NOUN
cana-2105	307	9	with	with	ADP
cana-2105	307	10	symmetrical	symmetrical	ADJ
cana-2105	307	11	arrangements	arrangement	NOUN
cana-2105	307	12	about	about	ADP
cana-2105	307	13	the	the	DET
cana-2105	307	14	real	real	ADJ
cana-2105	307	15	axis	axis	NOUN
cana-2105	307	16	.	.	PUNCT
cana-2105	308	1	notably	notably	ADV
cana-2105	308	2	,	,	PUNCT
cana-2105	308	3	when	when	SCONJ
cana-2105	308	4	α	α	PROPN
cana-2105	308	5	is	be	AUX
cana-2105	308	6	close	close	ADJ
cana-2105	308	7	to	to	ADP
cana-2105	308	8	zero	zero	NUM
cana-2105	308	9	,	,	PUNCT
cana-2105	308	10	signifying	signify	VERB
cana-2105	308	11	a	a	DET
cana-2105	308	12	small	small	ADJ
cana-2105	308	13	value	value	NOUN
cana-2105	308	14	,	,	PUNCT
cana-2105	308	15	the	the	DET
cana-2105	308	16	resulting	result	VERB
cana-2105	308	17	mandelbrot	mandelbrot	NOUN
cana-2105	308	18	sets	set	NOUN
cana-2105	308	19	are	be	AUX
cana-2105	308	20	characterized	characterize	VERB
cana-2105	308	21	by	by	ADP
cana-2105	308	22	a	a	DET
cana-2105	308	23	significant	significant	ADJ
cana-2105	308	24	size	size	NOUN
cana-2105	308	25	,	,	PUNCT
cana-2105	308	26	showcasing	showcase	VERB
cana-2105	308	27	a	a	DET
cana-2105	308	28	remarkable	remarkable	ADJ
cana-2105	308	29	structure	structure	NOUN
cana-2105	308	30	reminiscent	reminiscent	ADJ
cana-2105	308	31	of	of	ADP
cana-2105	308	32	beautiful	beautiful	ADJ
cana-2105	308	33	,	,	PUNCT
cana-2105	308	34	hair	hair	NOUN
cana-2105	308	35	-	-	PUNCT
cana-2105	308	36	like	like	ADJ
cana-2105	308	37	patterns	pattern	NOUN
cana-2105	308	38	.	.	PUNCT
cana-2105	309	1	the	the	DET
cana-2105	309	2	entire	entire	ADJ
cana-2105	309	3	set	set	NOUN
cana-2105	309	4	is	be	AUX
cana-2105	309	5	adorned	adorn	VERB
cana-2105	309	6	with	with	ADP
cana-2105	309	7	a	a	DET
cana-2105	309	8	rich	rich	ADJ
cana-2105	309	9	brown	brown	ADJ
cana-2105	309	10	color	color	NOUN
cana-2105	309	11	,	,	PUNCT
cana-2105	309	12	creating	create	VERB
cana-2105	309	13	an	an	DET
cana-2105	309	14	aesthetically	aesthetically	ADV
cana-2105	309	15	pleasing	pleasing	ADJ
cana-2105	309	16	and	and	CCONJ
cana-2105	309	17	intricate	intricate	ADJ
cana-2105	309	18	design	design	NOUN
cana-2105	309	19	.	.	PUNCT
cana-2105	310	1	as	as	ADP
cana-2105	310	2	α	α	NOUN
cana-2105	310	3	increases	increase	NOUN
cana-2105	310	4	,	,	PUNCT
cana-2105	310	5	a	a	DET
cana-2105	310	6	notable	notable	ADJ
cana-2105	310	7	transformation	transformation	NOUN
cana-2105	310	8	occurs	occur	VERB
cana-2105	310	9	.	.	PUNCT
cana-2105	311	1	the	the	DET
cana-2105	311	2	size	size	NOUN
cana-2105	311	3	of	of	ADP
cana-2105	311	4	the	the	DET
cana-2105	311	5	mandelbrot	mandelbrot	NOUN
cana-2105	311	6	sets	set	VERB
cana-2105	311	7	gradually	gradually	ADV
cana-2105	311	8	diminishes	diminish	VERB
cana-2105	311	9	,	,	PUNCT
cana-2105	311	10	accompanied	accompany	VERB
cana-2105	311	11	by	by	ADP
cana-2105	311	12	an	an	DET
cana-2105	311	13	increase	increase	NOUN
cana-2105	311	14	in	in	ADP
cana-2105	311	15	the	the	DET
cana-2105	311	16	intensity	intensity	NOUN
cana-2105	311	17	of	of	ADP
cana-2105	311	18	the	the	DET
cana-2105	311	19	sky	sky	NOUN
cana-2105	311	20	-	-	PUNCT
cana-2105	311	21	blue	blue	ADJ
cana-2105	311	22	hue	hue	NOUN
cana-2105	311	23	along	along	ADP
cana-2105	311	24	the	the	DET
cana-2105	311	25	boundary	boundary	NOUN
cana-2105	311	26	of	of	ADP
cana-2105	311	27	the	the	DET
cana-2105	311	28	sets	set	NOUN
cana-2105	311	29	.	.	PUNCT
cana-2105	312	1	this	this	DET
cana-2105	312	2	alteration	alteration	NOUN
cana-2105	312	3	in	in	ADP
cana-2105	312	4	color	color	NOUN
cana-2105	312	5	dynamics	dynamic	NOUN
cana-2105	312	6	adds	add	VERB
cana-2105	312	7	a	a	DET
cana-2105	312	8	captivating	captivating	ADJ
cana-2105	312	9	contrast	contrast	NOUN
cana-2105	312	10	to	to	ADP
cana-2105	312	11	the	the	DET
cana-2105	312	12	fractal	fractal	ADJ
cana-2105	312	13	patterns	pattern	NOUN
cana-2105	312	14	.	.	PUNCT
cana-2105	313	1	when	when	SCONJ
cana-2105	313	2	α	α	PROPN
cana-2105	313	3	approaches	approach	VERB
cana-2105	313	4	a	a	DET
cana-2105	313	5	value	value	NOUN
cana-2105	313	6	near	near	ADP
cana-2105	313	7	1	1	NUM
cana-2105	313	8	,	,	PUNCT
cana-2105	313	9	a	a	DET
cana-2105	313	10	distinct	distinct	ADJ
cana-2105	313	11	visual	visual	ADJ
cana-2105	313	12	effect	effect	NOUN
cana-2105	313	13	emerges	emerge	VERB
cana-2105	313	14	.	.	PUNCT
cana-2105	314	1	the	the	DET
cana-2105	314	2	mandelbrot	mandelbrot	PROPN
cana-2105	314	3	set	set	VERB
cana-2105	314	4	becomes	become	VERB
cana-2105	314	5	disconnected	disconnected	ADJ
cana-2105	314	6	and	and	CCONJ
cana-2105	314	7	elongated	elongate	VERB
cana-2105	314	8	along	along	ADP
cana-2105	314	9	the	the	DET
cana-2105	314	10	real	real	ADJ
cana-2105	314	11	axis	axis	NOUN
cana-2105	314	12	,	,	PUNCT
cana-2105	314	13	presenting	present	VERB
cana-2105	314	14	a	a	DET
cana-2105	314	15	unique	unique	ADJ
cana-2105	314	16	and	and	CCONJ
cana-2105	314	17	intriguing	intriguing	ADJ
cana-2105	314	18	characteristic	characteristic	ADJ
cana-2105	314	19	that	that	PRON
cana-2105	314	20	sets	set	VERB
cana-2105	314	21	it	it	PRON
cana-2105	314	22	apart	apart	ADV
cana-2105	314	23	from	from	ADP
cana-2105	314	24	the	the	DET
cana-2105	314	25	patterns	pattern	NOUN
cana-2105	314	26	observed	observe	VERB
cana-2105	314	27	at	at	ADP
cana-2105	314	28	lower	low	ADJ
cana-2105	314	29	α	α	NOUN
cana-2105	314	30	values	value	NOUN
cana-2105	314	31	.	.	PUNCT
cana-2105	315	1	this	this	DET
cana-2105	315	2	variation	variation	NOUN
cana-2105	315	3	in	in	ADP
cana-2105	315	4	structure	structure	NOUN
cana-2105	315	5	and	and	CCONJ
cana-2105	315	6	coloration	coloration	NOUN
cana-2105	315	7	showcases	showcase	VERB
cana-2105	315	8	the	the	DET
cana-2105	315	9	sensitivity	sensitivity	NOUN
cana-2105	315	10	of	of	ADP
cana-2105	315	11	the	the	DET
cana-2105	315	12	fractal	fractal	ADJ
cana-2105	315	13	patterns	pattern	NOUN
cana-2105	315	14	to	to	ADP
cana-2105	315	15	changes	change	NOUN
cana-2105	315	16	in	in	ADP
cana-2105	315	17	the	the	DET
cana-2105	315	18	parameter	parameter	NOUN
cana-2105	315	19	α	α	PROPN
cana-2105	315	20	.	.	PUNCT
cana-2105	316	1	communications	communication	NOUN
cana-2105	316	2	on	on	ADP
cana-2105	316	3	applied	apply	VERB
cana-2105	316	4	nonlinear	nonlinear	ADJ
cana-2105	316	5	analysis	analysis	NOUN
cana-2105	316	6	issn	issn	NOUN
cana-2105	316	7	:	:	PUNCT
cana-2105	316	8	1074	1074	NUM
cana-2105	316	9	-	-	PUNCT
cana-2105	316	10	133x	133x	NUM
cana-2105	316	11	vol	vol	NOUN
cana-2105	316	12	32	32	NUM
cana-2105	316	13	no	no	NOUN
cana-2105	316	14	.	.	PUNCT
cana-2105	317	1	1s	1s	NUM
cana-2105	317	2	(	(	PUNCT
cana-2105	317	3	2025	2025	NUM
cana-2105	317	4	)	)	PUNCT
cana-2105	317	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	317	6	83	83	NUM
cana-2105	317	7	(	(	PUNCT
cana-2105	317	8	a	a	NOUN
cana-2105	317	9	)	)	PUNCT
cana-2105	317	10	α	α	NOUN
cana-2105	317	11	=	=	SYM
cana-2105	317	12	0.0001	0.0001	NUM
cana-2105	317	13	(	(	PUNCT
cana-2105	317	14	b	b	NOUN
cana-2105	317	15	)	)	PUNCT
cana-2105	317	16	α	α	NOUN
cana-2105	318	1	=	=	NOUN
cana-2105	318	2	0.003	0.003	NUM
cana-2105	318	3	(	(	PUNCT
cana-2105	318	4	c	c	NOUN
cana-2105	318	5	)	)	PUNCT
cana-2105	318	6	α	α	NOUN
cana-2105	318	7	=	=	NOUN
cana-2105	318	8	0.213	0.213	NUM
cana-2105	318	9	(	(	PUNCT
cana-2105	318	10	d	d	NOUN
cana-2105	318	11	)	)	PUNCT
cana-2105	318	12	α	α	NOUN
cana-2105	318	13	=	=	SYM
cana-2105	318	14	0.513	0.513	NUM
cana-2105	318	15	(	(	PUNCT
cana-2105	318	16	e	e	NOUN
cana-2105	318	17	)	)	PUNCT
cana-2105	318	18	α	α	NOUN
cana-2105	318	19	=	=	SYM
cana-2105	318	20	751	751	NUM
cana-2105	318	21	(	(	PUNCT
cana-2105	318	22	f	f	X
cana-2105	318	23	)	)	PUNCT
cana-2105	318	24	α	α	NOUN
cana-2105	318	25	=	=	SYM
cana-2105	318	26	1	1	NUM
cana-2105	318	27	figure	figure	NOUN
cana-2105	318	28	13	13	NUM
cana-2105	318	29	:	:	PUNCT
cana-2105	318	30	the	the	DET
cana-2105	318	31	impact	impact	NOUN
cana-2105	318	32	on	on	ADP
cana-2105	318	33	mandelbrot	mandelbrot	NOUN
cana-2105	318	34	sets	set	NOUN
cana-2105	318	35	for	for	ADP
cana-2105	318	36	varying	vary	VERB
cana-2105	318	37	the	the	DET
cana-2105	318	38	parameter	parameter	NOUN
cana-2105	319	1	α	α	PROPN
cana-2105	319	2	4.2.4	4.2.4	NUM
cana-2105	319	3	mandelbrot	mandelbrot	NOUN
cana-2105	319	4	set	set	VERB
cana-2105	319	5	for	for	ADP
cana-2105	319	6	the	the	DET
cana-2105	319	7	function	function	NOUN
cana-2105	319	8	tcz	tcz	NOUN
cana-2105	319	9	=	=	SYM
cana-2105	319	10	sin(zk	sin(zk	NOUN
cana-2105	319	11	)	)	PUNCT
cana-2105	320	1	+	+	CCONJ
cana-2105	320	2	az	az	PROPN
cana-2105	320	3	+	+	CCONJ
cana-2105	320	4	c	c	NOUN
cana-2105	320	5	varying	vary	VERB
cana-2105	320	6	the	the	DET
cana-2105	320	7	parameter	parameter	NOUN
cana-2105	320	8	β	β	NOUN
cana-2105	320	9	we	we	PRON
cana-2105	320	10	generate	generate	VERB
cana-2105	320	11	captivating	captivate	VERB
cana-2105	320	12	fractal	fractal	ADJ
cana-2105	320	13	patterns	pattern	NOUN
cana-2105	320	14	,	,	PUNCT
cana-2105	320	15	as	as	SCONJ
cana-2105	320	16	illustrated	illustrate	VERB
cana-2105	320	17	in	in	ADP
cana-2105	320	18	figure	figure	NOUN
cana-2105	320	19	14	14	NUM
cana-2105	320	20	,	,	PUNCT
cana-2105	320	21	by	by	ADP
cana-2105	320	22	manipulating	manipulate	VERB
cana-2105	320	23	the	the	DET
cana-2105	320	24	parameter	parameter	NOUN
cana-2105	320	25	β	β	NOUN
cana-2105	320	26	.	.	PUNCT
cana-2105	321	1	each	each	DET
cana-2105	321	2	specific	specific	ADJ
cana-2105	321	3	value	value	NOUN
cana-2105	321	4	of	of	ADP
cana-2105	321	5	β	β	PROPN
cana-2105	321	6	results	result	NOUN
cana-2105	321	7	in	in	ADP
cana-2105	321	8	mandelbrot	mandelbrot	NOUN
cana-2105	321	9	sets	set	NOUN
cana-2105	321	10	exhibiting	exhibit	VERB
cana-2105	321	11	symmetrical	symmetrical	ADJ
cana-2105	321	12	arrangements	arrangement	NOUN
cana-2105	321	13	about	about	ADP
cana-2105	321	14	the	the	DET
cana-2105	321	15	real	real	ADJ
cana-2105	321	16	axis	axis	NOUN
cana-2105	321	17	.	.	PUNCT
cana-2105	322	1	when	when	SCONJ
cana-2105	322	2	β	β	X
cana-2105	322	3	is	be	AUX
cana-2105	322	4	close	close	ADJ
cana-2105	322	5	to	to	ADP
cana-2105	322	6	zero	zero	NUM
cana-2105	322	7	,	,	PUNCT
cana-2105	322	8	the	the	DET
cana-2105	322	9	resulting	result	VERB
cana-2105	322	10	mandelbrot	mandelbrot	NOUN
cana-2105	322	11	sets	set	VERB
cana-2105	322	12	showcase	showcase	VERB
cana-2105	322	13	a	a	DET
cana-2105	322	14	substantial	substantial	ADJ
cana-2105	322	15	size	size	NOUN
cana-2105	322	16	,	,	PUNCT
cana-2105	322	17	featuring	feature	VERB
cana-2105	322	18	two	two	NUM
cana-2105	322	19	prominent	prominent	ADJ
cana-2105	322	20	sky	sky	NOUN
cana-2105	322	21	-	-	PUNCT
cana-2105	322	22	blue	blue	ADJ
cana-2105	322	23	lashes	lash	NOUN
cana-2105	322	24	along	along	ADP
cana-2105	322	25	the	the	DET
cana-2105	322	26	imaginary	imaginary	ADJ
cana-2105	322	27	axis	axis	NOUN
cana-2105	322	28	.	.	PUNCT
cana-2105	323	1	the	the	DET
cana-2105	323	2	entirety	entirety	NOUN
cana-2105	323	3	of	of	ADP
cana-2105	323	4	the	the	DET
cana-2105	323	5	set	set	NOUN
cana-2105	323	6	is	be	AUX
cana-2105	323	7	adorned	adorn	VERB
cana-2105	323	8	with	with	ADP
cana-2105	323	9	a	a	DET
cana-2105	323	10	rich	rich	ADJ
cana-2105	323	11	brown	brown	ADJ
cana-2105	323	12	color	color	NOUN
cana-2105	323	13	,	,	PUNCT
cana-2105	323	14	contributing	contribute	VERB
cana-2105	323	15	to	to	ADP
cana-2105	323	16	an	an	DET
cana-2105	323	17	aesthetically	aesthetically	ADV
cana-2105	323	18	pleasing	pleasing	ADJ
cana-2105	323	19	and	and	CCONJ
cana-2105	323	20	intricate	intricate	ADJ
cana-2105	323	21	design	design	NOUN
cana-2105	323	22	.	.	PUNCT
cana-2105	324	1	as	as	ADP
cana-2105	324	2	β	β	NOUN
cana-2105	324	3	increases	increase	NOUN
cana-2105	324	4	,	,	PUNCT
cana-2105	324	5	a	a	DET
cana-2105	324	6	significant	significant	ADJ
cana-2105	324	7	transformation	transformation	NOUN
cana-2105	324	8	unfolds	unfold	VERB
cana-2105	324	9	.	.	PUNCT
cana-2105	325	1	the	the	DET
cana-2105	325	2	size	size	NOUN
cana-2105	325	3	of	of	ADP
cana-2105	325	4	the	the	DET
cana-2105	325	5	mandelbrot	mandelbrot	NOUN
cana-2105	325	6	sets	set	VERB
cana-2105	325	7	gradually	gradually	ADV
cana-2105	325	8	diminishes	diminish	VERB
cana-2105	325	9	,	,	PUNCT
cana-2105	325	10	concurrent	concurrent	ADJ
cana-2105	325	11	with	with	ADP
cana-2105	325	12	an	an	DET
cana-2105	325	13	intensification	intensification	NOUN
cana-2105	325	14	of	of	ADP
cana-2105	325	15	the	the	DET
cana-2105	325	16	sky	sky	NOUN
cana-2105	325	17	-	-	PUNCT
cana-2105	325	18	blue	blue	ADJ
cana-2105	325	19	hue	hue	NOUN
cana-2105	325	20	along	along	ADP
cana-2105	325	21	the	the	DET
cana-2105	325	22	sets	set	NOUN
cana-2105	325	23	’	'	PUNCT
cana-2105	325	24	boundaries	boundary	NOUN
cana-2105	325	25	.	.	PUNCT
cana-2105	326	1	this	this	DET
cana-2105	326	2	shift	shift	NOUN
cana-2105	326	3	in	in	ADP
cana-2105	326	4	color	color	NOUN
cana-2105	326	5	dynamics	dynamic	NOUN
cana-2105	326	6	introduces	introduce	VERB
cana-2105	326	7	a	a	DET
cana-2105	326	8	captivating	captivating	ADJ
cana-2105	326	9	contrast	contrast	NOUN
cana-2105	326	10	to	to	ADP
cana-2105	326	11	the	the	DET
cana-2105	326	12	fractal	fractal	ADJ
cana-2105	326	13	patterns	pattern	NOUN
cana-2105	326	14	.	.	PUNCT
cana-2105	327	1	a	a	DET
cana-2105	327	2	distinct	distinct	ADJ
cana-2105	327	3	visual	visual	ADJ
cana-2105	327	4	effect	effect	NOUN
cana-2105	327	5	emerges	emerge	VERB
cana-2105	327	6	as	as	SCONJ
cana-2105	327	7	β	β	PROPN
cana-2105	327	8	approaches	approach	VERB
cana-2105	327	9	a	a	DET
cana-2105	327	10	value	value	NOUN
cana-2105	327	11	near	near	ADP
cana-2105	327	12	1	1	NUM
cana-2105	327	13	.	.	PUNCT
cana-2105	328	1	the	the	DET
cana-2105	328	2	mandelbrot	mandelbrot	NOUN
cana-2105	328	3	set	set	VERB
cana-2105	328	4	takes	take	VERB
cana-2105	328	5	on	on	ADP
cana-2105	328	6	a	a	DET
cana-2105	328	7	disconnected	disconnected	ADJ
cana-2105	328	8	and	and	CCONJ
cana-2105	328	9	elongated	elongate	VERB
cana-2105	328	10	form	form	NOUN
cana-2105	328	11	along	along	ADP
cana-2105	328	12	the	the	DET
cana-2105	328	13	real	real	ADJ
cana-2105	328	14	axis	axis	NOUN
cana-2105	328	15	,	,	PUNCT
cana-2105	328	16	and	and	CCONJ
cana-2105	328	17	small	small	ADJ
cana-2105	328	18	dot	dot	NOUN
cana-2105	328	19	-	-	PUNCT
cana-2105	328	20	like	like	ADJ
cana-2105	328	21	structures	structure	NOUN
cana-2105	328	22	in	in	ADP
cana-2105	328	23	yellow	yellow	ADJ
cana-2105	328	24	color	color	NOUN
cana-2105	328	25	become	become	VERB
cana-2105	328	26	apparent	apparent	ADJ
cana-2105	328	27	on	on	ADP
cana-2105	328	28	the	the	DET
cana-2105	328	29	outer	outer	ADJ
cana-2105	328	30	parts	part	NOUN
cana-2105	328	31	of	of	ADP
cana-2105	328	32	the	the	DET
cana-2105	328	33	mandelbrot	mandelbrot	NOUN
cana-2105	328	34	sets	set	VERB
cana-2105	328	35	.	.	PUNCT
cana-2105	329	1	this	this	DET
cana-2105	329	2	variation	variation	NOUN
cana-2105	329	3	in	in	ADP
cana-2105	329	4	structure	structure	NOUN
cana-2105	329	5	and	and	CCONJ
cana-2105	329	6	coloration	coloration	NOUN
cana-2105	329	7	underscores	underscore	VERB
cana-2105	329	8	the	the	DET
cana-2105	329	9	sensitivity	sensitivity	NOUN
cana-2105	329	10	of	of	ADP
cana-2105	329	11	the	the	DET
cana-2105	329	12	fractal	fractal	ADJ
cana-2105	329	13	patterns	pattern	NOUN
cana-2105	329	14	to	to	ADP
cana-2105	329	15	alterations	alteration	NOUN
cana-2105	329	16	in	in	ADP
cana-2105	329	17	the	the	DET
cana-2105	329	18	parameter	parameter	NOUN
cana-2105	329	19	β	β	NOUN
cana-2105	329	20	.	.	PUNCT
cana-2105	329	21	communications	communication	NOUN
cana-2105	329	22	on	on	ADP
cana-2105	329	23	applied	apply	VERB
cana-2105	329	24	nonlinear	nonlinear	ADJ
cana-2105	329	25	analysis	analysis	NOUN
cana-2105	329	26	issn	issn	NOUN
cana-2105	329	27	:	:	PUNCT
cana-2105	329	28	1074	1074	NUM
cana-2105	329	29	-	-	PUNCT
cana-2105	329	30	133x	133x	NUM
cana-2105	329	31	vol	vol	NOUN
cana-2105	329	32	32	32	NUM
cana-2105	329	33	no	no	NOUN
cana-2105	329	34	.	.	PUNCT
cana-2105	330	1	1s	1s	NUM
cana-2105	330	2	(	(	PUNCT
cana-2105	330	3	2025	2025	NUM
cana-2105	330	4	)	)	PUNCT
cana-2105	330	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	330	6	84	84	NUM
cana-2105	330	7	(	(	PUNCT
cana-2105	330	8	a	a	NOUN
cana-2105	330	9	)	)	PUNCT
cana-2105	330	10	β	β	NOUN
cana-2105	330	11	=	=	PUNCT
cana-2105	330	12	0.0001	0.0001	NUM
cana-2105	330	13	(	(	PUNCT
cana-2105	330	14	b	b	NOUN
cana-2105	330	15	)	)	PUNCT
cana-2105	330	16	β	β	NOUN
cana-2105	330	17	=	=	NOUN
cana-2105	330	18	0.004	0.004	NUM
cana-2105	330	19	(	(	PUNCT
cana-2105	330	20	c	c	NOUN
cana-2105	330	21	)	)	PUNCT
cana-2105	330	22	β	β	NOUN
cana-2105	330	23	=	=	PUNCT
cana-2105	330	24	0.321	0.321	NUM
cana-2105	330	25	(	(	PUNCT
cana-2105	330	26	d	d	NOUN
cana-2105	330	27	)	)	PUNCT
cana-2105	330	28	β	β	NOUN
cana-2105	331	1	=	=	NOUN
cana-2105	331	2	0.497	0.497	NUM
cana-2105	331	3	(	(	PUNCT
cana-2105	331	4	e	e	NOUN
cana-2105	331	5	)	)	PUNCT
cana-2105	331	6	β	β	NOUN
cana-2105	331	7	=	=	SYM
cana-2105	331	8	0.803	0.803	NUM
cana-2105	331	9	(	(	PUNCT
cana-2105	331	10	f	f	X
cana-2105	331	11	)	)	PUNCT
cana-2105	331	12	β	β	NOUN
cana-2105	331	13	=	=	SYM
cana-2105	331	14	0.975	0.975	NUM
cana-2105	331	15	figure	figure	NOUN
cana-2105	331	16	14	14	NUM
cana-2105	331	17	:	:	PUNCT
cana-2105	331	18	the	the	DET
cana-2105	331	19	impact	impact	NOUN
cana-2105	331	20	on	on	ADP
cana-2105	331	21	mandelbrot	mandelbrot	NOUN
cana-2105	331	22	sets	set	NOUN
cana-2105	331	23	for	for	ADP
cana-2105	331	24	varying	vary	VERB
cana-2105	331	25	the	the	DET
cana-2105	331	26	parameter	parameter	NOUN
cana-2105	331	27	β	β	PROPN
cana-2105	331	28	4.2.5	4.2.5	NUM
cana-2105	331	29	mandelbrot	mandelbrot	NOUN
cana-2105	331	30	set	set	VERB
cana-2105	331	31	for	for	ADP
cana-2105	331	32	the	the	DET
cana-2105	331	33	function	function	NOUN
cana-2105	331	34	tcz	tcz	NOUN
cana-2105	331	35	=	=	SYM
cana-2105	331	36	sin(zk	sin(zk	NOUN
cana-2105	331	37	)	)	PUNCT
cana-2105	331	38	+	+	CCONJ
cana-2105	331	39	az	az	PROPN
cana-2105	331	40	+	+	CCONJ
cana-2105	331	41	c	c	NOUN
cana-2105	331	42	varying	vary	VERB
cana-2105	331	43	the	the	DET
cana-2105	331	44	parameter	parameter	NOUN
cana-2105	331	45	γ	γ	NOUN
cana-2105	331	46	we	we	PRON
cana-2105	331	47	create	create	VERB
cana-2105	331	48	captivating	captivate	VERB
cana-2105	331	49	fractal	fractal	ADJ
cana-2105	331	50	patterns	pattern	NOUN
cana-2105	331	51	,	,	PUNCT
cana-2105	331	52	as	as	SCONJ
cana-2105	331	53	depicted	depict	VERB
cana-2105	331	54	in	in	ADP
cana-2105	331	55	figure	figure	NOUN
cana-2105	331	56	15	15	NUM
cana-2105	331	57	,	,	PUNCT
cana-2105	331	58	by	by	ADP
cana-2105	331	59	varying	vary	VERB
cana-2105	331	60	the	the	DET
cana-2105	331	61	parameter	parameter	NOUN
cana-2105	331	62	γ	γ	PROPN
cana-2105	331	63	.	.	PUNCT
cana-2105	331	64	each	each	DET
cana-2105	331	65	specific	specific	ADJ
cana-2105	331	66	value	value	NOUN
cana-2105	331	67	of	of	ADP
cana-2105	331	68	γ	γ	PROPN
cana-2105	331	69	gives	give	VERB
cana-2105	331	70	rise	rise	NOUN
cana-2105	331	71	to	to	ADP
cana-2105	331	72	mandelbrot	mandelbrot	PROPN
cana-2105	331	73	sets	set	NOUN
cana-2105	331	74	that	that	PRON
cana-2105	331	75	exhibit	exhibit	VERB
cana-2105	331	76	symmetrical	symmetrical	ADJ
cana-2105	331	77	arrangements	arrangement	NOUN
cana-2105	331	78	about	about	ADP
cana-2105	331	79	the	the	DET
cana-2105	331	80	real	real	ADJ
cana-2105	331	81	axis	axis	NOUN
cana-2105	331	82	.	.	PUNCT
cana-2105	332	1	when	when	SCONJ
cana-2105	332	2	γ	γ	X
cana-2105	332	3	is	be	AUX
cana-2105	332	4	close	close	ADJ
cana-2105	332	5	to	to	ADP
cana-2105	332	6	zero	zero	NUM
cana-2105	332	7	,	,	PUNCT
cana-2105	332	8	the	the	DET
cana-2105	332	9	resulting	result	VERB
cana-2105	332	10	mandelbrot	mandelbrot	NOUN
cana-2105	332	11	sets	set	NOUN
cana-2105	332	12	display	display	VERB
cana-2105	332	13	a	a	DET
cana-2105	332	14	significant	significant	ADJ
cana-2105	332	15	size	size	NOUN
cana-2105	332	16	,	,	PUNCT
cana-2105	332	17	featuring	feature	VERB
cana-2105	332	18	two	two	NUM
cana-2105	332	19	prominent	prominent	ADJ
cana-2105	332	20	sky	sky	NOUN
cana-2105	332	21	-	-	PUNCT
cana-2105	332	22	blue	blue	ADJ
cana-2105	332	23	lashes	lash	NOUN
cana-2105	332	24	along	along	ADP
cana-2105	332	25	the	the	DET
cana-2105	332	26	imaginary	imaginary	ADJ
cana-2105	332	27	axis	axis	NOUN
cana-2105	332	28	.	.	PUNCT
cana-2105	333	1	the	the	DET
cana-2105	333	2	entire	entire	ADJ
cana-2105	333	3	set	set	NOUN
cana-2105	333	4	is	be	AUX
cana-2105	333	5	adorned	adorn	VERB
cana-2105	333	6	with	with	ADP
cana-2105	333	7	a	a	DET
cana-2105	333	8	rich	rich	ADJ
cana-2105	333	9	brown	brown	ADJ
cana-2105	333	10	color	color	NOUN
cana-2105	333	11	,	,	PUNCT
cana-2105	333	12	contributing	contribute	VERB
cana-2105	333	13	to	to	ADP
cana-2105	333	14	an	an	DET
cana-2105	333	15	aesthetically	aesthetically	ADV
cana-2105	333	16	pleasing	pleasing	ADJ
cana-2105	333	17	and	and	CCONJ
cana-2105	333	18	intricate	intricate	ADJ
cana-2105	333	19	design	design	NOUN
cana-2105	333	20	.	.	PUNCT
cana-2105	334	1	this	this	DET
cana-2105	334	2	configuration	configuration	NOUN
cana-2105	334	3	showcases	showcase	VERB
cana-2105	334	4	the	the	DET
cana-2105	334	5	sensitivity	sensitivity	NOUN
cana-2105	334	6	of	of	ADP
cana-2105	334	7	the	the	DET
cana-2105	334	8	fractal	fractal	ADJ
cana-2105	334	9	patterns	pattern	NOUN
cana-2105	334	10	to	to	ADP
cana-2105	334	11	variations	variation	NOUN
cana-2105	334	12	in	in	ADP
cana-2105	334	13	the	the	DET
cana-2105	334	14	parameter	parameter	NOUN
cana-2105	334	15	γ	γ	PROPN
cana-2105	334	16	,	,	PUNCT
cana-2105	334	17	producing	produce	VERB
cana-2105	334	18	visually	visually	ADV
cana-2105	334	19	dynamic	dynamic	ADJ
cana-2105	334	20	and	and	CCONJ
cana-2105	334	21	appealing	appealing	ADJ
cana-2105	334	22	results	result	NOUN
cana-2105	334	23	.	.	PUNCT
cana-2105	335	1	with	with	ADP
cana-2105	335	2	an	an	DET
cana-2105	335	3	increase	increase	NOUN
cana-2105	335	4	in	in	ADP
cana-2105	335	5	γ	γ	PROPN
cana-2105	335	6	,	,	PUNCT
cana-2105	335	7	the	the	DET
cana-2105	335	8	size	size	NOUN
cana-2105	335	9	of	of	ADP
cana-2105	335	10	the	the	DET
cana-2105	335	11	mandelbrot	mandelbrot	NOUN
cana-2105	335	12	sets	set	VERB
cana-2105	335	13	gradually	gradually	ADV
cana-2105	335	14	decreases	decrease	VERB
cana-2105	335	15	,	,	PUNCT
cana-2105	335	16	accompanied	accompany	VERB
cana-2105	335	17	by	by	ADP
cana-2105	335	18	an	an	DET
cana-2105	335	19	intensification	intensification	NOUN
cana-2105	335	20	of	of	ADP
cana-2105	335	21	the	the	DET
cana-2105	335	22	sky	sky	NOUN
cana-2105	335	23	-	-	PUNCT
cana-2105	335	24	blue	blue	ADJ
cana-2105	335	25	hue	hue	NOUN
cana-2105	335	26	along	along	ADP
cana-2105	335	27	the	the	DET
cana-2105	335	28	boundaries	boundary	NOUN
cana-2105	335	29	of	of	ADP
cana-2105	335	30	the	the	DET
cana-2105	335	31	sets	set	NOUN
cana-2105	335	32	.	.	PUNCT
cana-2105	336	1	this	this	DET
cana-2105	336	2	alteration	alteration	NOUN
cana-2105	336	3	in	in	ADP
cana-2105	336	4	color	color	NOUN
cana-2105	336	5	dynamics	dynamic	NOUN
cana-2105	336	6	introduces	introduce	VERB
cana-2105	336	7	a	a	DET
cana-2105	336	8	captivating	captivating	ADJ
cana-2105	336	9	contrast	contrast	NOUN
cana-2105	336	10	to	to	ADP
cana-2105	336	11	the	the	DET
cana-2105	336	12	fractal	fractal	ADJ
cana-2105	336	13	patterns	pattern	NOUN
cana-2105	336	14	.	.	PUNCT
cana-2105	337	1	a	a	DET
cana-2105	337	2	distinct	distinct	ADJ
cana-2105	337	3	visual	visual	ADJ
cana-2105	337	4	effect	effect	NOUN
cana-2105	337	5	emerges	emerge	VERB
cana-2105	337	6	as	as	SCONJ
cana-2105	337	7	γ	γ	PROPN
cana-2105	337	8	approaches	approach	VERB
cana-2105	337	9	a	a	DET
cana-2105	337	10	value	value	NOUN
cana-2105	337	11	near	near	ADP
cana-2105	337	12	1	1	NUM
cana-2105	337	13	,	,	PUNCT
cana-2105	337	14	and	and	CCONJ
cana-2105	337	15	small	small	ADJ
cana-2105	337	16	dot	dot	NOUN
cana-2105	337	17	-	-	PUNCT
cana-2105	337	18	like	like	ADJ
cana-2105	337	19	structures	structure	NOUN
cana-2105	337	20	in	in	ADP
cana-2105	337	21	yellow	yellow	ADJ
cana-2105	337	22	color	color	NOUN
cana-2105	337	23	become	become	VERB
cana-2105	337	24	apparent	apparent	ADJ
cana-2105	337	25	on	on	ADP
cana-2105	337	26	the	the	DET
cana-2105	337	27	outer	outer	ADJ
cana-2105	337	28	parts	part	NOUN
cana-2105	337	29	of	of	ADP
cana-2105	337	30	the	the	DET
cana-2105	337	31	mandelbrot	mandelbrot	NOUN
cana-2105	337	32	sets	set	VERB
cana-2105	337	33	.	.	PUNCT
cana-2105	338	1	this	this	DET
cana-2105	338	2	variation	variation	NOUN
cana-2105	338	3	in	in	ADP
cana-2105	338	4	structure	structure	NOUN
cana-2105	338	5	and	and	CCONJ
cana-2105	338	6	coloration	coloration	NOUN
cana-2105	338	7	highlights	highlight	VERB
cana-2105	338	8	the	the	DET
cana-2105	338	9	sensitivity	sensitivity	NOUN
cana-2105	338	10	of	of	ADP
cana-2105	338	11	the	the	DET
cana-2105	338	12	fractal	fractal	ADJ
cana-2105	338	13	patterns	pattern	NOUN
cana-2105	338	14	to	to	ADP
cana-2105	338	15	changes	change	NOUN
cana-2105	338	16	in	in	ADP
cana-2105	338	17	the	the	DET
cana-2105	338	18	parameter	parameter	NOUN
cana-2105	338	19	γ	γ	PROPN
cana-2105	338	20	,	,	PUNCT
cana-2105	338	21	resulting	result	VERB
cana-2105	338	22	in	in	ADP
cana-2105	338	23	visually	visually	ADV
cana-2105	338	24	dynamic	dynamic	ADJ
cana-2105	338	25	and	and	CCONJ
cana-2105	338	26	intriguing	intriguing	ADJ
cana-2105	338	27	patterns	pattern	NOUN
cana-2105	338	28	.	.	PUNCT
cana-2105	339	1	communications	communication	NOUN
cana-2105	339	2	on	on	ADP
cana-2105	339	3	applied	apply	VERB
cana-2105	339	4	nonlinear	nonlinear	ADJ
cana-2105	339	5	analysis	analysis	NOUN
cana-2105	339	6	issn	issn	NOUN
cana-2105	339	7	:	:	PUNCT
cana-2105	339	8	1074	1074	NUM
cana-2105	339	9	-	-	PUNCT
cana-2105	339	10	133x	133x	NUM
cana-2105	339	11	vol	vol	NOUN
cana-2105	339	12	32	32	NUM
cana-2105	339	13	no	no	NOUN
cana-2105	339	14	.	.	PUNCT
cana-2105	340	1	1s	1s	NUM
cana-2105	340	2	(	(	PUNCT
cana-2105	340	3	2025	2025	NUM
cana-2105	340	4	)	)	PUNCT
cana-2105	340	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	340	6	85	85	NUM
cana-2105	340	7	(	(	PUNCT
cana-2105	340	8	a	a	NOUN
cana-2105	340	9	)	)	PUNCT
cana-2105	340	10	γ	γ	NOUN
cana-2105	340	11	=	=	SYM
cana-2105	340	12	0.0001	0.0001	NUM
cana-2105	340	13	(	(	PUNCT
cana-2105	340	14	b	b	NOUN
cana-2105	340	15	)	)	PUNCT
cana-2105	340	16	γ	γ	NOUN
cana-2105	340	17	=	=	SYM
cana-2105	340	18	0.002	0.002	NUM
cana-2105	340	19	(	(	PUNCT
cana-2105	340	20	c	c	NOUN
cana-2105	340	21	)	)	PUNCT
cana-2105	340	22	γ	γ	NOUN
cana-2105	340	23	=	=	SYM
cana-2105	340	24	0.356	0.356	NUM
cana-2105	340	25	(	(	PUNCT
cana-2105	340	26	d	d	NOUN
cana-2105	340	27	)	)	PUNCT
cana-2105	340	28	γ	γ	NOUN
cana-2105	340	29	=	=	SYM
cana-2105	340	30	0.557	0.557	NUM
cana-2105	340	31	(	(	PUNCT
cana-2105	340	32	e	e	NOUN
cana-2105	340	33	)	)	PUNCT
cana-2105	340	34	γ	γ	NOUN
cana-2105	340	35	=	=	SYM
cana-2105	340	36	0.796	0.796	NUM
cana-2105	340	37	(	(	PUNCT
cana-2105	340	38	f	f	X
cana-2105	340	39	)	)	PUNCT
cana-2105	340	40	γ	γ	NOUN
cana-2105	340	41	=	=	SYM
cana-2105	340	42	1	1	NUM
cana-2105	340	43	figure	figure	NOUN
cana-2105	340	44	15	15	NUM
cana-2105	340	45	:	:	PUNCT
cana-2105	340	46	the	the	DET
cana-2105	340	47	impact	impact	NOUN
cana-2105	340	48	on	on	ADP
cana-2105	340	49	mandelbrot	mandelbrot	NOUN
cana-2105	340	50	sets	set	NOUN
cana-2105	340	51	for	for	ADP
cana-2105	340	52	varying	vary	VERB
cana-2105	340	53	the	the	DET
cana-2105	340	54	parameter	parameter	NOUN
cana-2105	340	55	γ	γ	X
cana-2105	340	56	4.2.6	4.2.6	PROPN
cana-2105	340	57	mandelbrot	mandelbrot	NOUN
cana-2105	340	58	set	set	VERB
cana-2105	340	59	for	for	ADP
cana-2105	340	60	the	the	DET
cana-2105	340	61	function	function	NOUN
cana-2105	340	62	tcz	tcz	NOUN
cana-2105	340	63	=	=	SYM
cana-2105	340	64	sin(zk	sin(zk	NOUN
cana-2105	340	65	)	)	PUNCT
cana-2105	341	1	+	+	CCONJ
cana-2105	341	2	az	az	PROPN
cana-2105	341	3	+	+	CCONJ
cana-2105	341	4	c	c	NOUN
cana-2105	341	5	varying	vary	VERB
cana-2105	341	6	the	the	DET
cana-2105	341	7	parameter	parameter	NOUN
cana-2105	341	8	δ	δ	PROPN
cana-2105	341	9	we	we	PRON
cana-2105	341	10	generate	generate	VERB
cana-2105	341	11	captivating	captivate	VERB
cana-2105	341	12	fractal	fractal	ADJ
cana-2105	341	13	patterns	pattern	NOUN
cana-2105	341	14	,	,	PUNCT
cana-2105	341	15	as	as	SCONJ
cana-2105	341	16	illustrated	illustrate	VERB
cana-2105	341	17	in	in	ADP
cana-2105	341	18	figure	figure	NOUN
cana-2105	341	19	16	16	NUM
cana-2105	341	20	,	,	PUNCT
cana-2105	341	21	by	by	ADP
cana-2105	341	22	varying	vary	VERB
cana-2105	341	23	the	the	DET
cana-2105	341	24	parameter	parameter	PROPN
cana-2105	341	25	δ	δ	PROPN
cana-2105	341	26	.	.	PUNCT
cana-2105	342	1	each	each	DET
cana-2105	342	2	δ	δ	PROPN
cana-2105	342	3	results	result	VERB
cana-2105	342	4	in	in	ADP
cana-2105	342	5	mandelbrot	mandelbrot	NOUN
cana-2105	342	6	sets	set	NOUN
cana-2105	342	7	that	that	PRON
cana-2105	342	8	exhibit	exhibit	VERB
cana-2105	342	9	symmetrical	symmetrical	ADJ
cana-2105	342	10	arrangements	arrangement	NOUN
cana-2105	342	11	about	about	ADP
cana-2105	342	12	the	the	DET
cana-2105	342	13	real	real	ADJ
cana-2105	342	14	axis	axis	NOUN
cana-2105	342	15	.	.	PUNCT
cana-2105	343	1	when	when	SCONJ
cana-2105	343	2	δ	δ	PROPN
cana-2105	343	3	is	be	AUX
cana-2105	343	4	close	close	ADJ
cana-2105	343	5	to	to	ADP
cana-2105	343	6	zero	zero	NUM
cana-2105	343	7	,	,	PUNCT
cana-2105	343	8	the	the	DET
cana-2105	343	9	resulting	result	VERB
cana-2105	343	10	mandelbrot	mandelbrot	NOUN
cana-2105	343	11	sets	set	VERB
cana-2105	343	12	showcase	showcase	NOUN
cana-2105	343	13	a	a	DET
cana-2105	343	14	significant	significant	ADJ
cana-2105	343	15	size	size	NOUN
cana-2105	343	16	,	,	PUNCT
cana-2105	343	17	featuring	feature	VERB
cana-2105	343	18	two	two	NUM
cana-2105	343	19	prominent	prominent	ADJ
cana-2105	343	20	sky	sky	NOUN
cana-2105	343	21	-	-	PUNCT
cana-2105	343	22	blue	blue	ADJ
cana-2105	343	23	lashes	lash	NOUN
cana-2105	343	24	along	along	ADP
cana-2105	343	25	the	the	DET
cana-2105	343	26	imaginary	imaginary	ADJ
cana-2105	343	27	axis	axis	NOUN
cana-2105	343	28	.	.	PUNCT
cana-2105	344	1	the	the	DET
cana-2105	344	2	entire	entire	ADJ
cana-2105	344	3	set	set	NOUN
cana-2105	344	4	is	be	AUX
cana-2105	344	5	adorned	adorn	VERB
cana-2105	344	6	with	with	ADP
cana-2105	344	7	a	a	DET
cana-2105	344	8	rich	rich	ADJ
cana-2105	344	9	brown	brown	ADJ
cana-2105	344	10	color	color	NOUN
cana-2105	344	11	,	,	PUNCT
cana-2105	344	12	contributing	contribute	VERB
cana-2105	344	13	to	to	ADP
cana-2105	344	14	an	an	DET
cana-2105	344	15	aesthetically	aesthetically	ADV
cana-2105	344	16	pleasing	pleasing	ADJ
cana-2105	344	17	and	and	CCONJ
cana-2105	344	18	intricate	intricate	ADJ
cana-2105	344	19	design	design	NOUN
cana-2105	344	20	.	.	PUNCT
cana-2105	345	1	as	as	SCONJ
cana-2105	345	2	δ	δ	PROPN
cana-2105	345	3	increases	increase	NOUN
cana-2105	345	4	,	,	PUNCT
cana-2105	345	5	the	the	DET
cana-2105	345	6	size	size	NOUN
cana-2105	345	7	of	of	ADP
cana-2105	345	8	the	the	DET
cana-2105	345	9	mandelbrot	mandelbrot	NOUN
cana-2105	345	10	sets	set	VERB
cana-2105	345	11	gradually	gradually	ADV
cana-2105	345	12	diminishes	diminish	VERB
cana-2105	345	13	,	,	PUNCT
cana-2105	345	14	accompanied	accompany	VERB
cana-2105	345	15	by	by	ADP
cana-2105	345	16	an	an	DET
cana-2105	345	17	intensification	intensification	NOUN
cana-2105	345	18	of	of	ADP
cana-2105	345	19	the	the	DET
cana-2105	345	20	sky	sky	NOUN
cana-2105	345	21	-	-	PUNCT
cana-2105	345	22	blue	blue	ADJ
cana-2105	345	23	hue	hue	NOUN
cana-2105	345	24	along	along	ADP
cana-2105	345	25	the	the	DET
cana-2105	345	26	boundaries	boundary	NOUN
cana-2105	345	27	of	of	ADP
cana-2105	345	28	the	the	DET
cana-2105	345	29	sets	set	NOUN
cana-2105	345	30	.	.	PUNCT
cana-2105	346	1	a	a	DET
cana-2105	346	2	distinct	distinct	ADJ
cana-2105	346	3	visual	visual	ADJ
cana-2105	346	4	effect	effect	NOUN
cana-2105	346	5	emerges	emerge	VERB
cana-2105	346	6	as	as	SCONJ
cana-2105	346	7	δ	δ	PROPN
cana-2105	346	8	approaches	approach	VERB
cana-2105	346	9	a	a	DET
cana-2105	346	10	value	value	NOUN
cana-2105	346	11	near	near	ADP
cana-2105	346	12	1	1	NUM
cana-2105	346	13	,	,	PUNCT
cana-2105	346	14	and	and	CCONJ
cana-2105	346	15	small	small	ADJ
cana-2105	346	16	dot	dot	NOUN
cana-2105	346	17	-	-	PUNCT
cana-2105	346	18	like	like	ADJ
cana-2105	346	19	structures	structure	NOUN
cana-2105	346	20	in	in	ADP
cana-2105	346	21	yellow	yellow	ADJ
cana-2105	346	22	color	color	NOUN
cana-2105	346	23	become	become	VERB
cana-2105	346	24	apparent	apparent	ADJ
cana-2105	346	25	on	on	ADP
cana-2105	346	26	the	the	DET
cana-2105	346	27	outer	outer	ADJ
cana-2105	346	28	parts	part	NOUN
cana-2105	346	29	of	of	ADP
cana-2105	346	30	the	the	DET
cana-2105	346	31	mandelbrot	mandelbrot	NOUN
cana-2105	346	32	sets	set	VERB
cana-2105	346	33	.	.	PUNCT
cana-2105	347	1	this	this	DET
cana-2105	347	2	variation	variation	NOUN
cana-2105	347	3	in	in	ADP
cana-2105	347	4	structure	structure	NOUN
cana-2105	347	5	and	and	CCONJ
cana-2105	347	6	coloration	coloration	NOUN
cana-2105	347	7	highlights	highlight	VERB
cana-2105	347	8	the	the	DET
cana-2105	347	9	sensitivity	sensitivity	NOUN
cana-2105	347	10	of	of	ADP
cana-2105	347	11	the	the	DET
cana-2105	347	12	fractal	fractal	ADJ
cana-2105	347	13	patterns	pattern	NOUN
cana-2105	347	14	to	to	ADP
cana-2105	347	15	changes	change	NOUN
cana-2105	347	16	in	in	ADP
cana-2105	347	17	the	the	DET
cana-2105	347	18	parameter	parameter	PROPN
cana-2105	347	19	δ	δ	PROPN
cana-2105	347	20	,	,	PUNCT
cana-2105	347	21	resulting	result	VERB
cana-2105	347	22	in	in	ADP
cana-2105	347	23	visually	visually	ADV
cana-2105	347	24	dynamic	dynamic	ADJ
cana-2105	347	25	and	and	CCONJ
cana-2105	347	26	intriguing	intriguing	ADJ
cana-2105	347	27	patterns	pattern	NOUN
cana-2105	347	28	.	.	PUNCT
cana-2105	348	1	communications	communication	NOUN
cana-2105	348	2	on	on	ADP
cana-2105	348	3	applied	apply	VERB
cana-2105	348	4	nonlinear	nonlinear	ADJ
cana-2105	348	5	analysis	analysis	NOUN
cana-2105	348	6	issn	issn	NOUN
cana-2105	348	7	:	:	PUNCT
cana-2105	348	8	1074	1074	NUM
cana-2105	348	9	-	-	PUNCT
cana-2105	348	10	133x	133x	NUM
cana-2105	348	11	vol	vol	NOUN
cana-2105	348	12	32	32	NUM
cana-2105	348	13	no	no	NOUN
cana-2105	348	14	.	.	PUNCT
cana-2105	349	1	1s	1s	NUM
cana-2105	349	2	(	(	PUNCT
cana-2105	349	3	2025	2025	NUM
cana-2105	349	4	)	)	PUNCT
cana-2105	349	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	349	6	86	86	NUM
cana-2105	349	7	(	(	PUNCT
cana-2105	349	8	a	a	NOUN
cana-2105	349	9	)	)	PUNCT
cana-2105	349	10	δ	δ	NOUN
cana-2105	349	11	=	=	PUNCT
cana-2105	350	1	0.00001	0.00001	NUM
cana-2105	350	2	(	(	PUNCT
cana-2105	350	3	b	b	NOUN
cana-2105	350	4	)	)	PUNCT
cana-2105	350	5	δ	δ	NOUN
cana-2105	350	6	=	=	NOUN
cana-2105	350	7	0.01	0.01	NUM
cana-2105	350	8	(	(	PUNCT
cana-2105	350	9	c	c	NOUN
cana-2105	350	10	)	)	PUNCT
cana-2105	350	11	δ	δ	X
cana-2105	350	12	=	=	NOUN
cana-2105	351	1	0.38	0.38	NUM
cana-2105	351	2	(	(	PUNCT
cana-2105	351	3	d	d	NOUN
cana-2105	351	4	)	)	PUNCT
cana-2105	351	5	δ	δ	X
cana-2105	351	6	=	=	PUNCT
cana-2105	351	7	0.478	0.478	NUM
cana-2105	351	8	(	(	PUNCT
cana-2105	351	9	e	e	NOUN
cana-2105	351	10	)	)	PUNCT
cana-2105	351	11	δ	δ	X
cana-2105	351	12	=	=	PUNCT
cana-2105	351	13	0.809	0.809	NUM
cana-2105	351	14	(	(	PUNCT
cana-2105	351	15	f	f	X
cana-2105	351	16	)	)	PUNCT
cana-2105	351	17	δ	δ	NOUN
cana-2105	351	18	=	=	SYM
cana-2105	351	19	1	1	NUM
cana-2105	351	20	figure	figure	NOUN
cana-2105	351	21	16	16	NUM
cana-2105	351	22	:	:	PUNCT
cana-2105	351	23	the	the	DET
cana-2105	351	24	impact	impact	NOUN
cana-2105	351	25	on	on	ADP
cana-2105	351	26	mandelbrot	mandelbrot	NOUN
cana-2105	351	27	sets	set	NOUN
cana-2105	351	28	for	for	ADP
cana-2105	351	29	varying	vary	VERB
cana-2105	351	30	the	the	DET
cana-2105	351	31	parameter	parameter	NOUN
cana-2105	351	32	δ	δ	PROPN
cana-2105	351	33	4.2.7	4.2.7	NUM
cana-2105	351	34	mandelbrot	mandelbrot	NOUN
cana-2105	351	35	set	set	VERB
cana-2105	351	36	for	for	ADP
cana-2105	351	37	the	the	DET
cana-2105	351	38	function	function	NOUN
cana-2105	351	39	tcz	tcz	NOUN
cana-2105	351	40	=	=	SYM
cana-2105	351	41	sin(zk	sin(zk	NOUN
cana-2105	351	42	)	)	PUNCT
cana-2105	352	1	+	+	CCONJ
cana-2105	352	2	az	az	PROPN
cana-2105	352	3	+	+	CCONJ
cana-2105	352	4	c	c	NOUN
cana-2105	352	5	varying	vary	VERB
cana-2105	352	6	the	the	DET
cana-2105	352	7	parameter	parameter	NOUN
cana-2105	353	1	k	k	PROPN
cana-2105	354	1	we	we	PRON
cana-2105	354	2	generate	generate	VERB
cana-2105	354	3	captivating	captivate	VERB
cana-2105	354	4	fractal	fractal	ADJ
cana-2105	354	5	patterns	pattern	NOUN
cana-2105	354	6	,	,	PUNCT
cana-2105	354	7	as	as	SCONJ
cana-2105	354	8	showcased	showcase	VERB
cana-2105	354	9	in	in	ADP
cana-2105	354	10	figure	figure	NOUN
cana-2105	354	11	17	17	NUM
cana-2105	354	12	,	,	PUNCT
cana-2105	354	13	by	by	ADP
cana-2105	354	14	varying	vary	VERB
cana-2105	354	15	the	the	DET
cana-2105	354	16	parameter	parameter	NOUN
cana-2105	354	17	k.	k.	PROPN
cana-2105	355	1	the	the	DET
cana-2105	355	2	behavior	behavior	NOUN
cana-2105	355	3	of	of	ADP
cana-2105	355	4	the	the	DET
cana-2105	355	5	mandelbrot	mandelbrot	NOUN
cana-2105	355	6	sets	set	VERB
cana-2105	355	7	is	be	AUX
cana-2105	355	8	contingent	contingent	ADJ
cana-2105	355	9	on	on	ADP
cana-2105	355	10	whether	whether	SCONJ
cana-2105	355	11	k	k	PROPN
cana-2105	355	12	is	be	AUX
cana-2105	355	13	an	an	DET
cana-2105	355	14	even	even	ADV
cana-2105	355	15	or	or	CCONJ
cana-2105	355	16	odd	odd	ADJ
cana-2105	355	17	natural	natural	ADJ
cana-2105	355	18	number	number	NOUN
cana-2105	355	19	.	.	PUNCT
cana-2105	356	1	for	for	ADP
cana-2105	356	2	even	even	ADV
cana-2105	356	3	values	value	NOUN
cana-2105	356	4	of	of	ADP
cana-2105	356	5	k	k	NOUN
cana-2105	356	6	,	,	PUNCT
cana-2105	356	7	the	the	DET
cana-2105	356	8	resulting	result	VERB
cana-2105	356	9	fractals	fractal	NOUN
cana-2105	356	10	display	display	NOUN
cana-2105	356	11	symmetry	symmetry	NOUN
cana-2105	356	12	solely	solely	ADV
cana-2105	356	13	concerning	concern	VERB
cana-2105	356	14	the	the	DET
cana-2105	356	15	real	real	ADJ
cana-2105	356	16	axis	axis	NOUN
cana-2105	356	17	.	.	PUNCT
cana-2105	357	1	in	in	ADP
cana-2105	357	2	contrast	contrast	NOUN
cana-2105	357	3	,	,	PUNCT
cana-2105	357	4	when	when	SCONJ
cana-2105	357	5	k	k	PROPN
cana-2105	357	6	is	be	AUX
cana-2105	357	7	an	an	DET
cana-2105	357	8	odd	odd	ADJ
cana-2105	357	9	natural	natural	ADJ
cana-2105	357	10	number	number	NOUN
cana-2105	357	11	,	,	PUNCT
cana-2105	357	12	the	the	DET
cana-2105	357	13	mandelbrot	mandelbrot	NOUN
cana-2105	357	14	sets	set	VERB
cana-2105	357	15	exhibit	exhibit	VERB
cana-2105	357	16	symmetrical	symmetrical	ADJ
cana-2105	357	17	characteristics	characteristic	NOUN
cana-2105	357	18	about	about	ADP
cana-2105	357	19	both	both	CCONJ
cana-2105	357	20	the	the	DET
cana-2105	357	21	real	real	ADJ
cana-2105	357	22	and	and	CCONJ
cana-2105	357	23	imaginary	imaginary	ADJ
cana-2105	357	24	axes	axis	NOUN
cana-2105	357	25	.	.	PUNCT
cana-2105	358	1	for	for	ADP
cana-2105	358	2	the	the	DET
cana-2105	358	3	specific	specific	ADJ
cana-2105	358	4	case	case	NOUN
cana-2105	358	5	of	of	ADP
cana-2105	358	6	k	k	PROPN
cana-2105	358	7	=	=	SYM
cana-2105	358	8	3	3	NUM
cana-2105	358	9	,	,	PUNCT
cana-2105	358	10	the	the	DET
cana-2105	358	11	fractals	fractal	NOUN
cana-2105	358	12	have	have	VERB
cana-2105	358	13	a	a	DET
cana-2105	358	14	unique	unique	ADJ
cana-2105	358	15	appearance	appearance	NOUN
cana-2105	358	16	reminiscent	reminiscent	ADJ
cana-2105	358	17	of	of	ADP
cana-2105	358	18	a	a	DET
cana-2105	358	19	brown	brown	ADJ
cana-2105	358	20	spider	spider	NOUN
cana-2105	358	21	-	-	PUNCT
cana-2105	358	22	like	like	ADJ
cana-2105	358	23	shape	shape	NOUN
cana-2105	358	24	.	.	PUNCT
cana-2105	359	1	as	as	ADP
cana-2105	359	2	the	the	DET
cana-2105	359	3	parameter	parameter	NOUN
cana-2105	359	4	k	k	PROPN
cana-2105	359	5	increases	increase	NOUN
cana-2105	359	6	,	,	PUNCT
cana-2105	359	7	there	there	PRON
cana-2105	359	8	is	be	VERB
cana-2105	359	9	a	a	DET
cana-2105	359	10	noticeable	noticeable	ADJ
cana-2105	359	11	reduction	reduction	NOUN
cana-2105	359	12	in	in	ADP
cana-2105	359	13	the	the	DET
cana-2105	359	14	size	size	NOUN
cana-2105	359	15	of	of	ADP
cana-2105	359	16	the	the	DET
cana-2105	359	17	mandelbrot	mandelbrot	NOUN
cana-2105	359	18	sets	set	VERB
cana-2105	359	19	.	.	PUNCT
cana-2105	360	1	the	the	DET
cana-2105	360	2	sets	set	NOUN
cana-2105	360	3	transform	transform	VERB
cana-2105	360	4	into	into	ADP
cana-2105	360	5	circular	circular	ADJ
cana-2105	360	6	shapes	shape	NOUN
cana-2105	360	7	,	,	PUNCT
cana-2105	360	8	and	and	CCONJ
cana-2105	360	9	the	the	DET
cana-2105	360	10	number	number	NOUN
cana-2105	360	11	of	of	ADP
cana-2105	360	12	primary	primary	ADJ
cana-2105	360	13	lashes	lash	NOUN
cana-2105	360	14	corresponds	correspond	VERB
cana-2105	360	15	to	to	ADP
cana-2105	360	16	k−	k−	PROPN
cana-2105	360	17	1	1	NUM
cana-2105	360	18	.	.	PUNCT
cana-2105	361	1	additionally	additionally	ADV
cana-2105	361	2	,	,	PUNCT
cana-2105	361	3	intricate	intricate	ADJ
cana-2105	361	4	structures	structure	NOUN
cana-2105	361	5	emerge	emerge	VERB
cana-2105	361	6	at	at	ADP
cana-2105	361	7	the	the	DET
cana-2105	361	8	tips	tip	NOUN
cana-2105	361	9	of	of	ADP
cana-2105	361	10	each	each	DET
cana-2105	361	11	lash	lash	NOUN
cana-2105	361	12	,	,	PUNCT
cana-2105	361	13	adding	add	VERB
cana-2105	361	14	complexity	complexity	NOUN
cana-2105	361	15	to	to	ADP
cana-2105	361	16	the	the	DET
cana-2105	361	17	overall	overall	ADJ
cana-2105	361	18	visual	visual	ADJ
cana-2105	361	19	composition	composition	NOUN
cana-2105	361	20	.	.	PUNCT
cana-2105	362	1	this	this	DET
cana-2105	362	2	detailed	detailed	ADJ
cana-2105	362	3	variation	variation	NOUN
cana-2105	362	4	in	in	ADP
cana-2105	362	5	the	the	DET
cana-2105	362	6	value	value	NOUN
cana-2105	362	7	of	of	ADP
cana-2105	362	8	k	k	PROPN
cana-2105	362	9	significantly	significantly	ADV
cana-2105	362	10	influences	influence	VERB
cana-2105	362	11	the	the	DET
cana-2105	362	12	mandelbrot	mandelbrot	NOUN
cana-2105	362	13	sets	set	VERB
cana-2105	362	14	’	'	PUNCT
cana-2105	362	15	symmetry	symmetry	NOUN
cana-2105	362	16	,	,	PUNCT
cana-2105	362	17	size	size	NOUN
cana-2105	362	18	,	,	PUNCT
cana-2105	362	19	and	and	CCONJ
cana-2105	362	20	the	the	DET
cana-2105	362	21	formation	formation	NOUN
cana-2105	362	22	of	of	ADP
cana-2105	362	23	intricate	intricate	ADJ
cana-2105	362	24	details	detail	NOUN
cana-2105	362	25	in	in	ADP
cana-2105	362	26	the	the	DET
cana-2105	362	27	fractal	fractal	ADJ
cana-2105	362	28	patterns	pattern	NOUN
cana-2105	362	29	.	.	PUNCT
cana-2105	363	1	communications	communication	NOUN
cana-2105	363	2	on	on	ADP
cana-2105	363	3	applied	apply	VERB
cana-2105	363	4	nonlinear	nonlinear	ADJ
cana-2105	363	5	analysis	analysis	NOUN
cana-2105	363	6	issn	issn	NOUN
cana-2105	363	7	:	:	PUNCT
cana-2105	363	8	1074	1074	NUM
cana-2105	363	9	-	-	PUNCT
cana-2105	363	10	133x	133x	NUM
cana-2105	363	11	vol	vol	NOUN
cana-2105	363	12	32	32	NUM
cana-2105	363	13	no	no	NOUN
cana-2105	363	14	.	.	PUNCT
cana-2105	364	1	1s	1s	NUM
cana-2105	364	2	(	(	PUNCT
cana-2105	364	3	2025	2025	NUM
cana-2105	364	4	)	)	PUNCT
cana-2105	364	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	364	6	87	87	NUM
cana-2105	364	7	(	(	PUNCT
cana-2105	364	8	a	a	NOUN
cana-2105	364	9	)	)	PUNCT
cana-2105	364	10	k	k	NOUN
cana-2105	365	1	=	=	SYM
cana-2105	365	2	2	2	NUM
cana-2105	365	3	(	(	PUNCT
cana-2105	365	4	b	b	NOUN
cana-2105	365	5	)	)	PUNCT
cana-2105	365	6	k	k	NOUN
cana-2105	365	7	=	=	SYM
cana-2105	365	8	3	3	NUM
cana-2105	365	9	(	(	PUNCT
cana-2105	365	10	c	c	NOUN
cana-2105	365	11	)	)	PUNCT
cana-2105	365	12	k	k	NOUN
cana-2105	366	1	=	=	SYM
cana-2105	366	2	4	4	NUM
cana-2105	366	3	(	(	PUNCT
cana-2105	366	4	d	d	NOUN
cana-2105	366	5	)	)	PUNCT
cana-2105	366	6	k	k	NOUN
cana-2105	367	1	=	=	SYM
cana-2105	367	2	5	5	NUM
cana-2105	367	3	(	(	PUNCT
cana-2105	367	4	e	e	NOUN
cana-2105	367	5	)	)	PUNCT
cana-2105	367	6	k	k	NOUN
cana-2105	368	1	=	=	SYM
cana-2105	368	2	10	10	NUM
cana-2105	368	3	(	(	PUNCT
cana-2105	368	4	f	f	X
cana-2105	368	5	)	)	PUNCT
cana-2105	368	6	k	k	NOUN
cana-2105	369	1	=	=	SYM
cana-2105	369	2	15	15	NUM
cana-2105	369	3	figure	figure	NOUN
cana-2105	369	4	17	17	NUM
cana-2105	369	5	:	:	PUNCT
cana-2105	369	6	the	the	DET
cana-2105	369	7	impact	impact	NOUN
cana-2105	369	8	on	on	ADP
cana-2105	369	9	mandelbrot	mandelbrot	NOUN
cana-2105	369	10	sets	set	NOUN
cana-2105	369	11	for	for	ADP
cana-2105	369	12	varying	vary	VERB
cana-2105	369	13	the	the	DET
cana-2105	369	14	parameter	parameter	NOUN
cana-2105	369	15	k	k	PROPN
cana-2105	369	16	5	5	NUM
cana-2105	369	17	conclusions	conclusion	NOUN
cana-2105	369	18	certainly	certainly	ADV
cana-2105	369	19	!	!	PUNCT
cana-2105	370	1	the	the	DET
cana-2105	370	2	paper	paper	NOUN
cana-2105	370	3	discusses	discuss	VERB
cana-2105	370	4	a	a	DET
cana-2105	370	5	novel	novel	ADJ
cana-2105	370	6	approach	approach	NOUN
cana-2105	370	7	for	for	ADP
cana-2105	370	8	establishing	establish	VERB
cana-2105	370	9	escape	escape	NOUN
cana-2105	370	10	criteria	criterion	NOUN
cana-2105	370	11	for	for	ADP
cana-2105	370	12	the	the	DET
cana-2105	370	13	complex	complex	ADJ
cana-2105	370	14	sine	sine	ADJ
cana-2105	370	15	function	function	NOUN
cana-2105	370	16	tc(z	tc(z	PUNCT
cana-2105	370	17	)	)	PUNCT
cana-2105	371	1	=	=	SYM
cana-2105	371	2	sin(zk)+az+c	sin(zk)+az+c	PROPN
cana-2105	371	3	.	.	PUNCT
cana-2105	372	1	the	the	DET
cana-2105	372	2	method	method	NOUN
cana-2105	372	3	involves	involve	VERB
cana-2105	372	4	a	a	DET
cana-2105	372	5	four	four	NUM
cana-2105	372	6	-	-	PUNCT
cana-2105	372	7	step	step	NOUN
cana-2105	372	8	iterative	iterative	NOUN
cana-2105	372	9	scheme	scheme	NOUN
cana-2105	372	10	extended	extend	VERB
cana-2105	372	11	with	with	ADP
cana-2105	372	12	s	s	NOUN
cana-2105	372	13	-	-	NOUN
cana-2105	372	14	convexity	convexity	NOUN
cana-2105	372	15	.	.	PUNCT
cana-2105	373	1	this	this	DET
cana-2105	373	2	approach	approach	NOUN
cana-2105	373	3	is	be	AUX
cana-2105	373	4	implemented	implement	VERB
cana-2105	373	5	in	in	ADP
cana-2105	373	6	algorithms	algorithms	NOUN
cana-2105	373	7	1	1	NUM
cana-2105	373	8	and	and	CCONJ
cana-2105	373	9	2	2	NUM
cana-2105	373	10	,	,	PUNCT
cana-2105	373	11	which	which	PRON
cana-2105	373	12	enable	enable	VERB
cana-2105	373	13	the	the	DET
cana-2105	373	14	visualization	visualization	NOUN
cana-2105	373	15	of	of	ADP
cana-2105	373	16	julia	julia	PROPN
cana-2105	373	17	and	and	CCONJ
cana-2105	373	18	mandelbrot	mandelbrot	PROPN
cana-2105	373	19	sets	set	VERB
cana-2105	373	20	through	through	ADP
cana-2105	373	21	a	a	DET
cana-2105	373	22	four	four	NUM
cana-2105	373	23	-	-	PUNCT
cana-2105	373	24	step	step	NOUN
cana-2105	373	25	iteration	iteration	NOUN
cana-2105	373	26	orbit	orbit	NOUN
cana-2105	373	27	.	.	PUNCT
cana-2105	374	1	the	the	DET
cana-2105	374	2	size	size	NOUN
cana-2105	374	3	of	of	ADP
cana-2105	374	4	the	the	DET
cana-2105	374	5	generated	generate	VERB
cana-2105	374	6	fractals	fractal	NOUN
cana-2105	374	7	is	be	AUX
cana-2105	374	8	influenced	influence	VERB
cana-2105	374	9	by	by	ADP
cana-2105	374	10	the	the	DET
cana-2105	374	11	convexity	convexity	NOUN
cana-2105	374	12	parameter	parameter	NOUN
cana-2105	374	13	s	s	PROPN
cana-2105	374	14	,	,	PUNCT
cana-2105	374	15	with	with	ADP
cana-2105	374	16	larger	large	ADJ
cana-2105	374	17	values	value	NOUN
cana-2105	374	18	of	of	ADP
cana-2105	374	19	s	s	PRON
cana-2105	374	20	generally	generally	ADV
cana-2105	374	21	resulting	result	VERB
cana-2105	374	22	in	in	ADP
cana-2105	374	23	larger	large	ADJ
cana-2105	374	24	fractals	fractal	NOUN
cana-2105	374	25	.	.	PUNCT
cana-2105	375	1	however	however	ADV
cana-2105	375	2	,	,	PUNCT
cana-2105	375	3	when	when	SCONJ
cana-2105	375	4	parameters	parameter	NOUN
cana-2105	375	5	like	like	ADP
cana-2105	375	6	α	α	PROPN
cana-2105	375	7	,	,	PUNCT
cana-2105	375	8	β	β	X
cana-2105	375	9	,	,	PUNCT
cana-2105	375	10	γ	γ	X
cana-2105	375	11	,	,	PUNCT
cana-2105	375	12	and	and	CCONJ
cana-2105	375	13	δ	δ	PROPN
cana-2105	375	14	approach	approach	NOUN
cana-2105	375	15	1	1	NUM
cana-2105	375	16	,	,	PUNCT
cana-2105	375	17	the	the	DET
cana-2105	375	18	size	size	NOUN
cana-2105	375	19	of	of	ADP
cana-2105	375	20	the	the	DET
cana-2105	375	21	fractals	fractal	NOUN
cana-2105	375	22	decreases	decrease	NOUN
cana-2105	375	23	,	,	PUNCT
cana-2105	375	24	and	and	CCONJ
cana-2105	375	25	many	many	ADJ
cana-2105	375	26	points	point	NOUN
cana-2105	375	27	escape	escape	VERB
cana-2105	375	28	to	to	ADP
cana-2105	375	29	infinity	infinity	NOUN
cana-2105	375	30	,	,	PUNCT
cana-2105	375	31	making	make	VERB
cana-2105	375	32	the	the	DET
cana-2105	375	33	images	image	NOUN
cana-2105	375	34	of	of	ADP
cana-2105	375	35	the	the	DET
cana-2105	375	36	fractals	fractal	NOUN
cana-2105	375	37	weaker	weak	ADJ
cana-2105	375	38	.	.	PUNCT
cana-2105	376	1	parameters	parameter	NOUN
cana-2105	376	2	a	a	PRON
cana-2105	376	3	and	and	CCONJ
cana-2105	376	4	c	c	AUX
cana-2105	376	5	play	play	VERB
cana-2105	376	6	a	a	DET
cana-2105	376	7	crucial	crucial	ADJ
cana-2105	376	8	role	role	NOUN
cana-2105	376	9	in	in	ADP
cana-2105	376	10	determining	determine	VERB
cana-2105	376	11	the	the	DET
cana-2105	376	12	specific	specific	ADJ
cana-2105	376	13	shape	shape	NOUN
cana-2105	376	14	and	and	CCONJ
cana-2105	376	15	symmetry	symmetry	NOUN
cana-2105	376	16	of	of	ADP
cana-2105	376	17	the	the	DET
cana-2105	376	18	fractals	fractal	NOUN
cana-2105	376	19	.	.	PUNCT
cana-2105	377	1	changing	change	VERB
cana-2105	377	2	these	these	DET
cana-2105	377	3	parameters	parameter	NOUN
cana-2105	377	4	leads	lead	VERB
cana-2105	377	5	to	to	ADP
cana-2105	377	6	different	different	ADJ
cana-2105	377	7	patterns	pattern	NOUN
cana-2105	377	8	,	,	PUNCT
cana-2105	377	9	symmetries	symmetry	NOUN
cana-2105	377	10	,	,	PUNCT
cana-2105	377	11	and	and	CCONJ
cana-2105	377	12	visual	visual	ADJ
cana-2105	377	13	characteristics	characteristic	NOUN
cana-2105	377	14	in	in	ADP
cana-2105	377	15	the	the	DET
cana-2105	377	16	generated	generate	VERB
cana-2105	377	17	fractals	fractal	NOUN
cana-2105	377	18	.	.	PUNCT
cana-2105	378	1	notably	notably	ADV
cana-2105	378	2	,	,	PUNCT
cana-2105	378	3	certain	certain	ADJ
cana-2105	378	4	fractals	fractal	NOUN
cana-2105	378	5	exhibit	exhibit	VERB
cana-2105	378	6	patterns	pattern	NOUN
cana-2105	378	7	resembling	resemble	VERB
cana-2105	378	8	spiders	spider	NOUN
cana-2105	378	9	,	,	PUNCT
cana-2105	378	10	flowers	flower	NOUN
cana-2105	378	11	,	,	PUNCT
cana-2105	378	12	or	or	CCONJ
cana-2105	378	13	other	other	ADJ
cana-2105	378	14	natural	natural	ADJ
cana-2105	378	15	phenomena	phenomenon	NOUN
cana-2105	378	16	,	,	PUNCT
cana-2105	378	17	emphasizing	emphasize	VERB
cana-2105	378	18	the	the	DET
cana-2105	378	19	fascinating	fascinating	ADJ
cana-2105	378	20	connection	connection	NOUN
cana-2105	378	21	between	between	ADP
cana-2105	378	22	mathematical	mathematical	ADJ
cana-2105	378	23	fractals	fractal	NOUN
cana-2105	378	24	and	and	CCONJ
cana-2105	378	25	the	the	DET
cana-2105	378	26	complexity	complexity	NOUN
cana-2105	378	27	found	find	VERB
cana-2105	378	28	in	in	ADP
cana-2105	378	29	nature	nature	NOUN
cana-2105	378	30	.	.	PUNCT
cana-2105	379	1	the	the	DET
cana-2105	379	2	parameter	parameter	NOUN
cana-2105	379	3	k	k	PROPN
cana-2105	379	4	is	be	AUX
cana-2105	379	5	discussed	discuss	VERB
cana-2105	379	6	as	as	ADP
cana-2105	379	7	influencing	influence	VERB
cana-2105	379	8	the	the	DET
cana-2105	379	9	compactness	compactness	NOUN
cana-2105	379	10	and	and	CCONJ
cana-2105	379	11	appearance	appearance	NOUN
cana-2105	379	12	of	of	ADP
cana-2105	379	13	the	the	DET
cana-2105	379	14	fractals	fractal	NOUN
cana-2105	379	15	.	.	PUNCT
cana-2105	380	1	higher	high	ADJ
cana-2105	380	2	values	value	NOUN
cana-2105	380	3	of	of	ADP
cana-2105	380	4	k	k	PROPN
cana-2105	380	5	result	result	NOUN
cana-2105	380	6	in	in	ADP
cana-2105	380	7	more	more	ADJ
cana-2105	380	8	compact	compact	ADJ
cana-2105	380	9	fractals	fractal	NOUN
cana-2105	380	10	with	with	ADP
cana-2105	380	11	circular	circular	ADJ
cana-2105	380	12	or	or	CCONJ
cana-2105	380	13	rounded	rounded	ADJ
cana-2105	380	14	shapes	shape	NOUN
cana-2105	380	15	,	,	PUNCT
cana-2105	380	16	featuring	feature	VERB
cana-2105	380	17	numerous	numerous	ADJ
cana-2105	380	18	lashes	lash	NOUN
cana-2105	380	19	in	in	ADP
cana-2105	380	20	the	the	DET
cana-2105	380	21	case	case	NOUN
cana-2105	380	22	of	of	ADP
cana-2105	380	23	julia	julia	PROPN
cana-2105	380	24	sets	set	NOUN
cana-2105	380	25	and	and	CCONJ
cana-2105	380	26	k	k	NOUN
cana-2105	380	27	−	−	PROPN
cana-2105	380	28	1	1	NUM
cana-2105	380	29	lashes	lash	NOUN
cana-2105	380	30	in	in	ADP
cana-2105	380	31	the	the	DET
cana-2105	380	32	case	case	NOUN
cana-2105	380	33	of	of	ADP
cana-2105	380	34	mandelbrot	mandelbrot	NOUN
cana-2105	380	35	sets	set	VERB
cana-2105	380	36	.	.	PUNCT
cana-2105	381	1	this	this	DET
cana-2105	381	2	change	change	NOUN
cana-2105	381	3	in	in	ADP
cana-2105	381	4	shape	shape	NOUN
cana-2105	381	5	is	be	AUX
cana-2105	381	6	attributed	attribute	VERB
cana-2105	381	7	to	to	ADP
cana-2105	381	8	the	the	DET
cana-2105	381	9	iterative	iterative	NOUN
cana-2105	381	10	process	process	NOUN
cana-2105	381	11	and	and	CCONJ
cana-2105	381	12	the	the	DET
cana-2105	381	13	communications	communication	NOUN
cana-2105	381	14	on	on	ADP
cana-2105	381	15	applied	apply	VERB
cana-2105	381	16	nonlinear	nonlinear	ADJ
cana-2105	381	17	analysis	analysis	NOUN
cana-2105	381	18	issn	issn	NOUN
cana-2105	381	19	:	:	PUNCT
cana-2105	381	20	1074	1074	NUM
cana-2105	381	21	-	-	PUNCT
cana-2105	381	22	133x	133x	NUM
cana-2105	381	23	vol	vol	NOUN
cana-2105	381	24	32	32	NUM
cana-2105	382	1	no	no	NOUN
cana-2105	382	2	.	.	PUNCT
cana-2105	383	1	1s	1s	NUM
cana-2105	383	2	(	(	PUNCT
cana-2105	383	3	2025	2025	NUM
cana-2105	383	4	)	)	PUNCT
cana-2105	383	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	383	6	88	88	NUM
cana-2105	383	7	specific	specific	ADJ
cana-2105	383	8	dynamics	dynamic	NOUN
cana-2105	383	9	of	of	ADP
cana-2105	383	10	the	the	DET
cana-2105	383	11	underlying	underlie	VERB
cana-2105	383	12	function	function	NOUN
cana-2105	383	13	.	.	PUNCT
cana-2105	384	1	the	the	DET
cana-2105	384	2	paper	paper	NOUN
cana-2105	384	3	suggests	suggest	VERB
cana-2105	384	4	practical	practical	ADJ
cana-2105	384	5	applications	application	NOUN
cana-2105	384	6	in	in	ADP
cana-2105	384	7	the	the	DET
cana-2105	384	8	cloth	cloth	NOUN
cana-2105	384	9	and	and	CCONJ
cana-2105	384	10	ceramics	ceramic	NOUN
cana-2105	384	11	industries	industry	NOUN
cana-2105	384	12	.	.	PUNCT
cana-2105	385	1	textile	textile	NOUN
cana-2105	385	2	engineers	engineer	NOUN
cana-2105	385	3	can	can	AUX
cana-2105	385	4	utilize	utilize	VERB
cana-2105	385	5	the	the	DET
cana-2105	385	6	generated	generate	VERB
cana-2105	385	7	fractal	fractal	ADJ
cana-2105	385	8	patterns	pattern	NOUN
cana-2105	385	9	to	to	PART
cana-2105	385	10	design	design	VERB
cana-2105	385	11	unique	unique	ADJ
cana-2105	385	12	and	and	CCONJ
cana-2105	385	13	visually	visually	ADV
cana-2105	385	14	appealing	appealing	ADJ
cana-2105	385	15	fabric	fabric	NOUN
cana-2105	385	16	patterns	pattern	NOUN
cana-2105	385	17	.	.	PUNCT
cana-2105	386	1	the	the	DET
cana-2105	386	2	findings	finding	NOUN
cana-2105	386	3	of	of	ADP
cana-2105	386	4	the	the	DET
cana-2105	386	5	paper	paper	NOUN
cana-2105	386	6	contribute	contribute	VERB
cana-2105	386	7	to	to	ADP
cana-2105	386	8	a	a	DET
cana-2105	386	9	deeper	deep	ADJ
cana-2105	386	10	understanding	understanding	NOUN
cana-2105	386	11	of	of	ADP
cana-2105	386	12	the	the	DET
cana-2105	386	13	behavior	behavior	NOUN
cana-2105	386	14	and	and	CCONJ
cana-2105	386	15	characteristics	characteristic	NOUN
cana-2105	386	16	of	of	ADP
cana-2105	386	17	fractal	fractal	ADJ
cana-2105	386	18	sets	set	NOUN
cana-2105	386	19	,	,	PUNCT
cana-2105	386	20	showcasing	showcase	VERB
cana-2105	386	21	the	the	DET
cana-2105	386	22	potential	potential	NOUN
cana-2105	386	23	of	of	ADP
cana-2105	386	24	the	the	DET
cana-2105	386	25	four	four	NUM
cana-2105	386	26	-	-	PUNCT
cana-2105	386	27	step	step	NOUN
cana-2105	386	28	iteration	iteration	NOUN
cana-2105	386	29	scheme	scheme	NOUN
cana-2105	386	30	in	in	ADP
cana-2105	386	31	generating	generate	VERB
cana-2105	386	32	intricate	intricate	ADJ
cana-2105	386	33	and	and	CCONJ
cana-2105	386	34	captivating	captivating	ADJ
cana-2105	386	35	fractals	fractal	NOUN
cana-2105	386	36	.	.	PUNCT
cana-2105	387	1	the	the	DET
cana-2105	387	2	future	future	ADJ
cana-2105	387	3	direction	direction	NOUN
cana-2105	387	4	mentioned	mention	VERB
cana-2105	387	5	involves	involve	VERB
cana-2105	387	6	extending	extend	VERB
cana-2105	387	7	the	the	DET
cana-2105	387	8	results	result	NOUN
cana-2105	387	9	for	for	ADP
cana-2105	387	10	the	the	DET
cana-2105	387	11	jungck	jungck	NOUN
cana-2105	387	12	-	-	PUNCT
cana-2105	387	13	four	four	NUM
cana-2105	387	14	step	step	NOUN
cana-2105	387	15	iteration	iteration	NOUN
cana-2105	387	16	with	with	ADP
cana-2105	387	17	s	s	NOUN
cana-2105	387	18	-	-	NOUN
cana-2105	387	19	convexity	convexity	NOUN
cana-2105	387	20	,	,	PUNCT
cana-2105	387	21	indicating	indicate	VERB
cana-2105	387	22	potential	potential	ADJ
cana-2105	387	23	advancements	advancement	NOUN
cana-2105	387	24	and	and	CCONJ
cana-2105	387	25	applications	application	NOUN
cana-2105	387	26	of	of	ADP
cana-2105	387	27	the	the	DET
cana-2105	387	28	proposed	propose	VERB
cana-2105	387	29	methodology	methodology	NOUN
cana-2105	387	30	.	.	PUNCT
cana-2105	388	1	acknowledgement	acknowledgement	PROPN
cana-2105	388	2	acknowledging	acknowledge	VERB
cana-2105	388	3	the	the	DET
cana-2105	388	4	referee	referee	NOUN
cana-2105	388	5	’s	’s	PART
cana-2105	388	6	contribution	contribution	NOUN
cana-2105	388	7	to	to	ADP
cana-2105	388	8	enhancing	enhance	VERB
cana-2105	388	9	the	the	DET
cana-2105	388	10	readability	readability	NOUN
cana-2105	388	11	of	of	ADP
cana-2105	388	12	this	this	DET
cana-2105	388	13	paper	paper	NOUN
cana-2105	388	14	is	be	AUX
cana-2105	388	15	essential	essential	ADJ
cana-2105	388	16	.	.	PUNCT
cana-2105	389	1	their	their	PRON
cana-2105	389	2	valuable	valuable	ADJ
cana-2105	389	3	feedback	feedback	NOUN
cana-2105	389	4	and	and	CCONJ
cana-2105	389	5	suggestions	suggestion	NOUN
cana-2105	389	6	likely	likely	ADV
cana-2105	389	7	played	play	VERB
cana-2105	389	8	a	a	DET
cana-2105	389	9	crucial	crucial	ADJ
cana-2105	389	10	role	role	NOUN
cana-2105	389	11	in	in	ADP
cana-2105	389	12	refining	refine	VERB
cana-2105	389	13	the	the	DET
cana-2105	389	14	clarity	clarity	NOUN
cana-2105	389	15	and	and	CCONJ
cana-2105	389	16	coherence	coherence	NOUN
cana-2105	389	17	of	of	ADP
cana-2105	389	18	the	the	DET
cana-2105	389	19	content	content	NOUN
cana-2105	389	20	,	,	PUNCT
cana-2105	389	21	ensuring	ensure	VERB
cana-2105	389	22	that	that	SCONJ
cana-2105	389	23	the	the	DET
cana-2105	389	24	research	research	NOUN
cana-2105	389	25	findings	finding	NOUN
cana-2105	389	26	were	be	AUX
cana-2105	389	27	effectively	effectively	ADV
cana-2105	389	28	communicated	communicate	VERB
cana-2105	389	29	to	to	ADP
cana-2105	389	30	the	the	DET
cana-2105	389	31	intended	intended	ADJ
cana-2105	389	32	audience	audience	NOUN
cana-2105	389	33	.	.	PUNCT
cana-2105	390	1	references	reference	NOUN
cana-2105	390	2	[	[	X
cana-2105	390	3	1	1	NUM
cana-2105	390	4	]	]	PUNCT
cana-2105	390	5	m.	m.	NOUN
cana-2105	390	6	abbas	abbas	PROPN
cana-2105	390	7	,	,	PUNCT
cana-2105	390	8	h.	h.	PROPN
cana-2105	390	9	iqbal	iqbal	PROPN
cana-2105	390	10	,	,	PUNCT
cana-2105	390	11	and	and	CCONJ
cana-2105	390	12	m.	m.	PROPN
cana-2105	390	13	de	de	PROPN
cana-2105	390	14	la	la	PROPN
cana-2105	390	15	sen	sen	PROPN
cana-2105	390	16	.	.	PROPN
cana-2105	390	17	generation	generation	NOUN
cana-2105	390	18	of	of	ADP
cana-2105	390	19	julia	julia	PROPN
cana-2105	390	20	and	and	CCONJ
cana-2105	390	21	madelbrot	madelbrot	PROPN
cana-2105	390	22	sets	set	NOUN
cana-2105	390	23	via	via	ADP
cana-2105	390	24	fixed	fix	VERB
cana-2105	390	25	points	point	NOUN
cana-2105	390	26	.	.	PUNCT
cana-2105	391	1	symmetry	symmetry	NOUN
cana-2105	391	2	,	,	PUNCT
cana-2105	391	3	12:1–19	12:1–19	NUM
cana-2105	391	4	,	,	PUNCT
cana-2105	391	5	01	01	NUM
cana-2105	391	6	2020	2020	NUM
cana-2105	391	7	.	.	PUNCT
cana-2105	392	1	[	[	X
cana-2105	392	2	2	2	NUM
cana-2105	392	3	]	]	X
cana-2105	392	4	n.	n.	NOUN
cana-2105	392	5	adhikari	adhikari	PROPN
cana-2105	392	6	and	and	CCONJ
cana-2105	392	7	w.	w.	PROPN
cana-2105	392	8	sintunavarat	sintunavarat	PROPN
cana-2105	392	9	.	.	PUNCT
cana-2105	393	1	exploring	explore	VERB
cana-2105	393	2	the	the	DET
cana-2105	393	3	julia	julia	PROPN
cana-2105	393	4	and	and	CCONJ
cana-2105	393	5	mandelbrot	mandelbrot	PROPN
cana-2105	393	6	sets	set	NOUN
cana-2105	393	7	of	of	ADP
cana-2105	393	8	zp+	zp+	NOUN
cana-2105	393	9	log	log	VERB
cana-2105	393	10	ct	ct	NOUN
cana-2105	393	11	using	use	VERB
cana-2105	393	12	a	a	DET
cana-2105	393	13	four	four	NUM
cana-2105	393	14	-	-	PUNCT
cana-2105	393	15	step	step	NOUN
cana-2105	393	16	iteration	iteration	NOUN
cana-2105	393	17	scheme	scheme	NOUN
cana-2105	393	18	extended	extend	VERB
cana-2105	393	19	with	with	ADP
cana-2105	393	20	s	s	NOUN
cana-2105	393	21	-	-	NOUN
cana-2105	393	22	convexity	convexity	NOUN
cana-2105	393	23	.	.	PUNCT
cana-2105	394	1	mathematics	mathematic	NOUN
cana-2105	394	2	and	and	CCONJ
cana-2105	394	3	computers	computer	NOUN
cana-2105	394	4	in	in	ADP
cana-2105	394	5	simulation	simulation	NOUN
cana-2105	394	6	,	,	PUNCT
cana-2105	394	7	220:357–381	220:357–381	NUM
cana-2105	394	8	,	,	PUNCT
cana-2105	394	9	2024	2024	NUM
cana-2105	394	10	.	.	PUNCT
cana-2105	395	1	[	[	X
cana-2105	395	2	3	3	X
cana-2105	395	3	]	]	X
cana-2105	395	4	n.	n.	PROPN
cana-2105	395	5	adhikari	adhikari	PROPN
cana-2105	395	6	and	and	CCONJ
cana-2105	395	7	w.	w.	PROPN
cana-2105	395	8	sintunavarat	sintunavarat	PROPN
cana-2105	395	9	.	.	PUNCT
cana-2105	396	1	the	the	DET
cana-2105	396	2	julia	julia	PROPN
cana-2105	396	3	and	and	CCONJ
cana-2105	396	4	mandelbrot	mandelbrot	PROPN
cana-2105	396	5	sets	set	VERB
cana-2105	396	6	for	for	ADP
cana-2105	396	7	the	the	DET
cana-2105	396	8	complexvalued	complexvalue	VERB
cana-2105	396	9	function	function	NOUN
cana-2105	396	10	exhibit	exhibit	VERB
cana-2105	396	11	mann	mann	PROPN
cana-2105	396	12	and	and	CCONJ
cana-2105	396	13	picard	picard	PROPN
cana-2105	396	14	–	–	PUNCT
cana-2105	396	15	mann	mann	PROPN
cana-2105	396	16	orbits	orbit	NOUN
cana-2105	396	17	along	along	ADP
cana-2105	396	18	with	with	ADP
cana-2105	396	19	s	s	NOUN
cana-2105	396	20	-	-	NOUN
cana-2105	396	21	convexity	convexity	NOUN
cana-2105	396	22	.	.	PUNCT
cana-2105	397	1	chaos	chaos	NOUN
cana-2105	397	2	,	,	PUNCT
cana-2105	397	3	solitons	soliton	NOUN
cana-2105	397	4	and	and	CCONJ
cana-2105	397	5	fractals	fractal	NOUN
cana-2105	397	6	,	,	PUNCT
cana-2105	397	7	181:114600	181:114600	NUM
cana-2105	397	8	,	,	PUNCT
cana-2105	397	9	2024	2024	NUM
cana-2105	397	10	.	.	PUNCT
cana-2105	398	1	[	[	X
cana-2105	398	2	4	4	X
cana-2105	398	3	]	]	X
cana-2105	398	4	d.	d.	PROPN
cana-2105	398	5	ashish	ashish	PROPN
cana-2105	398	6	,	,	PUNCT
cana-2105	398	7	m.	m.	NOUN
cana-2105	398	8	rani	rani	PROPN
cana-2105	398	9	,	,	PUNCT
cana-2105	398	10	and	and	CCONJ
cana-2105	398	11	r.	r.	PROPN
cana-2105	398	12	chugh	chugh	NOUN
cana-2105	398	13	.	.	PUNCT
cana-2105	399	1	julia	julia	PROPN
cana-2105	399	2	sets	set	NOUN
cana-2105	399	3	and	and	CCONJ
cana-2105	399	4	mandelbrot	mandelbrot	NOUN
cana-2105	399	5	sets	set	NOUN
cana-2105	399	6	in	in	ADP
cana-2105	399	7	noor	noor	PROPN
cana-2105	399	8	orbit	orbit	PROPN
cana-2105	399	9	.	.	PUNCT
cana-2105	400	1	applied	apply	VERB
cana-2105	400	2	mathematics	mathematic	NOUN
cana-2105	400	3	and	and	CCONJ
cana-2105	400	4	computation	computation	NOUN
cana-2105	400	5	,	,	PUNCT
cana-2105	400	6	228:615–631	228:615–631	NUM
cana-2105	400	7	,	,	PUNCT
cana-2105	400	8	02	02	NUM
cana-2105	400	9	2014	2014	NUM
cana-2105	400	10	.	.	PUNCT
cana-2105	401	1	[	[	X
cana-2105	401	2	5	5	NUM
cana-2105	401	3	]	]	PUNCT
cana-2105	401	4	p.	p.	NOUN
cana-2105	401	5	fatou	fatou	NOUN
cana-2105	401	6	.	.	PUNCT
cana-2105	402	1	sur	sur	PROPN
cana-2105	402	2	les	les	PROPN
cana-2105	402	3	substitutions	substitution	NOUN
cana-2105	402	4	rationnelles	rationnelle	NOUN
cana-2105	402	5	.	.	PUNCT
cana-2105	403	1	c.	c.	PROPN
cana-2105	403	2	r.	r.	PROPN
cana-2105	403	3	acad	acad	PROPN
cana-2105	403	4	.	.	PUNCT
cana-2105	404	1	sci	sci	PROPN
cana-2105	404	2	.	.	PROPN
cana-2105	404	3	paris	paris	PROPN
cana-2105	404	4	,	,	PUNCT
cana-2105	404	5	164:806–808	164:806–808	NUM
cana-2105	404	6	,	,	PUNCT
cana-2105	404	7	1917	1917	NUM
cana-2105	404	8	.	.	PUNCT
cana-2105	405	1	[	[	X
cana-2105	405	2	6	6	NUM
cana-2105	405	3	]	]	PUNCT
cana-2105	405	4	g.	g.	PROPN
cana-2105	405	5	julia	julia	PROPN
cana-2105	405	6	.	.	PUNCT
cana-2105	406	1	mémoire	mémoire	PROPN
cana-2105	406	2	sur	sur	PROPN
cana-2105	406	3	l’itération	l’itération	PROPN
cana-2105	406	4	des	des	PROPN
cana-2105	406	5	fonctions	fonction	NOUN
cana-2105	406	6	rationnelles	rationnelle	NOUN
cana-2105	406	7	.	.	PUNCT
cana-2105	407	1	j.	j.	PROPN
cana-2105	407	2	math	math	PROPN
cana-2105	407	3	.	.	PUNCT
cana-2105	408	1	pures	pure	NOUN
cana-2105	408	2	appl	appl	PROPN
cana-2105	408	3	.	.	PROPN
cana-2105	408	4	,	,	PUNCT
cana-2105	408	5	8:47–74	8:47–74	NUM
cana-2105	408	6	,	,	PUNCT
cana-2105	408	7	1918	1918	NUM
cana-2105	408	8	.	.	PUNCT
cana-2105	409	1	[	[	X
cana-2105	409	2	7	7	X
cana-2105	409	3	]	]	PUNCT
cana-2105	409	4	m.	m.	NOUN
cana-2105	409	5	kumari	kumari	PROPN
cana-2105	409	6	,	,	PUNCT
cana-2105	409	7	d.	d.	PROPN
cana-2105	409	8	ashish	ashish	PROPN
cana-2105	409	9	,	,	PUNCT
cana-2105	409	10	and	and	CCONJ
cana-2105	409	11	r.	r.	PROPN
cana-2105	409	12	chugh	chugh	NOUN
cana-2105	409	13	.	.	PUNCT
cana-2105	410	1	new	new	ADJ
cana-2105	410	2	julia	julia	PROPN
cana-2105	410	3	and	and	CCONJ
cana-2105	410	4	mandelbrot	mandelbrot	PROPN
cana-2105	410	5	sets	set	VERB
cana-2105	410	6	for	for	ADP
cana-2105	410	7	a	a	DET
cana-2105	410	8	new	new	ADJ
cana-2105	410	9	faster	fast	ADJ
cana-2105	410	10	iterative	iterative	NOUN
cana-2105	410	11	process	process	NOUN
cana-2105	410	12	.	.	PUNCT
cana-2105	411	1	international	international	ADJ
cana-2105	411	2	journal	journal	NOUN
cana-2105	411	3	of	of	ADP
cana-2105	411	4	pure	pure	ADJ
cana-2105	411	5	and	and	CCONJ
cana-2105	411	6	apllied	apllie	VERB
cana-2105	411	7	mathematics	mathematic	NOUN
cana-2105	411	8	,	,	PUNCT
cana-2105	411	9	107:161–177	107:161–177	NUM
cana-2105	411	10	,	,	PUNCT
cana-2105	411	11	03	03	NUM
cana-2105	411	12	2016	2016	NUM
cana-2105	411	13	.	.	PUNCT
cana-2105	412	1	communications	communication	NOUN
cana-2105	412	2	on	on	ADP
cana-2105	412	3	applied	apply	VERB
cana-2105	412	4	nonlinear	nonlinear	ADJ
cana-2105	412	5	analysis	analysis	NOUN
cana-2105	412	6	issn	issn	NOUN
cana-2105	412	7	:	:	PUNCT
cana-2105	412	8	1074	1074	NUM
cana-2105	412	9	-	-	PUNCT
cana-2105	412	10	133x	133x	NUM
cana-2105	412	11	vol	vol	NOUN
cana-2105	412	12	32	32	NUM
cana-2105	412	13	no	no	NOUN
cana-2105	412	14	.	.	PUNCT
cana-2105	413	1	1s	1s	NUM
cana-2105	413	2	(	(	PUNCT
cana-2105	413	3	2025	2025	NUM
cana-2105	413	4	)	)	PUNCT
cana-2105	413	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	413	6	89	89	NUM
cana-2105	414	1	[	[	X
cana-2105	414	2	8	8	NUM
cana-2105	414	3	]	]	PUNCT
cana-2105	414	4	s.	s.	PROPN
cana-2105	414	5	kumari	kumari	PROPN
cana-2105	414	6	,	,	PUNCT
cana-2105	414	7	k.	k.	PROPN
cana-2105	414	8	gdawiec	gdawiec	PROPN
cana-2105	414	9	,	,	PUNCT
cana-2105	414	10	a.	a.	NOUN
cana-2105	414	11	nandal	nandal	NOUN
cana-2105	414	12	,	,	PUNCT
cana-2105	414	13	m.	m.	NOUN
cana-2105	414	14	postolache	postolache	NOUN
cana-2105	414	15	,	,	PUNCT
cana-2105	414	16	and	and	CCONJ
cana-2105	414	17	r.	r.	PROPN
cana-2105	414	18	chugh	chugh	NOUN
cana-2105	414	19	.	.	PUNCT
cana-2105	415	1	a	a	DET
cana-2105	415	2	novel	novel	ADJ
cana-2105	415	3	approach	approach	NOUN
cana-2105	415	4	to	to	PART
cana-2105	415	5	generate	generate	VERB
cana-2105	415	6	mandelbrot	mandelbrot	NOUN
cana-2105	415	7	sets	set	NOUN
cana-2105	415	8	,	,	PUNCT
cana-2105	415	9	julia	julia	PROPN
cana-2105	415	10	sets	set	NOUN
cana-2105	415	11	and	and	CCONJ
cana-2105	415	12	biomorphs	biomorph	NOUN
cana-2105	415	13	via	via	ADP
cana-2105	415	14	viscosity	viscosity	NOUN
cana-2105	415	15	approximation	approximation	NOUN
cana-2105	415	16	method	method	NOUN
cana-2105	415	17	.	.	PUNCT
cana-2105	416	1	chaos	chaos	NOUN
cana-2105	416	2	,	,	PUNCT
cana-2105	416	3	solitons	soliton	NOUN
cana-2105	416	4	and	and	CCONJ
cana-2105	416	5	fractals	fractal	NOUN
cana-2105	416	6	,	,	PUNCT
cana-2105	416	7	163:1–21	163:1–21	NUM
cana-2105	416	8	,	,	PUNCT
cana-2105	416	9	10	10	NUM
cana-2105	416	10	2022	2022	NUM
cana-2105	416	11	.	.	PUNCT
cana-2105	417	1	[	[	X
cana-2105	417	2	9	9	NUM
cana-2105	417	3	]	]	PUNCT
cana-2105	417	4	a.	a.	NOUN
cana-2105	417	5	lakhtakia	lakhtakia	NOUN
cana-2105	417	6	,	,	PUNCT
cana-2105	417	7	v.	v.	PROPN
cana-2105	417	8	v.	v.	ADP
cana-2105	417	9	varadan	varadan	PROPN
cana-2105	417	10	,	,	PUNCT
cana-2105	417	11	r.	r.	PROPN
cana-2105	417	12	messier	messier	X
cana-2105	417	13	,	,	PUNCT
cana-2105	417	14	and	and	CCONJ
cana-2105	417	15	varadan	varadan	PROPN
cana-2105	417	16	.	.	PUNCT
cana-2105	418	1	on	on	ADP
cana-2105	418	2	the	the	DET
cana-2105	418	3	symmetries	symmetry	NOUN
cana-2105	418	4	of	of	ADP
cana-2105	418	5	the	the	DET
cana-2105	418	6	julia	julia	PROPN
cana-2105	418	7	sets	set	NOUN
cana-2105	418	8	for	for	ADP
cana-2105	418	9	the	the	DET
cana-2105	418	10	process	process	NOUN
cana-2105	418	11	zp	zp	PROPN
cana-2105	418	12	+	+	CCONJ
cana-2105	418	13	c.	c.	PROPN
cana-2105	418	14	journal	journal	PROPN
cana-2105	418	15	of	of	ADP
cana-2105	418	16	physics	physics	PROPN
cana-2105	418	17	a	a	PRON
cana-2105	418	18	:	:	PUNCT
cana-2105	418	19	mathematical	mathematical	ADJ
cana-2105	418	20	and	and	CCONJ
cana-2105	418	21	theoretical	theoretical	ADJ
cana-2105	418	22	,	,	PUNCT
cana-2105	418	23	20(11):3533	20(11):3533	NUM
cana-2105	418	24	–	–	PUNCT
cana-2105	418	25	3535	3535	NUM
cana-2105	418	26	,	,	PUNCT
cana-2105	418	27	12	12	NUM
cana-2105	418	28	1987	1987	NUM
cana-2105	418	29	.	.	PUNCT
cana-2105	419	1	[	[	X
cana-2105	419	2	10	10	NUM
cana-2105	419	3	]	]	PUNCT
cana-2105	419	4	x.	x.	PROPN
cana-2105	419	5	liu	liu	PROPN
cana-2105	419	6	,	,	PUNCT
cana-2105	419	7	z.	z.	PROPN
cana-2105	419	8	zhu	zhu	PROPN
cana-2105	419	9	,	,	PUNCT
cana-2105	419	10	g.	g.	PROPN
cana-2105	419	11	wang	wang	PROPN
cana-2105	419	12	,	,	PUNCT
cana-2105	419	13	and	and	CCONJ
cana-2105	419	14	w.	w.	PROPN
cana-2105	419	15	zhu	zhu	PROPN
cana-2105	419	16	.	.	PROPN
cana-2105	420	1	composed	compose	VERB
cana-2105	420	2	accelerated	accelerate	VERB
cana-2105	420	3	escape	escape	NOUN
cana-2105	420	4	time	time	NOUN
cana-2105	420	5	algorithm	algorithm	NOUN
cana-2105	420	6	to	to	PART
cana-2105	420	7	construct	construct	VERB
cana-2105	420	8	the	the	DET
cana-2105	420	9	general	general	ADJ
cana-2105	420	10	mandelbrot	mandelbrot	NOUN
cana-2105	420	11	sets	set	VERB
cana-2105	420	12	.	.	PUNCT
cana-2105	421	1	fractals	fractal	NOUN
cana-2105	421	2	,	,	PUNCT
cana-2105	421	3	09:1–20	09:1–20	NUM
cana-2105	421	4	,	,	PUNCT
cana-2105	421	5	11	11	NUM
cana-2105	421	6	2011	2011	NUM
cana-2105	421	7	.	.	PUNCT
cana-2105	422	1	[	[	X
cana-2105	422	2	11	11	NUM
cana-2105	422	3	]	]	PUNCT
cana-2105	422	4	b.	b.	PROPN
cana-2105	422	5	mandelbrot	mandelbrot	PROPN
cana-2105	422	6	.	.	PUNCT
cana-2105	423	1	the	the	DET
cana-2105	423	2	fractal	fractal	ADJ
cana-2105	423	3	geometry	geometry	NOUN
cana-2105	423	4	of	of	ADP
cana-2105	423	5	nature	nature	NOUN
cana-2105	423	6	.	.	PUNCT
cana-2105	424	1	w.	w.	PROPN
cana-2105	424	2	h.	h.	PROPN
cana-2105	424	3	freeman	freeman	PROPN
cana-2105	424	4	:	:	PUNCT
cana-2105	424	5	new	new	PROPN
cana-2105	424	6	york	york	PROPN
cana-2105	424	7	,	,	PUNCT
cana-2105	424	8	1982	1982	NUM
cana-2105	424	9	.	.	PUNCT
cana-2105	425	1	[	[	X
cana-2105	425	2	12	12	NUM
cana-2105	425	3	]	]	PUNCT
cana-2105	425	4	m.	m.	NOUN
cana-2105	425	5	pinheiro	pinheiro	PROPN
cana-2105	425	6	.	.	PUNCT
cana-2105	426	1	s	s	X
cana-2105	426	2	-	-	PUNCT
cana-2105	426	3	convexity	convexity	NOUN
cana-2105	426	4	foundations	foundation	NOUN
cana-2105	426	5	for	for	ADP
cana-2105	426	6	analysis	analysis	NOUN
cana-2105	426	7	.	.	PUNCT
cana-2105	427	1	differential	differential	ADJ
cana-2105	427	2	geometry	geometry	NOUN
cana-2105	427	3	–	–	PUNCT
cana-2105	427	4	dynamical	dynamical	ADJ
cana-2105	427	5	systems	system	NOUN
cana-2105	427	6	,	,	PUNCT
cana-2105	427	7	pages	page	NOUN
cana-2105	427	8	257–262	257–262	NUM
cana-2105	427	9	,	,	PUNCT
cana-2105	427	10	2008	2008	NUM
cana-2105	427	11	.	.	PUNCT
cana-2105	428	1	[	[	X
cana-2105	428	2	13	13	NUM
cana-2105	428	3	]	]	X
cana-2105	428	4	b.	b.	PROPN
cana-2105	428	5	prasad	prasad	PROPN
cana-2105	428	6	and	and	CCONJ
cana-2105	428	7	k.	k.	PROPN
cana-2105	428	8	katiyar	katiyar	PROPN
cana-2105	428	9	.	.	PUNCT
cana-2105	429	1	fractals	fractal	NOUN
cana-2105	429	2	via	via	ADP
cana-2105	429	3	ishikawa	ishikawa	PROPN
cana-2105	429	4	iteration	iteration	NOUN
cana-2105	429	5	.	.	PUNCT
cana-2105	430	1	communications	communication	NOUN
cana-2105	430	2	in	in	ADP
cana-2105	430	3	computer	computer	NOUN
cana-2105	430	4	and	and	CCONJ
cana-2105	430	5	information	information	NOUN
cana-2105	430	6	science	science	NOUN
cana-2105	430	7	,	,	PUNCT
cana-2105	430	8	140:197–203	140:197–203	NUM
cana-2105	430	9	,	,	PUNCT
cana-2105	430	10	01	01	NUM
cana-2105	430	11	2011	2011	NUM
cana-2105	430	12	.	.	PUNCT
cana-2105	431	1	[	[	X
cana-2105	431	2	14	14	NUM
cana-2105	431	3	]	]	PUNCT
cana-2105	431	4	m.	m.	NOUN
cana-2105	431	5	rani	rani	PROPN
cana-2105	431	6	and	and	CCONJ
cana-2105	431	7	r.	r.	PROPN
cana-2105	431	8	agarwal	agarwal	PROPN
cana-2105	431	9	.	.	PUNCT
cana-2105	432	1	effect	effect	NOUN
cana-2105	432	2	of	of	ADP
cana-2105	432	3	stochastic	stochastic	ADJ
cana-2105	432	4	noise	noise	NOUN
cana-2105	432	5	on	on	ADP
cana-2105	432	6	superior	superior	ADJ
cana-2105	432	7	julia	julia	PROPN
cana-2105	432	8	sets	set	NOUN
cana-2105	432	9	.	.	PUNCT
cana-2105	433	1	j.	j.	PROPN
cana-2105	433	2	math	math	PROPN
cana-2105	433	3	.	.	PUNCT
cana-2105	434	1	imaging	imaging	NOUN
cana-2105	434	2	vis	vis	X
cana-2105	434	3	.	.	PROPN
cana-2105	434	4	,	,	PUNCT
cana-2105	434	5	36:63–68	36:63–68	NUM
cana-2105	434	6	,	,	PUNCT
cana-2105	434	7	2010	2010	NUM
cana-2105	434	8	.	.	PUNCT
cana-2105	435	1	[	[	X
cana-2105	435	2	15	15	NUM
cana-2105	435	3	]	]	PUNCT
cana-2105	435	4	a.	a.	NOUN
cana-2105	435	5	shahid	shahid	PROPN
cana-2105	435	6	,	,	PUNCT
cana-2105	435	7	w.	w.	PROPN
cana-2105	435	8	nazeer	nazeer	PROPN
cana-2105	435	9	,	,	PUNCT
cana-2105	435	10	and	and	CCONJ
cana-2105	435	11	k.	k.	PROPN
cana-2105	435	12	gdawiec	gdawiec	PROPN
cana-2105	435	13	.	.	PUNCT
cana-2105	436	1	the	the	DET
cana-2105	436	2	picard	picard	NOUN
cana-2105	436	3	–	–	PUNCT
cana-2105	436	4	mann	mann	PROPN
cana-2105	436	5	iteration	iteration	NOUN
cana-2105	436	6	with	with	ADP
cana-2105	436	7	sconvexity	sconvexity	NOUN
cana-2105	436	8	in	in	ADP
cana-2105	436	9	the	the	DET
cana-2105	436	10	generation	generation	NOUN
cana-2105	436	11	of	of	ADP
cana-2105	436	12	mandelbrot	mandelbrot	PROPN
cana-2105	436	13	and	and	CCONJ
cana-2105	436	14	julia	julia	PROPN
cana-2105	436	15	sets	set	NOUN
cana-2105	436	16	.	.	PUNCT
cana-2105	437	1	monatshefte	monatshefte	PROPN
cana-2105	437	2	für	für	PROPN
cana-2105	437	3	mathematik	mathematik	PROPN
cana-2105	437	4	,	,	PUNCT
cana-2105	437	5	195:1–20	195:1–20	NUM
cana-2105	437	6	,	,	PUNCT
cana-2105	437	7	08	08	NUM
cana-2105	437	8	2021	2021	NUM
cana-2105	437	9	.	.	PUNCT
cana-2105	438	1	[	[	X
cana-2105	438	2	16	16	NUM
cana-2105	438	3	]	]	X
cana-2105	438	4	w.	w.	PROPN
cana-2105	438	5	shatanawi	shatanawi	PROPN
cana-2105	438	6	,	,	PUNCT
cana-2105	438	7	a.	a.	NOUN
cana-2105	438	8	bataihah	bataihah	PROPN
cana-2105	438	9	,	,	PUNCT
cana-2105	438	10	and	and	CCONJ
cana-2105	438	11	a.	a.	NOUN
cana-2105	438	12	tallafha	tallafha	NOUN
cana-2105	438	13	.	.	PUNCT
cana-2105	439	1	four	four	NUM
cana-2105	439	2	-	-	PUNCT
cana-2105	439	3	step	step	NOUN
cana-2105	439	4	iteration	iteration	NOUN
cana-2105	439	5	scheme	scheme	NOUN
cana-2105	439	6	to	to	PART
cana-2105	439	7	approximate	approximate	VERB
cana-2105	439	8	fixed	fix	VERB
cana-2105	439	9	point	point	NOUN
cana-2105	439	10	for	for	ADP
cana-2105	439	11	weak	weak	ADJ
cana-2105	439	12	contractions	contraction	NOUN
cana-2105	439	13	.	.	PUNCT
cana-2105	440	1	computers	computer	NOUN
cana-2105	440	2	,	,	PUNCT
cana-2105	440	3	materials	material	NOUN
cana-2105	440	4	&	&	CCONJ
cana-2105	440	5	continua	continuum	NOUN
cana-2105	440	6	,	,	PUNCT
cana-2105	440	7	64:1491–1504	64:1491–1504	NUM
cana-2105	440	8	,	,	PUNCT
cana-2105	440	9	06	06	NUM
cana-2105	440	10	2020	2020	NUM
cana-2105	440	11	.	.	PUNCT
cana-2105	441	1	[	[	X
cana-2105	441	2	17	17	NUM
cana-2105	441	3	]	]	PUNCT
cana-2105	441	4	m.	m.	NOUN
cana-2105	441	5	tanveer	tanveer	PROPN
cana-2105	441	6	,	,	PUNCT
cana-2105	441	7	w.	w.	PROPN
cana-2105	441	8	nazeer	nazeer	PROPN
cana-2105	441	9	,	,	PUNCT
cana-2105	441	10	and	and	CCONJ
cana-2105	441	11	k.	k.	PROPN
cana-2105	441	12	gdawiec	gdawiec	PROPN
cana-2105	441	13	.	.	PUNCT
cana-2105	442	1	new	new	ADJ
cana-2105	442	2	escape	escape	NOUN
cana-2105	442	3	criteria	criterion	NOUN
cana-2105	442	4	for	for	ADP
cana-2105	442	5	complex	complex	ADJ
cana-2105	442	6	fractals	fractal	NOUN
cana-2105	442	7	generation	generation	NOUN
cana-2105	442	8	in	in	ADP
cana-2105	442	9	jungck	jungck	PROPN
cana-2105	442	10	-	-	PUNCT
cana-2105	442	11	cr	cr	PROPN
cana-2105	442	12	orbit	orbit	PROPN
cana-2105	442	13	.	.	PUNCT
cana-2105	443	1	indian	indian	PROPN
cana-2105	443	2	journal	journal	PROPN
cana-2105	443	3	of	of	ADP
cana-2105	443	4	pure	pure	ADJ
cana-2105	443	5	and	and	CCONJ
cana-2105	443	6	applied	applied	ADJ
cana-2105	443	7	mathematics	mathematic	NOUN
cana-2105	443	8	,	,	PUNCT
cana-2105	443	9	51:1285–1303	51:1285–1303	NUM
cana-2105	443	10	,	,	PUNCT
cana-2105	443	11	12	12	NUM
cana-2105	443	12	2020	2020	NUM
cana-2105	443	13	.	.	PUNCT
cana-2105	444	1	[	[	X
cana-2105	444	2	18	18	NUM
cana-2105	444	3	]	]	PUNCT
cana-2105	444	4	a.	a.	NOUN
cana-2105	444	5	tassaddiq	tassaddiq	NOUN
cana-2105	444	6	.	.	PUNCT
cana-2105	445	1	general	general	ADJ
cana-2105	445	2	escape	escape	NOUN
cana-2105	445	3	criteria	criterion	NOUN
cana-2105	445	4	for	for	ADP
cana-2105	445	5	the	the	DET
cana-2105	445	6	generation	generation	NOUN
cana-2105	445	7	of	of	ADP
cana-2105	445	8	fractals	fractal	NOUN
cana-2105	445	9	in	in	ADP
cana-2105	445	10	extended	extended	ADJ
cana-2105	445	11	jungck	jungck	NOUN
cana-2105	445	12	–	–	PUNCT
cana-2105	445	13	noor	noor	PROPN
cana-2105	445	14	orbit	orbit	NOUN
cana-2105	445	15	.	.	PUNCT
cana-2105	446	1	mathematics	mathematic	NOUN
cana-2105	446	2	and	and	CCONJ
cana-2105	446	3	computers	computer	NOUN
cana-2105	446	4	in	in	ADP
cana-2105	446	5	simulation	simulation	NOUN
cana-2105	446	6	,	,	PUNCT
cana-2105	446	7	196:1–14	196:1–14	NUM
cana-2105	446	8	,	,	PUNCT
cana-2105	446	9	2022	2022	NUM
cana-2105	446	10	.	.	PUNCT
cana-2105	447	1	[	[	X
cana-2105	447	2	19	19	NUM
cana-2105	447	3	]	]	PUNCT
cana-2105	447	4	a.	a.	NOUN
cana-2105	447	5	tomar	tomar	PROPN
cana-2105	447	6	,	,	PUNCT
cana-2105	447	7	s.	s.	PROPN
cana-2105	447	8	antal	antal	PROPN
cana-2105	447	9	,	,	PUNCT
cana-2105	447	10	d.	d.	PROPN
cana-2105	447	11	prajapati	prajapati	PROPN
cana-2105	447	12	,	,	PUNCT
cana-2105	447	13	and	and	CCONJ
cana-2105	447	14	p.	p.	PROPN
cana-2105	447	15	agarwal	agarwal	PROPN
cana-2105	447	16	.	.	PUNCT
cana-2105	448	1	mandelbrot	mandelbrot	PROPN
cana-2105	448	2	fractals	fractal	NOUN
cana-2105	448	3	using	use	VERB
cana-2105	448	4	fixed	fix	VERB
cana-2105	448	5	-	-	PUNCT
cana-2105	448	6	point	point	NOUN
cana-2105	448	7	technique	technique	NOUN
cana-2105	448	8	of	of	ADP
cana-2105	448	9	sine	sine	ADJ
cana-2105	448	10	function	function	NOUN
cana-2105	448	11	.	.	PUNCT
cana-2105	449	1	proceedings	proceeding	NOUN
cana-2105	449	2	of	of	ADP
cana-2105	449	3	the	the	DET
cana-2105	449	4	institute	institute	NOUN
cana-2105	449	5	of	of	ADP
cana-2105	449	6	mathematics	mathematics	PROPN
cana-2105	449	7	and	and	CCONJ
cana-2105	449	8	mechanics	mechanic	NOUN
cana-2105	449	9	national	national	PROPN
cana-2105	449	10	academy	academy	PROPN
cana-2105	449	11	of	of	ADP
cana-2105	449	12	sciences	sciences	PROPN
cana-2105	449	13	of	of	ADP
cana-2105	449	14	azerbaijan	azerbaijan	PROPN
cana-2105	449	15	,	,	PUNCT
cana-2105	449	16	48:194–214	48:194–214	NUM
cana-2105	449	17	,	,	PUNCT
cana-2105	449	18	11	11	NUM
cana-2105	449	19	2022	2022	NUM
cana-2105	449	20	.	.	PUNCT
cana-2105	450	1	[	[	X
cana-2105	450	2	20	20	NUM
cana-2105	450	3	]	]	PUNCT
cana-2105	450	4	a.	a.	NOUN
cana-2105	450	5	tomar	tomar	PROPN
cana-2105	450	6	,	,	PUNCT
cana-2105	450	7	v.	v.	PROPN
cana-2105	450	8	kumar	kumar	PROPN
cana-2105	450	9	,	,	PUNCT
cana-2105	450	10	u.	u.	PROPN
cana-2105	450	11	rana	rana	PROPN
cana-2105	450	12	,	,	PUNCT
cana-2105	450	13	and	and	CCONJ
cana-2105	450	14	m.	m.	PROPN
cana-2105	450	15	sajid	sajid	PROPN
cana-2105	450	16	.	.	PUNCT
cana-2105	451	1	fractals	fractal	NOUN
cana-2105	451	2	as	as	ADP
cana-2105	451	3	julia	julia	PROPN
cana-2105	451	4	and	and	CCONJ
cana-2105	451	5	mandelbrot	mandelbrot	PROPN
cana-2105	451	6	sets	set	NOUN
cana-2105	451	7	of	of	ADP
cana-2105	451	8	complex	complex	ADJ
cana-2105	451	9	cosine	cosine	NOUN
cana-2105	451	10	functions	function	NOUN
cana-2105	451	11	via	via	ADP
cana-2105	451	12	fixed	fix	VERB
cana-2105	451	13	point	point	NOUN
cana-2105	451	14	iterations	iteration	NOUN
cana-2105	451	15	.	.	PUNCT
cana-2105	452	1	symmetry	symmetry	NOUN
cana-2105	452	2	,	,	PUNCT
cana-2105	452	3	2023:1–21	2023:1–21	NUM
cana-2105	452	4	,	,	PUNCT
cana-2105	452	5	02	02	NUM
cana-2105	452	6	2023	2023	NUM
cana-2105	452	7	.	.	PUNCT
cana-2105	453	1	[	[	X
cana-2105	453	2	21	21	NUM
cana-2105	453	3	]	]	X
cana-2105	453	4	c.	c.	PROPN
cana-2105	453	5	zou	zou	PROPN
cana-2105	453	6	,	,	PUNCT
cana-2105	453	7	a.	a.	NOUN
cana-2105	453	8	shahid	shahid	PROPN
cana-2105	453	9	,	,	PUNCT
cana-2105	453	10	a.	a.	NOUN
cana-2105	453	11	tassaddiq	tassaddiq	NOUN
cana-2105	453	12	,	,	PUNCT
cana-2105	453	13	a.	a.	PROPN
cana-2105	453	14	khan	khan	PROPN
cana-2105	453	15	,	,	PUNCT
cana-2105	453	16	and	and	CCONJ
cana-2105	453	17	m.	m.	PROPN
cana-2105	453	18	ahmad	ahmad	PROPN
cana-2105	453	19	.	.	PUNCT
cana-2105	454	1	mandelbrot	mandelbrot	PROPN
cana-2105	454	2	sets	set	NOUN
cana-2105	454	3	and	and	CCONJ
cana-2105	454	4	julia	julia	PROPN
cana-2105	454	5	sets	set	NOUN
cana-2105	454	6	in	in	ADP
cana-2105	454	7	picard	picard	NOUN
cana-2105	454	8	-	-	PUNCT
cana-2105	454	9	mann	mann	PROPN
cana-2105	454	10	orbit	orbit	NOUN
cana-2105	454	11	.	.	PUNCT
cana-2105	455	1	ieee	ieee	NOUN
cana-2105	455	2	access	access	NOUN
cana-2105	455	3	,	,	PUNCT
cana-2105	455	4	8:64411–64421	8:64411–64421	NUM
cana-2105	455	5	,	,	PUNCT
cana-2105	455	6	03	03	NUM
cana-2105	455	7	2020	2020	NUM
cana-2105	455	8	.	.	PUNCT
cana-2105	456	1	communications	communication	NOUN
cana-2105	456	2	on	on	ADP
cana-2105	456	3	applied	apply	VERB
cana-2105	456	4	nonlinear	nonlinear	ADJ
cana-2105	456	5	analysis	analysis	NOUN
cana-2105	456	6	issn	issn	NOUN
cana-2105	456	7	:	:	PUNCT
cana-2105	456	8	1074	1074	NUM
cana-2105	456	9	-	-	PUNCT
cana-2105	456	10	133x	133x	NUM
cana-2105	456	11	vol	vol	NOUN
cana-2105	456	12	32	32	NUM
cana-2105	456	13	no	no	NOUN
cana-2105	456	14	.	.	PUNCT
cana-2105	457	1	1s	1s	NUM
cana-2105	457	2	(	(	PUNCT
cana-2105	457	3	2025	2025	NUM
cana-2105	457	4	)	)	PUNCT
cana-2105	457	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-2105	457	6	90	90	NUM
cana-2105	457	7	introduction	introduction	NOUN
cana-2105	457	8	preliminaries	preliminary	NOUN
cana-2105	457	9	main	main	ADJ
cana-2105	457	10	results	result	NOUN
cana-2105	457	11	escape	escape	VERB
cana-2105	457	12	criteria	criterion	NOUN
cana-2105	457	13	for	for	ADP
cana-2105	457	14	complex	complex	ADJ
cana-2105	457	15	sine	sine	ADJ
cana-2105	457	16	functions	function	NOUN
cana-2105	457	17	generation	generation	NOUN
cana-2105	457	18	of	of	ADP
cana-2105	457	19	fractals	fractal	NOUN
cana-2105	457	20	julia	julia	PROPN
cana-2105	457	21	set	set	PROPN
cana-2105	457	22	julia	julia	PROPN
cana-2105	457	23	set	set	PROPN
cana-2105	457	24	for	for	ADP
cana-2105	457	25	the	the	DET
cana-2105	457	26	function	function	NOUN
cana-2105	458	1	tcz=	tcz=	PROPN
cana-2105	458	2	(	(	PUNCT
cana-2105	458	3	zk	zk	PROPN
cana-2105	458	4	)	)	PUNCT
cana-2105	459	1	+	+	CCONJ
cana-2105	459	2	az	az	PROPN
cana-2105	459	3	+	+	NOUN
cana-2105	459	4	c	c	NOUN
cana-2105	459	5	varying	vary	VERB
cana-2105	459	6	the	the	DET
cana-2105	459	7	parameter	parameter	NOUN
cana-2105	459	8	a	a	DET
cana-2105	459	9	julia	julia	PROPN
cana-2105	459	10	set	set	VERB
cana-2105	459	11	for	for	ADP
cana-2105	459	12	the	the	DET
cana-2105	459	13	function	function	NOUN
cana-2105	459	14	tcz=	tcz=	PROPN
cana-2105	459	15	(	(	PUNCT
cana-2105	459	16	zk	zk	PROPN
cana-2105	459	17	)	)	PUNCT
cana-2105	460	1	+	+	CCONJ
cana-2105	460	2	az	az	PROPN
cana-2105	460	3	+	+	NOUN
cana-2105	460	4	c	c	NOUN
cana-2105	460	5	varying	vary	VERB
cana-2105	460	6	the	the	DET
cana-2105	460	7	parameter	parameter	NOUN
cana-2105	460	8	c	c	PROPN
cana-2105	460	9	julia	julia	PROPN
cana-2105	460	10	set	set	VERB
cana-2105	460	11	for	for	ADP
cana-2105	460	12	the	the	DET
cana-2105	460	13	function	function	NOUN
cana-2105	460	14	tcz=	tcz=	PROPN
cana-2105	460	15	(	(	PUNCT
cana-2105	460	16	zk	zk	PROPN
cana-2105	460	17	)	)	PUNCT
cana-2105	461	1	+	+	CCONJ
cana-2105	461	2	az	az	PROPN
cana-2105	461	3	+	+	NOUN
cana-2105	461	4	c	c	NOUN
cana-2105	461	5	varying	vary	VERB
cana-2105	461	6	the	the	DET
cana-2105	461	7	convexity	convexity	NOUN
cana-2105	461	8	parameter	parameter	NOUN
cana-2105	461	9	s	s	PROPN
cana-2105	461	10	julia	julia	PROPN
cana-2105	461	11	set	set	VERB
cana-2105	461	12	for	for	ADP
cana-2105	461	13	the	the	DET
cana-2105	461	14	function	function	NOUN
cana-2105	461	15	tcz=	tcz=	PROPN
cana-2105	461	16	(	(	PUNCT
cana-2105	461	17	zk	zk	PROPN
cana-2105	461	18	)	)	PUNCT
cana-2105	461	19	+	+	CCONJ
cana-2105	461	20	az	az	PROPN
cana-2105	461	21	+	+	NOUN
cana-2105	461	22	c	c	NOUN
cana-2105	461	23	varying	vary	VERB
cana-2105	461	24	the	the	DET
cana-2105	461	25	parameter	parameter	NOUN
cana-2105	461	26	julia	julia	PROPN
cana-2105	461	27	set	set	PROPN
cana-2105	461	28	for	for	ADP
cana-2105	461	29	the	the	DET
cana-2105	461	30	function	function	NOUN
cana-2105	461	31	tcz=	tcz=	PROPN
cana-2105	461	32	(	(	PUNCT
cana-2105	461	33	zk	zk	PROPN
cana-2105	461	34	)	)	PUNCT
cana-2105	462	1	+	+	CCONJ
cana-2105	462	2	az	az	PROPN
cana-2105	462	3	+	+	NOUN
cana-2105	462	4	c	c	NOUN
cana-2105	462	5	varying	vary	VERB
cana-2105	462	6	the	the	DET
cana-2105	462	7	parameter	parameter	NOUN
cana-2105	462	8	julia	julia	PROPN
cana-2105	462	9	set	set	PROPN
cana-2105	462	10	for	for	ADP
cana-2105	462	11	the	the	DET
cana-2105	462	12	function	function	NOUN
cana-2105	462	13	tcz=	tcz=	PROPN
cana-2105	462	14	(	(	PUNCT
cana-2105	462	15	zk	zk	PROPN
cana-2105	462	16	)	)	PUNCT
cana-2105	463	1	+	+	CCONJ
cana-2105	463	2	az	az	PROPN
cana-2105	463	3	+	+	NOUN
cana-2105	463	4	c	c	NOUN
cana-2105	463	5	varying	vary	VERB
cana-2105	463	6	the	the	DET
cana-2105	463	7	parameter	parameter	NOUN
cana-2105	463	8	julia	julia	PROPN
cana-2105	463	9	set	set	PROPN
cana-2105	463	10	for	for	ADP
cana-2105	463	11	the	the	DET
cana-2105	463	12	function	function	NOUN
cana-2105	463	13	tcz=	tcz=	PROPN
cana-2105	463	14	(	(	PUNCT
cana-2105	463	15	zk	zk	PROPN
cana-2105	463	16	)	)	PUNCT
cana-2105	464	1	+	+	CCONJ
cana-2105	464	2	az	az	PROPN
cana-2105	464	3	+	+	NOUN
cana-2105	464	4	c	c	NOUN
cana-2105	464	5	varying	vary	VERB
cana-2105	464	6	the	the	DET
cana-2105	464	7	parameter	parameter	NOUN
cana-2105	464	8	julia	julia	PROPN
cana-2105	464	9	set	set	PROPN
cana-2105	464	10	for	for	ADP
cana-2105	464	11	the	the	DET
cana-2105	464	12	function	function	NOUN
cana-2105	464	13	tcz=	tcz=	PROPN
cana-2105	464	14	(	(	PUNCT
cana-2105	464	15	zk	zk	PROPN
cana-2105	464	16	)	)	PUNCT
cana-2105	465	1	+	+	CCONJ
cana-2105	465	2	az	az	PROPN
cana-2105	465	3	+	+	NOUN
cana-2105	465	4	c	c	NOUN
cana-2105	465	5	varying	vary	VERB
cana-2105	465	6	the	the	DET
cana-2105	465	7	parameter	parameter	NOUN
cana-2105	465	8	julia	julia	PROPN
cana-2105	465	9	set	set	PROPN
cana-2105	465	10	for	for	ADP
cana-2105	465	11	the	the	DET
cana-2105	465	12	function	function	NOUN
cana-2105	465	13	tcz=	tcz=	PROPN
cana-2105	465	14	(	(	PUNCT
cana-2105	465	15	zk	zk	PROPN
cana-2105	465	16	)	)	PUNCT
cana-2105	466	1	+	+	CCONJ
cana-2105	466	2	az	az	PROPN
cana-2105	466	3	+	+	NOUN
cana-2105	466	4	c	c	NOUN
cana-2105	466	5	varying	vary	VERB
cana-2105	466	6	the	the	DET
cana-2105	466	7	k	k	PROPN
cana-2105	466	8	mandelbrot	mandelbrot	PROPN
cana-2105	466	9	set	set	VERB
cana-2105	466	10	mandelbrot	mandelbrot	PROPN
cana-2105	466	11	set	set	VERB
cana-2105	466	12	for	for	ADP
cana-2105	466	13	the	the	DET
cana-2105	466	14	function	function	NOUN
cana-2105	467	1	tcz=	tcz=	PROPN
cana-2105	467	2	(	(	PUNCT
cana-2105	467	3	zk	zk	PROPN
cana-2105	467	4	)	)	PUNCT
cana-2105	468	1	+	+	CCONJ
cana-2105	468	2	az	az	PROPN
cana-2105	468	3	+	+	NOUN
cana-2105	468	4	c	c	NOUN
cana-2105	468	5	varying	vary	VERB
cana-2105	468	6	the	the	DET
cana-2105	468	7	parameter	parameter	NOUN
cana-2105	468	8	a	a	DET
cana-2105	468	9	mandelbrot	mandelbrot	NOUN
cana-2105	468	10	set	set	VERB
cana-2105	468	11	for	for	ADP
cana-2105	468	12	the	the	DET
cana-2105	468	13	function	function	NOUN
cana-2105	468	14	tcz=	tcz=	PROPN
cana-2105	468	15	(	(	PUNCT
cana-2105	468	16	zk	zk	PROPN
cana-2105	468	17	)	)	PUNCT
cana-2105	469	1	+	+	CCONJ
cana-2105	469	2	az	az	PROPN
cana-2105	469	3	+	+	NOUN
cana-2105	469	4	c	c	NOUN
cana-2105	469	5	varying	vary	VERB
cana-2105	469	6	the	the	DET
cana-2105	469	7	parameter	parameter	NOUN
cana-2105	469	8	s	s	PART
cana-2105	469	9	mandelbrot	mandelbrot	PROPN
cana-2105	469	10	set	set	VERB
cana-2105	469	11	for	for	ADP
cana-2105	469	12	the	the	DET
cana-2105	469	13	function	function	NOUN
cana-2105	469	14	tcz=	tcz=	PROPN
cana-2105	469	15	(	(	PUNCT
cana-2105	469	16	zk	zk	PROPN
cana-2105	469	17	)	)	PUNCT
cana-2105	470	1	+	+	CCONJ
cana-2105	470	2	az	az	PROPN
cana-2105	470	3	+	+	NOUN
cana-2105	470	4	c	c	NOUN
cana-2105	470	5	varying	vary	VERB
cana-2105	470	6	the	the	DET
cana-2105	470	7	parameter	parameter	NOUN
cana-2105	470	8	mandelbrot	mandelbrot	PROPN
cana-2105	470	9	set	set	VERB
cana-2105	470	10	for	for	ADP
cana-2105	470	11	the	the	DET
cana-2105	470	12	function	function	NOUN
cana-2105	470	13	tcz=	tcz=	PROPN
cana-2105	470	14	(	(	PUNCT
cana-2105	470	15	zk	zk	PROPN
cana-2105	470	16	)	)	PUNCT
cana-2105	471	1	+	+	CCONJ
cana-2105	471	2	az	az	PROPN
cana-2105	471	3	+	+	NOUN
cana-2105	471	4	c	c	NOUN
cana-2105	471	5	varying	vary	VERB
cana-2105	471	6	the	the	DET
cana-2105	471	7	parameter	parameter	NOUN
cana-2105	471	8	mandelbrot	mandelbrot	PROPN
cana-2105	471	9	set	set	VERB
cana-2105	471	10	for	for	ADP
cana-2105	471	11	the	the	DET
cana-2105	471	12	function	function	NOUN
cana-2105	471	13	tcz=	tcz=	PROPN
cana-2105	471	14	(	(	PUNCT
cana-2105	471	15	zk	zk	PROPN
cana-2105	471	16	)	)	PUNCT
cana-2105	472	1	+	+	CCONJ
cana-2105	472	2	az	az	PROPN
cana-2105	472	3	+	+	NOUN
cana-2105	472	4	c	c	NOUN
cana-2105	472	5	varying	vary	VERB
cana-2105	472	6	the	the	DET
cana-2105	472	7	parameter	parameter	NOUN
cana-2105	472	8	mandelbrot	mandelbrot	PROPN
cana-2105	472	9	set	set	VERB
cana-2105	472	10	for	for	ADP
cana-2105	472	11	the	the	DET
cana-2105	472	12	function	function	NOUN
cana-2105	472	13	tcz=	tcz=	PROPN
cana-2105	472	14	(	(	PUNCT
cana-2105	472	15	zk	zk	PROPN
cana-2105	472	16	)	)	PUNCT
cana-2105	473	1	+	+	CCONJ
cana-2105	473	2	az	az	PROPN
cana-2105	473	3	+	+	NOUN
cana-2105	473	4	c	c	NOUN
cana-2105	473	5	varying	vary	VERB
cana-2105	473	6	the	the	DET
cana-2105	473	7	parameter	parameter	NOUN
cana-2105	473	8	mandelbrot	mandelbrot	PROPN
cana-2105	473	9	set	set	VERB
cana-2105	473	10	for	for	ADP
cana-2105	473	11	the	the	DET
cana-2105	473	12	function	function	NOUN
cana-2105	473	13	tcz=	tcz=	PROPN
cana-2105	473	14	(	(	PUNCT
cana-2105	473	15	zk	zk	PROPN
cana-2105	473	16	)	)	PUNCT
cana-2105	474	1	+	+	CCONJ
cana-2105	474	2	az	az	PROPN
cana-2105	474	3	+	+	NOUN
cana-2105	474	4	c	c	NOUN
cana-2105	474	5	varying	vary	VERB
cana-2105	474	6	the	the	DET
cana-2105	474	7	parameter	parameter	NOUN
cana-2105	474	8	k	k	PROPN
cana-2105	474	9	conclusions	conclusion	NOUN