id	sid	tid	token	lemma	pos
concept-2079	1	1	microsoft	microsoft	PROPN
concept-2079	1	2	word	word	PROPN
concept-2079	1	3	somalwar	somalwar	PROPN
concept-2079	1	4	math	math	NOUN
concept-2079	1	5	final	final	ADJ
concept-2079	1	6	for	for	ADP
concept-2079	1	7	on	on	ADP
concept-2079	1	8	-	-	PUNCT
concept-2079	1	9	line	line	NOUN
concept-2079	1	10	edition.docx	edition.docx	PROPN
concept-2079	1	11	concept	concept	NOUN
concept-2079	1	12	,	,	PUNCT
concept-2079	1	13	vol	vol	NOUN
concept-2079	1	14	.	.	PUNCT
concept-2079	2	1	xxxix	xxxix	PROPN
concept-2079	2	2	(	(	PUNCT
concept-2079	2	3	2016	2016	NUM
concept-2079	2	4	)	)	PUNCT
concept-2079	2	5	1	1	NUM
concept-2079	2	6	analysis	analysis	NOUN
concept-2079	2	7	of	of	ADP
concept-2079	2	8	fractals	fractal	NOUN
concept-2079	2	9	from	from	ADP
concept-2079	2	10	a	a	DET
concept-2079	2	11	mathematical	mathematical	ADJ
concept-2079	2	12	and	and	CCONJ
concept-2079	2	13	real	real	ADJ
concept-2079	2	14	-	-	PUNCT
concept-2079	2	15	world	world	NOUN
concept-2079	2	16	perspective	perspective	NOUN
concept-2079	2	17	anup	anup	PROPN
concept-2079	2	18	a.	a.	PROPN
concept-2079	2	19	somalwar	somalwar	PROPN
concept-2079	2	20	mathematics	mathematics	PROPN
concept-2079	2	21	historical	historical	ADJ
concept-2079	2	22	background	background	NOUN
concept-2079	2	23	fractals	fractal	NOUN
concept-2079	2	24	give	give	VERB
concept-2079	2	25	us	we	PRON
concept-2079	2	26	a	a	DET
concept-2079	2	27	way	way	NOUN
concept-2079	2	28	to	to	PART
concept-2079	2	29	visually	visually	ADV
concept-2079	2	30	and	and	CCONJ
concept-2079	2	31	quantitatively	quantitatively	ADV
concept-2079	2	32	observe	observe	VERB
concept-2079	2	33	various	various	ADJ
concept-2079	2	34	abstract	abstract	ADJ
concept-2079	2	35	and	and	CCONJ
concept-2079	2	36	real	real	ADJ
concept-2079	2	37	-	-	PUNCT
concept-2079	2	38	world	world	NOUN
concept-2079	2	39	phenomena	phenomenon	NOUN
concept-2079	2	40	.	.	PUNCT
concept-2079	3	1	mathematician	mathematician	ADJ
concept-2079	3	2	benoit	benoit	PROPN
concept-2079	3	3	mandelbrot	mandelbrot	PROPN
concept-2079	3	4	coined	coin	VERB
concept-2079	3	5	the	the	DET
concept-2079	3	6	word	word	NOUN
concept-2079	3	7	“	"	PUNCT
concept-2079	3	8	fractal	fractal	NOUN
concept-2079	3	9	”	"	PUNCT
concept-2079	3	10	in	in	ADP
concept-2079	3	11	1975	1975	NUM
concept-2079	3	12	(	(	PUNCT
concept-2079	3	13	stewart	stewart	PROPN
concept-2079	3	14	,	,	PUNCT
concept-2079	3	15	clark	clark	PROPN
concept-2079	3	16	,	,	PUNCT
concept-2079	3	17	mandelbrot	mandelbrot	PROPN
concept-2079	3	18	,	,	PUNCT
concept-2079	3	19	et	et	PROPN
concept-2079	3	20	al	al	PROPN
concept-2079	3	21	.	.	PROPN
concept-2079	3	22	,	,	PUNCT
concept-2079	3	23	5	5	X
concept-2079	3	24	)	)	PUNCT
concept-2079	3	25	while	while	SCONJ
concept-2079	3	26	working	work	VERB
concept-2079	3	27	at	at	ADP
concept-2079	3	28	ibm	ibm	PROPN
concept-2079	3	29	but	but	CCONJ
concept-2079	3	30	other	other	ADJ
concept-2079	3	31	mathematicians	mathematician	NOUN
concept-2079	3	32	had	have	AUX
concept-2079	3	33	studied	study	VERB
concept-2079	3	34	these	these	DET
concept-2079	3	35	geometric	geometric	ADJ
concept-2079	3	36	structures	structure	NOUN
concept-2079	3	37	long	long	ADV
concept-2079	3	38	before	before	ADP
concept-2079	3	39	him	he	PRON
concept-2079	3	40	.	.	PUNCT
concept-2079	4	1	during	during	ADP
concept-2079	4	2	the	the	DET
concept-2079	4	3	18th	18th	ADJ
concept-2079	4	4	and	and	CCONJ
concept-2079	4	5	19th	19th	ADJ
concept-2079	4	6	centuries	century	NOUN
concept-2079	4	7	,	,	PUNCT
concept-2079	4	8	calculus	calculus	NOUN
concept-2079	4	9	was	be	AUX
concept-2079	4	10	gaining	gain	VERB
concept-2079	4	11	mass	mass	NOUN
concept-2079	4	12	appeal	appeal	NOUN
concept-2079	4	13	.	.	PUNCT
concept-2079	5	1	most	most	ADJ
concept-2079	5	2	mathematicians	mathematician	NOUN
concept-2079	5	3	of	of	ADP
concept-2079	5	4	this	this	DET
concept-2079	5	5	period	period	NOUN
concept-2079	5	6	believed	believe	VERB
concept-2079	5	7	that	that	SCONJ
concept-2079	5	8	all	all	DET
concept-2079	5	9	continuous	continuous	ADJ
concept-2079	5	10	curves	curve	NOUN
concept-2079	5	11	could	could	AUX
concept-2079	5	12	have	have	VERB
concept-2079	5	13	tangent	tangent	NOUN
concept-2079	5	14	lines	line	NOUN
concept-2079	5	15	drawn	draw	VERB
concept-2079	5	16	at	at	ADP
concept-2079	5	17	any	any	DET
concept-2079	5	18	point	point	NOUN
concept-2079	5	19	on	on	ADP
concept-2079	5	20	the	the	DET
concept-2079	5	21	function	function	NOUN
concept-2079	5	22	,	,	PUNCT
concept-2079	5	23	except	except	SCONJ
concept-2079	5	24	at	at	ADP
concept-2079	5	25	cusps	cusps	NOUN
concept-2079	5	26	.	.	PUNCT
concept-2079	6	1	in	in	ADP
concept-2079	6	2	1872	1872	NUM
concept-2079	6	3	,	,	PUNCT
concept-2079	6	4	mathematician	mathematician	ADJ
concept-2079	6	5	karl	karl	PROPN
concept-2079	6	6	weierstrass	weierstrass	PROPN
concept-2079	6	7	,	,	PUNCT
concept-2079	6	8	described	describe	VERB
concept-2079	6	9	a	a	DET
concept-2079	6	10	family	family	NOUN
concept-2079	6	11	of	of	ADP
concept-2079	6	12	curves	curve	NOUN
concept-2079	6	13	that	that	PRON
concept-2079	6	14	were	be	AUX
concept-2079	6	15	continuous	continuous	ADJ
concept-2079	6	16	but	but	CCONJ
concept-2079	6	17	not	not	PART
concept-2079	6	18	differentiable	differentiable	ADJ
concept-2079	6	19	at	at	ADP
concept-2079	6	20	any	any	DET
concept-2079	6	21	point	point	NOUN
concept-2079	6	22	(	(	PUNCT
concept-2079	6	23	stewart	stewart	PROPN
concept-2079	6	24	,	,	PUNCT
concept-2079	6	25	clark	clark	PROPN
concept-2079	6	26	,	,	PUNCT
concept-2079	6	27	mandelbrot	mandelbrot	PROPN
concept-2079	6	28	,	,	PUNCT
concept-2079	6	29	et	et	PROPN
concept-2079	6	30	al	al	PROPN
concept-2079	6	31	.	.	PROPN
concept-2079	6	32	,	,	PUNCT
concept-2079	6	33	6	6	NUM
concept-2079	6	34	-	-	SYM
concept-2079	6	35	7	7	NUM
concept-2079	6	36	)	)	PUNCT
concept-2079	6	37	.	.	PUNCT
concept-2079	7	1	this	this	DET
concept-2079	7	2	discovery	discovery	NOUN
concept-2079	7	3	surprised	surprise	VERB
concept-2079	7	4	mathematicians	mathematician	NOUN
concept-2079	7	5	because	because	SCONJ
concept-2079	7	6	it	it	PRON
concept-2079	7	7	challenged	challenge	VERB
concept-2079	7	8	current	current	ADJ
concept-2079	7	9	ideas	idea	NOUN
concept-2079	7	10	about	about	ADP
concept-2079	7	11	mathematics	mathematic	NOUN
concept-2079	7	12	(	(	PUNCT
concept-2079	7	13	eglash	eglash	NOUN
concept-2079	7	14	,	,	PUNCT
concept-2079	7	15	12	12	NUM
concept-2079	7	16	)	)	PUNCT
concept-2079	7	17	.	.	PUNCT
concept-2079	8	1	mathematicians	mathematician	NOUN
concept-2079	8	2	were	be	AUX
concept-2079	8	3	somewhat	somewhat	ADV
concept-2079	8	4	uncomfortable	uncomfortable	ADJ
concept-2079	8	5	with	with	ADP
concept-2079	8	6	the	the	DET
concept-2079	8	7	idea	idea	NOUN
concept-2079	8	8	of	of	ADP
concept-2079	8	9	continuous	continuous	ADJ
concept-2079	8	10	curves	curve	NOUN
concept-2079	8	11	that	that	PRON
concept-2079	8	12	could	could	AUX
concept-2079	8	13	repeat	repeat	VERB
concept-2079	8	14	,	,	PUNCT
concept-2079	8	15	or	or	CCONJ
concept-2079	8	16	iterate	iterate	NOUN
concept-2079	8	17	,	,	PUNCT
concept-2079	8	18	themselves	themselves	PRON
concept-2079	8	19	infinite	infinite	VERB
concept-2079	8	20	times	time	NOUN
concept-2079	8	21	within	within	ADP
concept-2079	8	22	a	a	DET
concept-2079	8	23	finite	finite	ADJ
concept-2079	8	24	space	space	NOUN
concept-2079	8	25	.	.	PUNCT
concept-2079	9	1	two	two	NUM
concept-2079	9	2	questions	question	NOUN
concept-2079	9	3	arose	arise	VERB
concept-2079	9	4	from	from	ADP
concept-2079	9	5	this	this	DET
concept-2079	9	6	period	period	NOUN
concept-2079	9	7	:	:	PUNCT
concept-2079	9	8	what	what	PRON
concept-2079	9	9	are	be	AUX
concept-2079	9	10	the	the	DET
concept-2079	9	11	dimensions	dimension	NOUN
concept-2079	9	12	of	of	ADP
concept-2079	9	13	these	these	DET
concept-2079	9	14	curves	curve	NOUN
concept-2079	9	15	,	,	PUNCT
concept-2079	9	16	and	and	CCONJ
concept-2079	9	17	can	can	AUX
concept-2079	9	18	we	we	PRON
concept-2079	9	19	measure	measure	VERB
concept-2079	9	20	the	the	DET
concept-2079	9	21	lengths	length	NOUN
concept-2079	9	22	of	of	ADP
concept-2079	9	23	these	these	DET
concept-2079	9	24	“	"	PUNCT
concept-2079	9	25	pathological	pathological	ADJ
concept-2079	9	26	curves	curve	NOUN
concept-2079	9	27	”	"	PUNCT
concept-2079	9	28	as	as	SCONJ
concept-2079	9	29	they	they	PRON
concept-2079	9	30	iterate	iterate	VERB
concept-2079	9	31	over	over	ADP
concept-2079	9	32	and	and	CCONJ
concept-2079	9	33	over	over	ADV
concept-2079	9	34	again	again	ADV
concept-2079	9	35	in	in	ADP
concept-2079	9	36	a	a	DET
concept-2079	9	37	finite	finite	ADJ
concept-2079	9	38	space	space	NOUN
concept-2079	9	39	?	?	PUNCT
concept-2079	10	1	in	in	ADP
concept-2079	10	2	the	the	DET
concept-2079	10	3	early	early	ADJ
concept-2079	10	4	20th	20th	ADJ
concept-2079	10	5	century	century	NOUN
concept-2079	10	6	,	,	PUNCT
concept-2079	10	7	mathematician	mathematician	ADJ
concept-2079	10	8	felix	felix	PROPN
concept-2079	10	9	hausdorff	hausdorff	PROPN
concept-2079	10	10	,	,	PUNCT
concept-2079	10	11	helped	help	VERB
concept-2079	10	12	make	make	VERB
concept-2079	10	13	the	the	DET
concept-2079	10	14	idea	idea	NOUN
concept-2079	10	15	of	of	ADP
concept-2079	10	16	fractional	fractional	ADJ
concept-2079	10	17	dimension	dimension	NOUN
concept-2079	10	18	clear	clear	ADJ
concept-2079	10	19	,	,	PUNCT
concept-2079	10	20	believing	believe	VERB
concept-2079	10	21	fractals	fractal	NOUN
concept-2079	10	22	to	to	PART
concept-2079	10	23	be	be	AUX
concept-2079	10	24	in	in	ADP
concept-2079	10	25	an	an	DET
concept-2079	10	26	in	in	NOUN
concept-2079	10	27	-	-	PUNCT
concept-2079	10	28	between	between	NOUN
concept-2079	10	29	dimension	dimension	NOUN
concept-2079	10	30	as	as	SCONJ
concept-2079	10	31	they	they	PRON
concept-2079	10	32	were	be	AUX
concept-2079	10	33	not	not	PART
concept-2079	10	34	quite	quite	ADV
concept-2079	10	35	two	two	NUM
concept-2079	10	36	-	-	PUNCT
concept-2079	10	37	dimensional	dimensional	ADJ
concept-2079	10	38	objects	object	NOUN
concept-2079	10	39	or	or	CCONJ
concept-2079	10	40	one	one	NUM
concept-2079	10	41	-	-	PUNCT
concept-2079	10	42	dimensional	dimensional	ADJ
concept-2079	10	43	mathematical	mathematical	ADJ
concept-2079	10	44	structures	structure	NOUN
concept-2079	10	45	.	.	PUNCT
concept-2079	11	1	his	his	PRON
concept-2079	11	2	main	main	ADJ
concept-2079	11	3	contribution	contribution	NOUN
concept-2079	11	4	to	to	ADP
concept-2079	11	5	this	this	DET
concept-2079	11	6	area	area	NOUN
concept-2079	11	7	of	of	ADP
concept-2079	11	8	mathematics	mathematic	NOUN
concept-2079	11	9	was	be	AUX
concept-2079	11	10	the	the	DET
concept-2079	11	11	hausdorff	hausdorff	NOUN
concept-2079	11	12	dimension	dimension	NOUN
concept-2079	11	13	(	(	PUNCT
concept-2079	11	14	barnsley	barnsley	NOUN
concept-2079	11	15	,	,	PUNCT
concept-2079	11	16	p.	p.	NOUN
concept-2079	11	17	171	171	NUM
concept-2079	11	18	):	):	PUNCT
concept-2079	11	19	𝑑	𝑑	PROPN
concept-2079	11	20	=	=	SYM
concept-2079	11	21	ln𝑁	ln𝑁	PROPN
concept-2079	11	22	ln	ln	NOUN
concept-2079	12	1	𝑠	𝑠	INTJ
concept-2079	12	2	where	where	SCONJ
concept-2079	12	3	d	d	NOUN
concept-2079	12	4	is	be	AUX
concept-2079	12	5	the	the	DET
concept-2079	12	6	dimension	dimension	NOUN
concept-2079	12	7	,	,	PUNCT
concept-2079	12	8	n	n	X
concept-2079	12	9	is	be	AUX
concept-2079	12	10	the	the	DET
concept-2079	12	11	number	number	NOUN
concept-2079	12	12	of	of	ADP
concept-2079	12	13	self	self	NOUN
concept-2079	12	14	-	-	PUNCT
concept-2079	12	15	similar	similar	ADJ
concept-2079	12	16	pieces	piece	NOUN
concept-2079	12	17	of	of	ADP
concept-2079	12	18	the	the	DET
concept-2079	12	19	geometric	geometric	ADJ
concept-2079	12	20	object	object	NOUN
concept-2079	12	21	in	in	ADP
concept-2079	12	22	question	question	NOUN
concept-2079	12	23	,	,	PUNCT
concept-2079	12	24	and	and	CCONJ
concept-2079	12	25	s	s	VERB
concept-2079	12	26	is	be	AUX
concept-2079	12	27	the	the	DET
concept-2079	12	28	scaling	scaling	NOUN
concept-2079	12	29	or	or	CCONJ
concept-2079	12	30	magnification	magnification	NOUN
concept-2079	12	31	factor	factor	NOUN
concept-2079	12	32	.	.	PUNCT
concept-2079	13	1	concept	concept	NOUN
concept-2079	13	2	,	,	PUNCT
concept-2079	13	3	vol	vol	NOUN
concept-2079	13	4	.	.	PUNCT
concept-2079	14	1	xxxix	xxxix	PROPN
concept-2079	14	2	(	(	PUNCT
concept-2079	14	3	2016	2016	NUM
concept-2079	14	4	)	)	PUNCT
concept-2079	14	5	2	2	NUM
concept-2079	14	6	mandelbrot	mandelbrot	NOUN
concept-2079	14	7	took	take	VERB
concept-2079	14	8	hausdorff	hausdorff	NOUN
concept-2079	14	9	's	's	PART
concept-2079	14	10	idea	idea	NOUN
concept-2079	14	11	one	one	NUM
concept-2079	14	12	-	-	PUNCT
concept-2079	14	13	step	step	NOUN
concept-2079	14	14	further	far	ADV
concept-2079	14	15	when	when	SCONJ
concept-2079	14	16	he	he	PRON
concept-2079	14	17	explored	explore	VERB
concept-2079	14	18	how	how	SCONJ
concept-2079	14	19	to	to	PART
concept-2079	14	20	measure	measure	VERB
concept-2079	14	21	the	the	DET
concept-2079	14	22	coastline	coastline	NOUN
concept-2079	14	23	of	of	ADP
concept-2079	14	24	great	great	ADJ
concept-2079	14	25	britain	britain	PROPN
concept-2079	14	26	using	use	VERB
concept-2079	14	27	different	different	ADJ
concept-2079	14	28	measures	measure	NOUN
concept-2079	14	29	.	.	PUNCT
concept-2079	15	1	he	he	PRON
concept-2079	15	2	determined	determine	VERB
concept-2079	15	3	that	that	SCONJ
concept-2079	15	4	if	if	SCONJ
concept-2079	15	5	you	you	PRON
concept-2079	15	6	use	use	VERB
concept-2079	15	7	a	a	DET
concept-2079	15	8	smaller	small	ADJ
concept-2079	15	9	and	and	CCONJ
concept-2079	15	10	smaller	small	ADJ
concept-2079	15	11	measuring	measuring	NOUN
concept-2079	15	12	instrument	instrument	NOUN
concept-2079	15	13	approaching	approach	VERB
concept-2079	15	14	a	a	DET
concept-2079	15	15	length	length	NOUN
concept-2079	15	16	of	of	ADP
concept-2079	15	17	zero	zero	NUM
concept-2079	15	18	units	unit	NOUN
concept-2079	15	19	,	,	PUNCT
concept-2079	15	20	the	the	DET
concept-2079	15	21	approximation	approximation	NOUN
concept-2079	15	22	of	of	ADP
concept-2079	15	23	the	the	DET
concept-2079	15	24	coast	coast	NOUN
concept-2079	15	25	gets	get	VERB
concept-2079	15	26	larger	large	ADJ
concept-2079	15	27	and	and	CCONJ
concept-2079	15	28	larger	large	ADJ
concept-2079	15	29	,	,	PUNCT
concept-2079	15	30	approaching	approach	VERB
concept-2079	15	31	infinity	infinity	NOUN
concept-2079	15	32	.	.	PUNCT
concept-2079	16	1	he	he	PRON
concept-2079	16	2	also	also	ADV
concept-2079	16	3	discusses	discuss	VERB
concept-2079	16	4	the	the	DET
concept-2079	16	5	idea	idea	NOUN
concept-2079	16	6	of	of	ADP
concept-2079	16	7	fractional	fractional	ADJ
concept-2079	16	8	dimension	dimension	NOUN
concept-2079	16	9	,	,	PUNCT
concept-2079	16	10	comparing	compare	VERB
concept-2079	16	11	the	the	DET
concept-2079	16	12	coastline	coastline	NOUN
concept-2079	16	13	of	of	ADP
concept-2079	16	14	england	england	PROPN
concept-2079	16	15	to	to	ADP
concept-2079	16	16	the	the	DET
concept-2079	16	17	koch	koch	PROPN
concept-2079	16	18	snowflake	snowflake	NOUN
concept-2079	16	19	,	,	PUNCT
concept-2079	16	20	yielding	yield	VERB
concept-2079	16	21	a	a	DET
concept-2079	16	22	dimension	dimension	NOUN
concept-2079	16	23	of	of	ADP
concept-2079	16	24	1.26	1.26	NUM
concept-2079	16	25	for	for	ADP
concept-2079	16	26	the	the	DET
concept-2079	16	27	koch	koch	PROPN
concept-2079	16	28	snowflake	snowflake	NOUN
concept-2079	16	29	and	and	CCONJ
concept-2079	16	30	1.25	1.25	NUM
concept-2079	16	31	for	for	ADP
concept-2079	16	32	the	the	DET
concept-2079	16	33	coastline	coastline	NOUN
concept-2079	16	34	(	(	PUNCT
concept-2079	16	35	mandelbrot	mandelbrot	PROPN
concept-2079	16	36	,	,	PUNCT
concept-2079	16	37	1	1	NUM
concept-2079	16	38	-	-	SYM
concept-2079	16	39	5	5	NUM
concept-2079	16	40	)	)	PUNCT
concept-2079	16	41	.	.	PUNCT
concept-2079	17	1	he	he	PRON
concept-2079	17	2	was	be	AUX
concept-2079	17	3	not	not	PART
concept-2079	17	4	implying	imply	VERB
concept-2079	17	5	that	that	SCONJ
concept-2079	17	6	the	the	DET
concept-2079	17	7	koch	koch	PROPN
concept-2079	17	8	snowflake	snowflake	NOUN
concept-2079	17	9	and	and	CCONJ
concept-2079	17	10	the	the	DET
concept-2079	17	11	coastline	coastline	NOUN
concept-2079	17	12	of	of	ADP
concept-2079	17	13	england	england	PROPN
concept-2079	17	14	had	have	VERB
concept-2079	17	15	the	the	DET
concept-2079	17	16	same	same	ADJ
concept-2079	17	17	structure	structure	NOUN
concept-2079	17	18	but	but	CCONJ
concept-2079	17	19	that	that	SCONJ
concept-2079	17	20	the	the	DET
concept-2079	17	21	overall	overall	ADJ
concept-2079	17	22	dimension	dimension	NOUN
concept-2079	17	23	,	,	PUNCT
concept-2079	17	24	or	or	CCONJ
concept-2079	17	25	statistical	statistical	ADJ
concept-2079	17	26	self	self	NOUN
concept-2079	17	27	-	-	PUNCT
concept-2079	17	28	similarity	similarity	NOUN
concept-2079	17	29	,	,	PUNCT
concept-2079	17	30	was	be	AUX
concept-2079	17	31	similar	similar	ADJ
concept-2079	17	32	.	.	PUNCT
concept-2079	18	1	this	this	DET
concept-2079	18	2	historical	historical	ADJ
concept-2079	18	3	background	background	NOUN
concept-2079	18	4	lays	lay	VERB
concept-2079	18	5	the	the	DET
concept-2079	18	6	groundwork	groundwork	NOUN
concept-2079	18	7	for	for	ADP
concept-2079	18	8	our	our	PRON
concept-2079	18	9	study	study	NOUN
concept-2079	18	10	of	of	ADP
concept-2079	18	11	the	the	DET
concept-2079	18	12	mathematics	mathematic	NOUN
concept-2079	18	13	underlying	underlie	VERB
concept-2079	18	14	fractals	fractal	NOUN
concept-2079	18	15	and	and	CCONJ
concept-2079	18	16	their	their	PRON
concept-2079	18	17	applications	application	NOUN
concept-2079	18	18	to	to	ADP
concept-2079	18	19	our	our	PRON
concept-2079	18	20	world	world	NOUN
concept-2079	18	21	.	.	PUNCT
concept-2079	19	1	definitions	definition	NOUN
concept-2079	19	2	and	and	CCONJ
concept-2079	19	3	classic	classic	ADJ
concept-2079	19	4	examples	example	NOUN
concept-2079	19	5	of	of	ADP
concept-2079	19	6	fractals	fractal	NOUN
concept-2079	19	7	a	a	DET
concept-2079	19	8	fractal	fractal	NOUN
concept-2079	19	9	is	be	AUX
concept-2079	19	10	“	"	PUNCT
concept-2079	19	11	a	a	DET
concept-2079	19	12	rough	rough	ADJ
concept-2079	19	13	or	or	CCONJ
concept-2079	19	14	fragmented	fragmented	ADJ
concept-2079	19	15	geometric	geometric	ADJ
concept-2079	19	16	shape	shape	NOUN
concept-2079	19	17	that	that	PRON
concept-2079	19	18	can	can	AUX
concept-2079	19	19	be	be	AUX
concept-2079	19	20	split	split	VERB
concept-2079	19	21	into	into	ADP
concept-2079	19	22	parts	part	NOUN
concept-2079	19	23	,	,	PUNCT
concept-2079	19	24	each	each	PRON
concept-2079	19	25	of	of	ADP
concept-2079	19	26	which	which	PRON
concept-2079	19	27	is	be	AUX
concept-2079	19	28	a	a	DET
concept-2079	19	29	reduced	reduce	VERB
concept-2079	19	30	-	-	PUNCT
concept-2079	19	31	size	size	NOUN
concept-2079	19	32	copy	copy	NOUN
concept-2079	19	33	of	of	ADP
concept-2079	19	34	the	the	DET
concept-2079	19	35	whole	whole	NOUN
concept-2079	19	36	”	"	PUNCT
concept-2079	19	37	(	(	PUNCT
concept-2079	19	38	frailey	frailey	ADJ
concept-2079	19	39	,	,	PUNCT
concept-2079	19	40	“	"	PUNCT
concept-2079	19	41	fractals	fractal	NOUN
concept-2079	19	42	”	"	PUNCT
concept-2079	19	43	)	)	PUNCT
concept-2079	19	44	.	.	PUNCT
concept-2079	20	1	four	four	NUM
concept-2079	20	2	main	main	ADJ
concept-2079	20	3	mathematical	mathematical	ADJ
concept-2079	20	4	characteristics	characteristic	NOUN
concept-2079	20	5	define	define	VERB
concept-2079	20	6	fractals	fractal	NOUN
concept-2079	20	7	:	:	PUNCT
concept-2079	20	8	recursion	recursion	NOUN
concept-2079	20	9	,	,	PUNCT
concept-2079	20	10	self	self	NOUN
concept-2079	20	11	-	-	PUNCT
concept-2079	20	12	similarity	similarity	NOUN
concept-2079	20	13	,	,	PUNCT
concept-2079	20	14	fractional	fractional	ADJ
concept-2079	20	15	or	or	CCONJ
concept-2079	20	16	non	non	ADJ
concept-2079	20	17	-	-	ADJ
concept-2079	20	18	integer	integer	ADJ
concept-2079	20	19	dimension	dimension	NOUN
concept-2079	20	20	,	,	PUNCT
concept-2079	20	21	and	and	CCONJ
concept-2079	20	22	the	the	DET
concept-2079	20	23	concept	concept	NOUN
concept-2079	20	24	of	of	ADP
concept-2079	20	25	infinity	infinity	NOUN
concept-2079	20	26	(	(	PUNCT
concept-2079	20	27	eglash	eglash	NOUN
concept-2079	20	28	,	,	PUNCT
concept-2079	20	29	17	17	NUM
concept-2079	20	30	)	)	PUNCT
concept-2079	20	31	.	.	PUNCT
concept-2079	21	1	1	1	X
concept-2079	21	2	.	.	X
concept-2079	21	3	recursion	recursion	NOUN
concept-2079	21	4	refers	refer	VERB
concept-2079	21	5	to	to	ADP
concept-2079	21	6	an	an	DET
concept-2079	21	7	algorithmic	algorithmic	ADJ
concept-2079	21	8	reliance	reliance	NOUN
concept-2079	21	9	on	on	ADP
concept-2079	21	10	the	the	DET
concept-2079	21	11	previous	previous	ADJ
concept-2079	21	12	iteration	iteration	NOUN
concept-2079	21	13	of	of	ADP
concept-2079	21	14	a	a	DET
concept-2079	21	15	fractal	fractal	NOUN
concept-2079	21	16	to	to	PART
concept-2079	21	17	produce	produce	VERB
concept-2079	21	18	the	the	DET
concept-2079	21	19	next	next	ADJ
concept-2079	21	20	iteration	iteration	NOUN
concept-2079	21	21	of	of	ADP
concept-2079	21	22	the	the	DET
concept-2079	21	23	fractal	fractal	ADJ
concept-2079	21	24	design	design	NOUN
concept-2079	21	25	.	.	PUNCT
concept-2079	22	1	a	a	DET
concept-2079	22	2	recursive	recursive	ADJ
concept-2079	22	3	example	example	NOUN
concept-2079	22	4	that	that	PRON
concept-2079	22	5	may	may	AUX
concept-2079	22	6	be	be	AUX
concept-2079	22	7	familiar	familiar	ADJ
concept-2079	22	8	to	to	ADP
concept-2079	22	9	readers	reader	NOUN
concept-2079	22	10	is	be	AUX
concept-2079	22	11	the	the	DET
concept-2079	22	12	fibonacci	fibonacci	NOUN
concept-2079	22	13	sequence	sequence	NOUN
concept-2079	22	14	:	:	PUNCT
concept-2079	22	15	1,1	1,1	NUM
concept-2079	22	16	,	,	PUNCT
concept-2079	22	17	2	2	NUM
concept-2079	22	18	,	,	PUNCT
concept-2079	22	19	3	3	NUM
concept-2079	22	20	,	,	PUNCT
concept-2079	22	21	5	5	NUM
concept-2079	22	22	,	,	PUNCT
concept-2079	22	23	8	8	NUM
concept-2079	22	24	…	…	NUM
concept-2079	22	25	which	which	PRON
concept-2079	22	26	can	can	AUX
concept-2079	22	27	be	be	AUX
concept-2079	22	28	defined	define	VERB
concept-2079	22	29	as	as	ADP
concept-2079	22	30	f1	f1	NOUN
concept-2079	22	31	=	=	SYM
concept-2079	22	32	1	1	NUM
concept-2079	22	33	,	,	PUNCT
concept-2079	22	34	f2	f2	PRON
concept-2079	22	35	=	=	NOUN
concept-2079	22	36	1	1	NUM
concept-2079	22	37	,	,	PUNCT
concept-2079	22	38	fn	fn	NOUN
concept-2079	22	39	=	=	NOUN
concept-2079	22	40	fn-1	fn-1	X
concept-2079	22	41	+	+	X
concept-2079	22	42	fn-2	fn-2	NOUN
concept-2079	22	43	,	,	PUNCT
concept-2079	22	44	where	where	SCONJ
concept-2079	22	45	fn	fn	NOUN
concept-2079	22	46	is	be	AUX
concept-2079	22	47	the	the	DET
concept-2079	22	48	nth	nth	ADJ
concept-2079	22	49	term	term	NOUN
concept-2079	22	50	of	of	ADP
concept-2079	22	51	the	the	DET
concept-2079	22	52	sequence	sequence	NOUN
concept-2079	22	53	,	,	PUNCT
concept-2079	22	54	and	and	CCONJ
concept-2079	22	55	fn-1	fn-1	VERB
concept-2079	22	56	and	and	CCONJ
concept-2079	22	57	fn-2	fn-2	ADV
concept-2079	22	58	are	be	AUX
concept-2079	22	59	the	the	DET
concept-2079	22	60	two	two	NUM
concept-2079	22	61	previous	previous	ADJ
concept-2079	22	62	terms	term	NOUN
concept-2079	22	63	.	.	PUNCT
concept-2079	23	1	2	2	X
concept-2079	23	2	.	.	X
concept-2079	23	3	self	self	NOUN
concept-2079	23	4	-	-	PUNCT
concept-2079	23	5	similarity	similarity	NOUN
concept-2079	23	6	refers	refer	VERB
concept-2079	23	7	to	to	ADP
concept-2079	23	8	a	a	DET
concept-2079	23	9	fractal	fractal	NOUN
concept-2079	23	10	representing	represent	VERB
concept-2079	23	11	its	its	PRON
concept-2079	23	12	original	original	ADJ
concept-2079	23	13	form	form	NOUN
concept-2079	23	14	at	at	ADP
concept-2079	23	15	different	different	ADJ
concept-2079	23	16	levels	level	NOUN
concept-2079	23	17	of	of	ADP
concept-2079	23	18	magnification	magnification	NOUN
concept-2079	23	19	;	;	PUNCT
concept-2079	23	20	in	in	ADP
concept-2079	23	21	layman	layman	PROPN
concept-2079	23	22	’s	’s	PART
concept-2079	23	23	terms	term	NOUN
concept-2079	23	24	,	,	PUNCT
concept-2079	23	25	whether	whether	SCONJ
concept-2079	23	26	you	you	PRON
concept-2079	23	27	zoom	zoom	VERB
concept-2079	23	28	in	in	ADP
concept-2079	23	29	or	or	CCONJ
concept-2079	23	30	out	out	ADP
concept-2079	23	31	of	of	ADP
concept-2079	23	32	the	the	DET
concept-2079	23	33	graphical	graphical	ADJ
concept-2079	23	34	representation	representation	NOUN
concept-2079	23	35	of	of	ADP
concept-2079	23	36	the	the	DET
concept-2079	23	37	fractal	fractal	NOUN
concept-2079	23	38	,	,	PUNCT
concept-2079	23	39	the	the	DET
concept-2079	23	40	fractal	fractal	NOUN
concept-2079	23	41	maintains	maintain	VERB
concept-2079	23	42	its	its	PRON
concept-2079	23	43	original	original	ADJ
concept-2079	23	44	structure	structure	NOUN
concept-2079	23	45	.	.	PUNCT
concept-2079	24	1	mandelbrot	mandelbrot	PROPN
concept-2079	24	2	(	(	PUNCT
concept-2079	24	3	p.	p.	NOUN
concept-2079	24	4	1	1	NUM
concept-2079	24	5	)	)	PUNCT
concept-2079	24	6	defined	define	VERB
concept-2079	24	7	statistical	statistical	ADJ
concept-2079	24	8	self	self	NOUN
concept-2079	24	9	-	-	PUNCT
concept-2079	24	10	similarity	similarity	NOUN
concept-2079	24	11	as	as	SCONJ
concept-2079	24	12	“	"	PUNCT
concept-2079	24	13	each	each	DET
concept-2079	24	14	portion	portion	NOUN
concept-2079	24	15	can	can	AUX
concept-2079	24	16	be	be	AUX
concept-2079	24	17	considered	consider	VERB
concept-2079	24	18	a	a	DET
concept-2079	24	19	reduced	reduce	VERB
concept-2079	24	20	scale	scale	NOUN
concept-2079	24	21	image	image	NOUN
concept-2079	24	22	of	of	ADP
concept-2079	24	23	the	the	DET
concept-2079	24	24	whole	whole	NOUN
concept-2079	24	25	,	,	PUNCT
concept-2079	24	26	”	"	PUNCT
concept-2079	24	27	referring	refer	VERB
concept-2079	24	28	to	to	ADP
concept-2079	24	29	the	the	DET
concept-2079	24	30	scaling	scaling	ADJ
concept-2079	24	31	dimension	dimension	NOUN
concept-2079	24	32	.	.	PUNCT
concept-2079	25	1	3	3	X
concept-2079	25	2	.	.	X
concept-2079	25	3	fractional	fractional	ADJ
concept-2079	25	4	dimension	dimension	NOUN
concept-2079	25	5	,	,	PUNCT
concept-2079	25	6	calculated	calculate	VERB
concept-2079	25	7	via	via	ADP
concept-2079	25	8	the	the	DET
concept-2079	25	9	hausdorff	hausdorff	PROPN
concept-2079	25	10	dimension	dimension	PROPN
concept-2079	25	11	definition	definition	NOUN
concept-2079	25	12	,	,	PUNCT
concept-2079	25	13	relates	relate	VERB
concept-2079	25	14	to	to	ADP
concept-2079	25	15	the	the	DET
concept-2079	25	16	self	self	NOUN
concept-2079	25	17	-	-	PUNCT
concept-2079	25	18	similarity	similarity	NOUN
concept-2079	25	19	characteristic	characteristic	NOUN
concept-2079	25	20	of	of	ADP
concept-2079	25	21	a	a	DET
concept-2079	25	22	fractal	fractal	NOUN
concept-2079	25	23	appearing	appear	VERB
concept-2079	25	24	the	the	DET
concept-2079	25	25	“	"	PUNCT
concept-2079	25	26	same	same	ADJ
concept-2079	25	27	”	"	PUNCT
concept-2079	25	28	despite	despite	SCONJ
concept-2079	25	29	the	the	DET
concept-2079	25	30	scaling	scale	VERB
concept-2079	25	31	factor	factor	NOUN
concept-2079	25	32	.	.	PUNCT
concept-2079	26	1	4	4	X
concept-2079	26	2	.	.	X
concept-2079	26	3	many	many	ADJ
concept-2079	26	4	fractals	fractal	NOUN
concept-2079	26	5	,	,	PUNCT
concept-2079	26	6	such	such	ADJ
concept-2079	26	7	as	as	ADP
concept-2079	26	8	the	the	DET
concept-2079	26	9	cantor	cantor	NOUN
concept-2079	26	10	set	set	NOUN
concept-2079	26	11	,	,	PUNCT
concept-2079	26	12	make	make	VERB
concept-2079	26	13	use	use	NOUN
concept-2079	26	14	of	of	ADP
concept-2079	26	15	the	the	DET
concept-2079	26	16	concept	concept	NOUN
concept-2079	26	17	of	of	ADP
concept-2079	26	18	infinity	infinity	NOUN
concept-2079	26	19	as	as	SCONJ
concept-2079	26	20	they	they	PRON
concept-2079	26	21	can	can	AUX
concept-2079	26	22	iterate	iterate	VERB
concept-2079	26	23	themselves	themselves	PRON
concept-2079	26	24	an	an	DET
concept-2079	26	25	infinite	infinite	ADJ
concept-2079	26	26	number	number	NOUN
concept-2079	26	27	of	of	ADP
concept-2079	26	28	times	time	NOUN
concept-2079	26	29	within	within	ADP
concept-2079	26	30	a	a	DET
concept-2079	26	31	finite	finite	ADJ
concept-2079	26	32	space	space	NOUN
concept-2079	26	33	.	.	PUNCT
concept-2079	27	1	concept	concept	NOUN
concept-2079	27	2	,	,	PUNCT
concept-2079	27	3	vol	vol	NOUN
concept-2079	27	4	.	.	PUNCT
concept-2079	28	1	xxxix	xxxix	PROPN
concept-2079	28	2	(	(	PUNCT
concept-2079	28	3	2016	2016	NUM
concept-2079	28	4	)	)	PUNCT
concept-2079	28	5	3	3	NUM
concept-2079	28	6	fractals	fractal	NOUN
concept-2079	28	7	are	be	AUX
concept-2079	28	8	examples	example	NOUN
concept-2079	28	9	of	of	ADP
concept-2079	28	10	dynamical	dynamical	ADJ
concept-2079	28	11	systems	system	NOUN
concept-2079	28	12	,	,	PUNCT
concept-2079	28	13	so	so	SCONJ
concept-2079	28	14	it	it	PRON
concept-2079	28	15	is	be	AUX
concept-2079	28	16	important	important	ADJ
concept-2079	28	17	to	to	PART
concept-2079	28	18	review	review	VERB
concept-2079	28	19	some	some	DET
concept-2079	28	20	important	important	ADJ
concept-2079	28	21	definitions	definition	NOUN
concept-2079	28	22	and	and	CCONJ
concept-2079	28	23	terms	term	NOUN
concept-2079	28	24	:	:	PUNCT
concept-2079	29	1	1	1	X
concept-2079	29	2	.	.	X
concept-2079	29	3	a	a	DET
concept-2079	29	4	dynamical	dynamical	ADJ
concept-2079	29	5	system	system	NOUN
concept-2079	29	6	,	,	PUNCT
concept-2079	29	7	in	in	ADP
concept-2079	29	8	very	very	ADV
concept-2079	29	9	simplistic	simplistic	ADJ
concept-2079	29	10	terms	term	NOUN
concept-2079	29	11	,	,	PUNCT
concept-2079	29	12	describes	describe	VERB
concept-2079	29	13	how	how	SCONJ
concept-2079	29	14	a	a	DET
concept-2079	29	15	set	set	NOUN
concept-2079	29	16	of	of	ADP
concept-2079	29	17	variables	variable	NOUN
concept-2079	29	18	behaves	behave	VERB
concept-2079	29	19	under	under	ADP
concept-2079	29	20	different	different	ADJ
concept-2079	29	21	states	state	NOUN
concept-2079	29	22	or	or	CCONJ
concept-2079	29	23	conditions	condition	NOUN
concept-2079	29	24	over	over	ADP
concept-2079	29	25	time	time	NOUN
concept-2079	29	26	(	(	PUNCT
concept-2079	29	27	devaney	devaney	PROPN
concept-2079	29	28	,	,	PUNCT
concept-2079	29	29	27	27	NUM
concept-2079	29	30	)	)	PUNCT
concept-2079	29	31	.	.	PUNCT
concept-2079	30	1	2	2	X
concept-2079	30	2	.	.	X
concept-2079	30	3	chaos	chaos	NOUN
concept-2079	30	4	describes	describe	VERB
concept-2079	30	5	the	the	DET
concept-2079	30	6	phenomenon	phenomenon	NOUN
concept-2079	30	7	that	that	PRON
concept-2079	30	8	occurs	occur	VERB
concept-2079	30	9	when	when	SCONJ
concept-2079	30	10	slight	slight	ADJ
concept-2079	30	11	changes	change	NOUN
concept-2079	30	12	to	to	ADP
concept-2079	30	13	initial	initial	ADJ
concept-2079	30	14	conditions	condition	NOUN
concept-2079	30	15	,	,	PUNCT
concept-2079	30	16	in	in	ADP
concept-2079	30	17	the	the	DET
concept-2079	30	18	dynamical	dynamical	ADJ
concept-2079	30	19	system	system	NOUN
concept-2079	30	20	,	,	PUNCT
concept-2079	30	21	result	result	VERB
concept-2079	30	22	in	in	ADP
concept-2079	30	23	varied	varied	ADJ
concept-2079	30	24	behavior	behavior	NOUN
concept-2079	30	25	for	for	ADP
concept-2079	30	26	the	the	DET
concept-2079	30	27	entire	entire	ADJ
concept-2079	30	28	system	system	NOUN
concept-2079	30	29	(	(	PUNCT
concept-2079	30	30	devaney	devaney	PROPN
concept-2079	30	31	,	,	PUNCT
concept-2079	30	32	49	49	NUM
concept-2079	30	33	-	-	SYM
concept-2079	30	34	50	50	NUM
concept-2079	30	35	)	)	PUNCT
concept-2079	30	36	.	.	PUNCT
concept-2079	31	1	a	a	DET
concept-2079	31	2	famous	famous	ADJ
concept-2079	31	3	example	example	NOUN
concept-2079	31	4	is	be	AUX
concept-2079	31	5	the	the	DET
concept-2079	31	6	lorenz	lorenz	PROPN
concept-2079	31	7	attractor	attractor	NOUN
concept-2079	31	8	.	.	PUNCT
concept-2079	32	1	this	this	DET
concept-2079	32	2	result	result	NOUN
concept-2079	32	3	was	be	AUX
concept-2079	32	4	produced	produce	VERB
concept-2079	32	5	after	after	SCONJ
concept-2079	32	6	dr	dr	PROPN
concept-2079	32	7	.	.	PROPN
concept-2079	32	8	edward	edward	PROPN
concept-2079	32	9	lorenz	lorenz	PROPN
concept-2079	32	10	was	be	AUX
concept-2079	32	11	trying	try	VERB
concept-2079	32	12	to	to	PART
concept-2079	32	13	make	make	VERB
concept-2079	32	14	weather	weather	NOUN
concept-2079	32	15	predictions	prediction	NOUN
concept-2079	32	16	using	use	VERB
concept-2079	32	17	differential	differential	ADJ
concept-2079	32	18	equations	equation	NOUN
concept-2079	32	19	and	and	CCONJ
concept-2079	32	20	found	find	VERB
concept-2079	32	21	you	you	PRON
concept-2079	32	22	could	could	AUX
concept-2079	32	23	not	not	PART
concept-2079	32	24	make	make	VERB
concept-2079	32	25	accurate	accurate	ADJ
concept-2079	32	26	long	long	ADJ
concept-2079	32	27	-	-	PUNCT
concept-2079	32	28	term	term	NOUN
concept-2079	32	29	predictions	prediction	NOUN
concept-2079	32	30	due	due	ADP
concept-2079	32	31	to	to	ADP
concept-2079	32	32	the	the	DET
concept-2079	32	33	chaotic	chaotic	ADJ
concept-2079	32	34	nature	nature	NOUN
concept-2079	32	35	of	of	ADP
concept-2079	32	36	the	the	DET
concept-2079	32	37	system	system	NOUN
concept-2079	32	38	.	.	PUNCT
concept-2079	33	1	3	3	X
concept-2079	33	2	.	.	X
concept-2079	33	3	when	when	SCONJ
concept-2079	33	4	polynomials	polynomial	NOUN
concept-2079	33	5	and	and	CCONJ
concept-2079	33	6	trigonometric	trigonometric	ADJ
concept-2079	33	7	functions	function	NOUN
concept-2079	33	8	are	be	AUX
concept-2079	33	9	iterated	iterate	VERB
concept-2079	33	10	,	,	PUNCT
concept-2079	33	11	they	they	PRON
concept-2079	33	12	produce	produce	VERB
concept-2079	33	13	simple	simple	ADJ
concept-2079	33	14	dynamical	dynamical	ADJ
concept-2079	33	15	systems	system	NOUN
concept-2079	33	16	.	.	PUNCT
concept-2079	34	1	the	the	DET
concept-2079	34	2	dynamics	dynamic	NOUN
concept-2079	34	3	of	of	ADP
concept-2079	34	4	these	these	DET
concept-2079	34	5	systems	system	NOUN
concept-2079	34	6	can	can	AUX
concept-2079	34	7	be	be	AUX
concept-2079	34	8	described	describe	VERB
concept-2079	34	9	by	by	ADP
concept-2079	34	10	orbits	orbit	NOUN
concept-2079	34	11	,	,	PUNCT
concept-2079	34	12	or	or	CCONJ
concept-2079	34	13	set	set	VERB
concept-2079	34	14	of	of	ADP
concept-2079	34	15	iterated	iterated	ADJ
concept-2079	34	16	points	point	NOUN
concept-2079	34	17	,	,	PUNCT
concept-2079	34	18	that	that	PRON
concept-2079	34	19	may	may	AUX
concept-2079	34	20	converge	converge	VERB
concept-2079	34	21	to	to	ADP
concept-2079	34	22	fixed	fix	VERB
concept-2079	34	23	point(s	point(s	NOUN
concept-2079	34	24	)	)	PUNCT
concept-2079	34	25	or	or	CCONJ
concept-2079	34	26	periodic	periodic	ADJ
concept-2079	34	27	points	point	NOUN
concept-2079	34	28	,	,	PUNCT
concept-2079	34	29	or	or	CCONJ
concept-2079	34	30	may	may	AUX
concept-2079	34	31	never	never	ADV
concept-2079	34	32	converge	converge	VERB
concept-2079	34	33	,	,	PUNCT
concept-2079	34	34	moving	move	VERB
concept-2079	34	35	chaotically	chaotically	ADV
concept-2079	34	36	throughout	throughout	ADP
concept-2079	34	37	the	the	DET
concept-2079	34	38	space	space	NOUN
concept-2079	34	39	.	.	PUNCT
concept-2079	35	1	4	4	X
concept-2079	35	2	.	.	NUM
concept-2079	35	3	fixed	fix	VERB
concept-2079	35	4	points	point	NOUN
concept-2079	35	5	can	can	AUX
concept-2079	35	6	behave	behave	VERB
concept-2079	35	7	as	as	ADP
concept-2079	35	8	attractors	attractor	NOUN
concept-2079	35	9	or	or	CCONJ
concept-2079	35	10	repellers	repeller	NOUN
concept-2079	35	11	.	.	PUNCT
concept-2079	36	1	if	if	SCONJ
concept-2079	36	2	a	a	DET
concept-2079	36	3	fixed	fix	VERB
concept-2079	36	4	point	point	NOUN
concept-2079	36	5	behaves	behave	VERB
concept-2079	36	6	as	as	ADP
concept-2079	36	7	an	an	DET
concept-2079	36	8	attractor	attractor	NOUN
concept-2079	36	9	,	,	PUNCT
concept-2079	36	10	nearby	nearby	ADJ
concept-2079	36	11	orbits	orbit	NOUN
concept-2079	36	12	of	of	ADP
concept-2079	36	13	the	the	DET
concept-2079	36	14	dynamical	dynamical	ADJ
concept-2079	36	15	system	system	NOUN
concept-2079	36	16	will	will	AUX
concept-2079	36	17	converge	converge	VERB
concept-2079	36	18	to	to	ADP
concept-2079	36	19	the	the	DET
concept-2079	36	20	value	value	NOUN
concept-2079	36	21	of	of	ADP
concept-2079	36	22	the	the	DET
concept-2079	36	23	fixed	fix	VERB
concept-2079	36	24	point	point	NOUN
concept-2079	36	25	.	.	PUNCT
concept-2079	37	1	however	however	ADV
concept-2079	37	2	,	,	PUNCT
concept-2079	37	3	on	on	ADP
concept-2079	37	4	the	the	DET
concept-2079	37	5	other	other	ADJ
concept-2079	37	6	hand	hand	NOUN
concept-2079	37	7	,	,	PUNCT
concept-2079	37	8	if	if	SCONJ
concept-2079	37	9	a	a	DET
concept-2079	37	10	fixed	fix	VERB
concept-2079	37	11	point	point	NOUN
concept-2079	37	12	behaves	behave	VERB
concept-2079	37	13	as	as	ADP
concept-2079	37	14	a	a	DET
concept-2079	37	15	repeller	repeller	NOUN
concept-2079	37	16	,	,	PUNCT
concept-2079	37	17	nearby	nearby	ADJ
concept-2079	37	18	orbits	orbit	NOUN
concept-2079	37	19	of	of	ADP
concept-2079	37	20	the	the	DET
concept-2079	37	21	dynamical	dynamical	ADJ
concept-2079	37	22	system	system	NOUN
concept-2079	37	23	will	will	AUX
concept-2079	37	24	not	not	PART
concept-2079	37	25	converge	converge	VERB
concept-2079	37	26	to	to	ADP
concept-2079	37	27	the	the	DET
concept-2079	37	28	value	value	NOUN
concept-2079	37	29	of	of	ADP
concept-2079	37	30	the	the	DET
concept-2079	37	31	fixed	fix	VERB
concept-2079	37	32	point	point	NOUN
concept-2079	37	33	of	of	ADP
concept-2079	37	34	interest	interest	NOUN
concept-2079	37	35	(	(	PUNCT
concept-2079	37	36	devaney	devaney	PROPN
concept-2079	37	37	,	,	PUNCT
concept-2079	37	38	17	17	NUM
concept-2079	37	39	-	-	SYM
concept-2079	37	40	37	37	NUM
concept-2079	37	41	)	)	PUNCT
concept-2079	37	42	.	.	PUNCT
concept-2079	38	1	through	through	ADP
concept-2079	38	2	the	the	DET
concept-2079	38	3	use	use	NOUN
concept-2079	38	4	of	of	ADP
concept-2079	38	5	phase	phase	NOUN
concept-2079	38	6	-	-	PUNCT
concept-2079	38	7	portraits	portrait	NOUN
concept-2079	38	8	and	and	CCONJ
concept-2079	38	9	cobweb	cobweb	ADJ
concept-2079	38	10	diagrams	diagram	NOUN
concept-2079	38	11	,	,	PUNCT
concept-2079	38	12	it	it	PRON
concept-2079	38	13	is	be	AUX
concept-2079	38	14	possible	possible	ADJ
concept-2079	38	15	to	to	PART
concept-2079	38	16	qualitatively	qualitatively	ADV
concept-2079	38	17	observe	observe	VERB
concept-2079	38	18	the	the	DET
concept-2079	38	19	behavior	behavior	NOUN
concept-2079	38	20	of	of	ADP
concept-2079	38	21	these	these	DET
concept-2079	38	22	dynamical	dynamical	ADJ
concept-2079	38	23	systems	system	NOUN
concept-2079	38	24	and	and	CCONJ
concept-2079	38	25	make	make	VERB
concept-2079	38	26	inferences	inference	NOUN
concept-2079	38	27	regarding	regard	VERB
concept-2079	38	28	their	their	PRON
concept-2079	38	29	behavior	behavior	NOUN
concept-2079	38	30	.	.	PUNCT
concept-2079	39	1	figure	figure	VERB
concept-2079	39	2	1	1	NUM
concept-2079	39	3	–	–	PUNCT
concept-2079	39	4	cobweb	cobweb	ADJ
concept-2079	39	5	diagram	diagram	NOUN
concept-2079	39	6	concept	concept	NOUN
concept-2079	39	7	,	,	PUNCT
concept-2079	39	8	vol	vol	NOUN
concept-2079	39	9	.	.	PUNCT
concept-2079	40	1	xxxix	xxxix	PROPN
concept-2079	40	2	(	(	PUNCT
concept-2079	40	3	2016	2016	NUM
concept-2079	40	4	)	)	PUNCT
concept-2079	40	5	4	4	NUM
concept-2079	40	6	the	the	DET
concept-2079	40	7	classic	classic	ADJ
concept-2079	40	8	example	example	NOUN
concept-2079	40	9	of	of	ADP
concept-2079	40	10	a	a	DET
concept-2079	40	11	fractal	fractal	NOUN
concept-2079	40	12	is	be	AUX
concept-2079	40	13	known	know	VERB
concept-2079	40	14	as	as	ADP
concept-2079	40	15	the	the	DET
concept-2079	40	16	cantor	cantor	PROPN
concept-2079	40	17	set	set	PROPN
concept-2079	40	18	,	,	PUNCT
concept-2079	40	19	created	create	VERB
concept-2079	40	20	by	by	ADP
concept-2079	40	21	georg	georg	PROPN
concept-2079	40	22	cantor	cantor	NOUN
concept-2079	40	23	.	.	PUNCT
concept-2079	41	1	he	he	PRON
concept-2079	41	2	devised	devise	VERB
concept-2079	41	3	this	this	DET
concept-2079	41	4	fractal	fractal	NOUN
concept-2079	41	5	by	by	ADP
concept-2079	41	6	taking	take	VERB
concept-2079	41	7	a	a	DET
concept-2079	41	8	line	line	NOUN
concept-2079	41	9	segment	segment	NOUN
concept-2079	41	10	of	of	ADP
concept-2079	41	11	length	length	NOUN
concept-2079	41	12	1	1	NUM
concept-2079	41	13	and	and	CCONJ
concept-2079	41	14	proceeded	proceed	VERB
concept-2079	41	15	to	to	PART
concept-2079	41	16	cut	cut	VERB
concept-2079	41	17	the	the	DET
concept-2079	41	18	line	line	NOUN
concept-2079	41	19	segment	segment	NOUN
concept-2079	41	20	into	into	ADP
concept-2079	41	21	pieces	piece	NOUN
concept-2079	41	22	by	by	ADP
concept-2079	41	23	removing	remove	VERB
concept-2079	41	24	the	the	DET
concept-2079	41	25	middle	middle	ADJ
concept-2079	41	26	third	third	NOUN
concept-2079	41	27	of	of	ADP
concept-2079	41	28	each	each	DET
concept-2079	41	29	line	line	NOUN
concept-2079	41	30	.	.	PUNCT
concept-2079	42	1	in	in	ADP
concept-2079	42	2	other	other	ADJ
concept-2079	42	3	words	word	NOUN
concept-2079	42	4	,	,	PUNCT
concept-2079	42	5	you	you	PRON
concept-2079	42	6	start	start	VERB
concept-2079	42	7	out	out	ADP
concept-2079	42	8	with	with	ADP
concept-2079	42	9	line	line	NOUN
concept-2079	42	10	segment	segment	NOUN
concept-2079	42	11	on	on	ADP
concept-2079	42	12	the	the	DET
concept-2079	42	13	real	real	ADJ
concept-2079	42	14	number	number	NOUN
concept-2079	42	15	line	line	NOUN
concept-2079	42	16	on	on	ADP
concept-2079	42	17	[	[	X
concept-2079	42	18	0,1	0,1	NUM
concept-2079	42	19	]	]	PUNCT
concept-2079	42	20	,	,	PUNCT
concept-2079	42	21	then	then	ADV
concept-2079	42	22	you	you	PRON
concept-2079	42	23	break	break	VERB
concept-2079	42	24	this	this	PRON
concept-2079	42	25	down	down	ADP
concept-2079	42	26	into	into	ADP
concept-2079	42	27	two	two	NUM
concept-2079	42	28	sub	sub	NOUN
concept-2079	42	29	-	-	NOUN
concept-2079	42	30	interval	interval	NOUN
concept-2079	42	31	[	[	X
concept-2079	42	32	0	0	NUM
concept-2079	42	33	,	,	PUNCT
concept-2079	42	34	 	 	SPACE
concept-2079	42	35	!	!	PUNCT
concept-2079	42	36	!	!	PUNCT
concept-2079	42	37	]	]	PUNCT
concept-2079	43	1	u	u	X
concept-2079	44	1	[	[	X
concept-2079	44	2	!	!	PUNCT
concept-2079	44	3	!	!	PUNCT
concept-2079	45	1	,	,	PUNCT
concept-2079	45	2	1	1	NUM
concept-2079	45	3	]	]	PUNCT
concept-2079	45	4	,	,	PUNCT
concept-2079	45	5	and	and	CCONJ
concept-2079	45	6	continue	continue	VERB
concept-2079	45	7	iterating	iterate	VERB
concept-2079	45	8	or	or	CCONJ
concept-2079	45	9	repeating	repeat	VERB
concept-2079	45	10	the	the	DET
concept-2079	45	11	process	process	NOUN
concept-2079	45	12	resulting	result	VERB
concept-2079	45	13	in	in	ADP
concept-2079	45	14	the	the	DET
concept-2079	45	15	union	union	NOUN
concept-2079	45	16	of	of	ADP
concept-2079	45	17	infinite	infinite	ADJ
concept-2079	45	18	sets	set	NOUN
concept-2079	45	19	,	,	PUNCT
concept-2079	45	20	each	each	DET
concept-2079	45	21	a	a	DET
concept-2079	45	22	subset	subset	NOUN
concept-2079	45	23	of	of	ADP
concept-2079	45	24	[	[	X
concept-2079	45	25	0,1	0,1	NUM
concept-2079	45	26	]	]	PUNCT
concept-2079	45	27	.	.	PUNCT
concept-2079	46	1	another	another	DET
concept-2079	46	2	interesting	interesting	ADJ
concept-2079	46	3	result	result	NOUN
concept-2079	46	4	is	be	AUX
concept-2079	46	5	what	what	PRON
concept-2079	46	6	happens	happen	VERB
concept-2079	46	7	to	to	ADP
concept-2079	46	8	the	the	DET
concept-2079	46	9	length	length	NOUN
concept-2079	46	10	of	of	ADP
concept-2079	46	11	the	the	DET
concept-2079	46	12	set	set	NOUN
concept-2079	46	13	upon	upon	SCONJ
concept-2079	46	14	iteration	iteration	NOUN
concept-2079	46	15	,	,	PUNCT
concept-2079	46	16	it	it	PRON
concept-2079	46	17	starts	start	VERB
concept-2079	46	18	out	out	ADP
concept-2079	46	19	at	at	ADP
concept-2079	46	20	1	1	NUM
concept-2079	46	21	,	,	PUNCT
concept-2079	46	22	then	then	ADV
concept-2079	46	23	1	1	NUM
concept-2079	46	24	 	 	SPACE
concept-2079	46	25	!	!	PUNCT
concept-2079	46	26	!	!	PUNCT
concept-2079	47	1	=	=	PUNCT
concept-2079	47	2	 	 	SPACE
concept-2079	47	3	!	!	PUNCT
concept-2079	47	4	!	!	PUNCT
concept-2079	48	1	,	,	PUNCT
concept-2079	48	2	followed	follow	VERB
concept-2079	48	3	by	by	ADP
concept-2079	48	4	!	!	PUNCT
concept-2079	48	5	!	!	PUNCT
concept-2079	48	6	 	 	SPACE
concept-2079	49	1	−	−	PROPN
concept-2079	49	2	!	!	PUNCT
concept-2079	49	3	!	!	PUNCT
concept-2079	50	1	(	(	PUNCT
concept-2079	50	2	!	!	PUNCT
concept-2079	50	3	!	!	PUNCT
concept-2079	50	4	)	)	PUNCT
concept-2079	51	1	=	=	PUNCT
concept-2079	51	2	!	!	PUNCT
concept-2079	51	3	!	!	PUNCT
concept-2079	52	1	−	−	INTJ
concept-2079	52	2	!	!	PUNCT
concept-2079	52	3	!	!	PUNCT
concept-2079	52	4	 	 	SPACE
concept-2079	53	1	=	=	PUNCT
concept-2079	53	2	!	!	PUNCT
concept-2079	53	3	!	!	PUNCT
concept-2079	54	1	,	,	PUNCT
concept-2079	54	2	 	 	SPACE
concept-2079	54	3	...	...	PUNCT
concept-2079	54	4	.	.	PUNCT
concept-2079	55	1	the	the	DET
concept-2079	55	2	length	length	NOUN
concept-2079	55	3	gets	get	VERB
concept-2079	55	4	smaller	small	ADJ
concept-2079	55	5	each	each	DET
concept-2079	55	6	time	time	NOUN
concept-2079	55	7	.	.	PUNCT
concept-2079	56	1	the	the	DET
concept-2079	56	2	geometric	geometric	ADJ
concept-2079	56	3	series	series	NOUN
concept-2079	56	4	!	!	PUNCT
concept-2079	56	5	!	!	PUNCT
concept-2079	56	6	!	!	PUNCT
concept-2079	56	7	!	!	PUNCT
concept-2079	56	8	!	!	PUNCT
concept-2079	57	1	𝑛	𝑛	PRON
concept-2079	57	2	 	 	SPACE
concept-2079	57	3	!	!	PUNCT
concept-2079	57	4	!	!	PUNCT
concept-2079	57	5	!	!	PUNCT
concept-2079	57	6	!	!	PUNCT
concept-2079	58	1	,	,	PUNCT
concept-2079	58	2	describes	describe	VERB
concept-2079	58	3	the	the	DET
concept-2079	58	4	lengths	length	NOUN
concept-2079	58	5	of	of	ADP
concept-2079	58	6	the	the	DET
concept-2079	58	7	all	all	DET
concept-2079	58	8	the	the	DET
concept-2079	58	9	segments	segment	NOUN
concept-2079	58	10	being	be	AUX
concept-2079	58	11	removed	remove	VERB
concept-2079	58	12	,	,	PUNCT
concept-2079	58	13	and	and	CCONJ
concept-2079	58	14	using	use	VERB
concept-2079	58	15	the	the	DET
concept-2079	58	16	results	result	NOUN
concept-2079	58	17	from	from	ADP
concept-2079	58	18	calculus	calculus	NOUN
concept-2079	58	19	,	,	PUNCT
concept-2079	58	20	we	we	PRON
concept-2079	58	21	know	know	VERB
concept-2079	58	22	this	this	DET
concept-2079	58	23	series	series	NOUN
concept-2079	58	24	converges	converge	VERB
concept-2079	58	25	to	to	ADP
concept-2079	58	26	!	!	PUNCT
concept-2079	59	1	𝑎	𝑎	X
concept-2079	59	2	!	!	PUNCT
concept-2079	59	3	!	!	PUNCT
concept-2079	59	4	!	!	PUNCT
concept-2079	60	1	𝑟	𝑟	X
concept-2079	60	2	=	=	PUNCT
concept-2079	60	3	!	!	PUNCT
concept-2079	60	4	!	!	PUNCT
concept-2079	60	5	!	!	PUNCT
concept-2079	60	6	!	!	PUNCT
concept-2079	60	7	!	!	PUNCT
concept-2079	60	8	!	!	PUNCT
concept-2079	61	1	=	=	PUNCT
concept-2079	61	2	!	!	PUNCT
concept-2079	61	3	!	!	PUNCT
concept-2079	61	4	!	!	PUNCT
concept-2079	61	5	!	!	PUNCT
concept-2079	62	1	=	=	PUNCT
concept-2079	62	2	1	1	NUM
concept-2079	62	3	,	,	PUNCT
concept-2079	62	4	where	where	SCONJ
concept-2079	62	5	a	a	PRON
concept-2079	62	6	is	be	AUX
concept-2079	62	7	the	the	DET
concept-2079	62	8	first	first	ADJ
concept-2079	62	9	term	term	NOUN
concept-2079	62	10	of	of	ADP
concept-2079	62	11	the	the	DET
concept-2079	62	12	geometric	geometric	ADJ
concept-2079	62	13	sequence	sequence	NOUN
concept-2079	62	14	and	and	CCONJ
concept-2079	62	15	r	r	NOUN
concept-2079	62	16	is	be	AUX
concept-2079	62	17	the	the	DET
concept-2079	62	18	common	common	ADJ
concept-2079	62	19	ratio	ratio	NOUN
concept-2079	62	20	(	(	PUNCT
concept-2079	62	21	crilly	crilly	ADV
concept-2079	62	22	,	,	PUNCT
concept-2079	62	23	earnshaw	earnshaw	PROPN
concept-2079	62	24	,	,	PUNCT
concept-2079	62	25	jones	jones	PROPN
concept-2079	62	26	,	,	PUNCT
concept-2079	62	27	10	10	NUM
concept-2079	62	28	)	)	PUNCT
concept-2079	62	29	.	.	PUNCT
concept-2079	63	1	however	however	ADV
concept-2079	63	2	,	,	PUNCT
concept-2079	63	3	if	if	SCONJ
concept-2079	63	4	the	the	DET
concept-2079	63	5	entire	entire	ADJ
concept-2079	63	6	length	length	NOUN
concept-2079	63	7	of	of	ADP
concept-2079	63	8	the	the	DET
concept-2079	63	9	interval	interval	NOUN
concept-2079	63	10	is	be	AUX
concept-2079	63	11	1	1	NUM
concept-2079	63	12	and	and	CCONJ
concept-2079	63	13	the	the	DET
concept-2079	63	14	convergence	convergence	NOUN
concept-2079	63	15	of	of	ADP
concept-2079	63	16	all	all	DET
concept-2079	63	17	the	the	DET
concept-2079	63	18	parts	part	NOUN
concept-2079	63	19	removed	remove	VERB
concept-2079	63	20	is	be	AUX
concept-2079	63	21	also	also	ADV
concept-2079	63	22	1	1	NUM
concept-2079	63	23	,	,	PUNCT
concept-2079	63	24	then	then	ADV
concept-2079	63	25	1	1	NUM
concept-2079	63	26	-1	-1	NOUN
concept-2079	63	27	=	=	SYM
concept-2079	63	28	0	0	NUM
concept-2079	63	29	,	,	PUNCT
concept-2079	63	30	meaning	mean	VERB
concept-2079	63	31	the	the	DET
concept-2079	63	32	length	length	NOUN
concept-2079	63	33	of	of	ADP
concept-2079	63	34	the	the	DET
concept-2079	63	35	entire	entire	ADJ
concept-2079	63	36	cantor	cantor	NOUN
concept-2079	63	37	set	set	NOUN
concept-2079	63	38	is	be	AUX
concept-2079	63	39	0	0	NUM
concept-2079	63	40	.	.	PUNCT
concept-2079	64	1	if	if	SCONJ
concept-2079	64	2	you	you	PRON
concept-2079	64	3	continue	continue	VERB
concept-2079	64	4	this	this	DET
concept-2079	64	5	recursive	recursive	ADJ
concept-2079	64	6	process	process	NOUN
concept-2079	64	7	,	,	PUNCT
concept-2079	64	8	the	the	DET
concept-2079	64	9	nth	nth	NOUN
concept-2079	64	10	iteration	iteration	NOUN
concept-2079	64	11	of	of	ADP
concept-2079	64	12	this	this	DET
concept-2079	64	13	fractal	fractal	NOUN
concept-2079	64	14	will	will	AUX
concept-2079	64	15	consist	consist	VERB
concept-2079	64	16	of	of	ADP
concept-2079	64	17	an	an	DET
concept-2079	64	18	infinite	infinite	ADJ
concept-2079	64	19	number	number	NOUN
concept-2079	64	20	of	of	ADP
concept-2079	64	21	points	point	NOUN
concept-2079	64	22	.	.	PUNCT
concept-2079	65	1	these	these	DET
concept-2079	65	2	points	point	NOUN
concept-2079	65	3	will	will	AUX
concept-2079	65	4	be	be	AUX
concept-2079	65	5	disconnected	disconnect	VERB
concept-2079	65	6	from	from	ADP
concept-2079	65	7	each	each	DET
concept-2079	65	8	other	other	ADJ
concept-2079	65	9	and	and	CCONJ
concept-2079	65	10	eventually	eventually	ADV
concept-2079	65	11	reach	reach	VERB
concept-2079	65	12	length	length	NOUN
concept-2079	65	13	zero	zero	NUM
concept-2079	65	14	on	on	ADP
concept-2079	65	15	[	[	X
concept-2079	65	16	0,1	0,1	NUM
concept-2079	65	17	]	]	PUNCT
concept-2079	65	18	.	.	PUNCT
concept-2079	66	1	the	the	DET
concept-2079	66	2	dimension	dimension	NOUN
concept-2079	66	3	of	of	ADP
concept-2079	66	4	the	the	DET
concept-2079	66	5	cantor	cantor	NOUN
concept-2079	66	6	set	set	NOUN
concept-2079	66	7	can	can	AUX
concept-2079	66	8	also	also	ADV
concept-2079	66	9	be	be	AUX
concept-2079	66	10	found	find	VERB
concept-2079	66	11	using	use	VERB
concept-2079	66	12	the	the	DET
concept-2079	66	13	hausdorff	hausdorff	NOUN
concept-2079	66	14	dimension	dimension	PROPN
concept-2079	66	15	definition	definition	NOUN
concept-2079	66	16	,	,	PUNCT
concept-2079	66	17	𝑑	𝑑	PROPN
concept-2079	66	18	=	=	X
concept-2079	66	19	!	!	PUNCT
concept-2079	66	20	"	"	PUNCT
concept-2079	66	21	 	 	SPACE
concept-2079	66	22	!	!	PUNCT
concept-2079	66	23	!	!	PUNCT
concept-2079	66	24	"	"	PUNCT
concept-2079	66	25	!	!	PUNCT
concept-2079	66	26	 	 	SPACE
concept-2079	67	1	=	=	PUNCT
concept-2079	67	2	!	!	PUNCT
concept-2079	67	3	"	"	PUNCT
concept-2079	67	4	!	!	PUNCT
concept-2079	67	5	!	!	PUNCT
concept-2079	67	6	"	"	PUNCT
concept-2079	67	7	 	 	SPACE
concept-2079	68	1	(	(	PUNCT
concept-2079	68	2	!	!	PUNCT
concept-2079	68	3	)	)	PUNCT
concept-2079	69	1	=	=	SYM
concept-2079	69	2	0.63	0.63	NUM
concept-2079	69	3	(	(	PUNCT
concept-2079	69	4	“	"	PUNCT
concept-2079	69	5	dimension	dimension	NOUN
concept-2079	69	6	of	of	ADP
concept-2079	69	7	cantor	cantor	PROPN
concept-2079	69	8	set	set	PROPN
concept-2079	69	9	”	"	PUNCT
concept-2079	69	10	)	)	PUNCT
concept-2079	69	11	.	.	PUNCT
concept-2079	70	1	notice	notice	NOUN
concept-2079	70	2	:	:	PUNCT
concept-2079	70	3	there	there	PRON
concept-2079	70	4	are	be	VERB
concept-2079	70	5	2𝑛	2𝑛	PROPN
concept-2079	70	6	 	 	SPACE
concept-2079	70	7	divisions	division	NOUN
concept-2079	70	8	of	of	ADP
concept-2079	70	9	the	the	DET
concept-2079	70	10	intervals	interval	NOUN
concept-2079	70	11	and	and	CCONJ
concept-2079	70	12	you	you	PRON
concept-2079	70	13	are	be	AUX
concept-2079	70	14	scaling	scale	VERB
concept-2079	70	15	down	down	ADP
concept-2079	70	16	the	the	DET
concept-2079	70	17	cantor	cantor	NOUN
concept-2079	70	18	set	set	VERB
concept-2079	70	19	each	each	DET
concept-2079	70	20	time	time	NOUN
concept-2079	70	21	by	by	ADP
concept-2079	70	22	a	a	DET
concept-2079	70	23	factor	factor	NOUN
concept-2079	70	24	of	of	ADP
concept-2079	70	25	3	3	NUM
concept-2079	70	26	or	or	CCONJ
concept-2079	70	27	one	one	NUM
concept-2079	70	28	third	third	NOUN
concept-2079	70	29	.	.	PUNCT
concept-2079	71	1	similarly	similarly	ADV
concept-2079	71	2	,	,	PUNCT
concept-2079	71	3	we	we	PRON
concept-2079	71	4	can	can	AUX
concept-2079	71	5	explore	explore	VERB
concept-2079	71	6	the	the	DET
concept-2079	71	7	behavior	behavior	NOUN
concept-2079	71	8	of	of	ADP
concept-2079	71	9	the	the	DET
concept-2079	71	10	koch	koch	PROPN
concept-2079	71	11	curve	curve	NOUN
concept-2079	71	12	created	create	VERB
concept-2079	71	13	by	by	ADP
concept-2079	71	14	helge	helge	PROPN
concept-2079	71	15	von	von	PROPN
concept-2079	71	16	koch	koch	PROPN
concept-2079	71	17	.	.	PUNCT
concept-2079	72	1	to	to	PART
concept-2079	72	2	create	create	VERB
concept-2079	72	3	the	the	DET
concept-2079	72	4	koch	koch	PROPN
concept-2079	72	5	curve	curve	NOUN
concept-2079	72	6	,	,	PUNCT
concept-2079	72	7	you	you	PRON
concept-2079	72	8	start	start	VERB
concept-2079	72	9	out	out	ADP
concept-2079	72	10	with	with	ADP
concept-2079	72	11	a	a	DET
concept-2079	72	12	line	line	NOUN
concept-2079	72	13	segment	segment	NOUN
concept-2079	72	14	of	of	ADP
concept-2079	72	15	with	with	ADP
concept-2079	72	16	length	length	NOUN
concept-2079	72	17	of	of	ADP
concept-2079	72	18	one	one	NUM
concept-2079	72	19	unit	unit	NOUN
concept-2079	72	20	.	.	PUNCT
concept-2079	73	1	instead	instead	ADV
concept-2079	73	2	of	of	ADP
concept-2079	73	3	removing	remove	VERB
concept-2079	73	4	the	the	DET
concept-2079	73	5	middle	middle	ADJ
concept-2079	73	6	-	-	PUNCT
concept-2079	73	7	thirds	third	NOUN
concept-2079	73	8	of	of	ADP
concept-2079	73	9	the	the	DET
concept-2079	73	10	line	line	NOUN
concept-2079	73	11	segment	segment	NOUN
concept-2079	73	12	as	as	SCONJ
concept-2079	73	13	you	you	PRON
concept-2079	73	14	do	do	VERB
concept-2079	73	15	in	in	ADP
concept-2079	73	16	the	the	DET
concept-2079	73	17	cantor	cantor	NOUN
concept-2079	73	18	set	set	NOUN
concept-2079	73	19	,	,	PUNCT
concept-2079	73	20	you	you	PRON
concept-2079	73	21	actually	actually	ADV
concept-2079	73	22	add	add	VERB
concept-2079	73	23	two	two	NUM
concept-2079	73	24	segments	segment	NOUN
concept-2079	73	25	of	of	ADP
concept-2079	73	26	length	length	NOUN
concept-2079	73	27	one	one	NUM
concept-2079	73	28	third	third	NOUN
concept-2079	73	29	of	of	ADP
concept-2079	73	30	the	the	DET
concept-2079	73	31	original	original	ADJ
concept-2079	73	32	line	line	NOUN
concept-2079	73	33	.	.	PUNCT
concept-2079	74	1	another	another	DET
concept-2079	74	2	way	way	NOUN
concept-2079	74	3	to	to	PART
concept-2079	74	4	think	think	VERB
concept-2079	74	5	about	about	ADP
concept-2079	74	6	this	this	PRON
concept-2079	74	7	is	be	AUX
concept-2079	74	8	that	that	SCONJ
concept-2079	74	9	you	you	PRON
concept-2079	74	10	take	take	VERB
concept-2079	74	11	the	the	DET
concept-2079	74	12	middle	middle	ADJ
concept-2079	74	13	third	third	NOUN
concept-2079	74	14	of	of	ADP
concept-2079	74	15	the	the	DET
concept-2079	74	16	original	original	ADJ
concept-2079	74	17	line	line	NOUN
concept-2079	74	18	segment	segment	NOUN
concept-2079	74	19	and	and	CCONJ
concept-2079	74	20	replace	replace	VERB
concept-2079	74	21	it	it	PRON
concept-2079	74	22	with	with	ADP
concept-2079	74	23	the	the	DET
concept-2079	74	24	top	top	ADJ
concept-2079	74	25	part	part	NOUN
concept-2079	74	26	of	of	ADP
concept-2079	74	27	an	an	DET
concept-2079	74	28	equilateral	equilateral	ADJ
concept-2079	74	29	triangle	triangle	NOUN
concept-2079	74	30	.	.	PUNCT
concept-2079	75	1	this	this	DET
concept-2079	75	2	process	process	NOUN
concept-2079	75	3	is	be	AUX
concept-2079	75	4	iterated	iterate	VERB
concept-2079	75	5	over	over	ADP
concept-2079	75	6	and	and	CCONJ
concept-2079	75	7	over	over	ADV
concept-2079	75	8	again	again	ADV
concept-2079	75	9	to	to	PART
concept-2079	75	10	produce	produce	VERB
concept-2079	75	11	more	more	ADJ
concept-2079	75	12	intricate	intricate	ADJ
concept-2079	75	13	geometric	geometric	ADJ
concept-2079	75	14	design	design	NOUN
concept-2079	75	15	.	.	PUNCT
concept-2079	76	1	you	you	PRON
concept-2079	76	2	can	can	AUX
concept-2079	76	3	clearly	clearly	ADV
concept-2079	76	4	see	see	VERB
concept-2079	76	5	that	that	SCONJ
concept-2079	76	6	through	through	ADP
concept-2079	76	7	the	the	DET
concept-2079	76	8	various	various	ADJ
concept-2079	76	9	iterations	iteration	NOUN
concept-2079	76	10	of	of	ADP
concept-2079	76	11	the	the	DET
concept-2079	76	12	koch	koch	PROPN
concept-2079	76	13	curve	curve	NOUN
concept-2079	76	14	,	,	PUNCT
concept-2079	76	15	since	since	SCONJ
concept-2079	76	16	you	you	PRON
concept-2079	76	17	are	be	AUX
concept-2079	76	18	adding	add	VERB
concept-2079	76	19	line	line	NOUN
concept-2079	76	20	segments	segment	NOUN
concept-2079	76	21	of	of	ADP
concept-2079	76	22	(	(	PUNCT
concept-2079	76	23	!	!	PUNCT
concept-2079	76	24	!	!	PUNCT
concept-2079	76	25	)	)	PUNCT
concept-2079	76	26	!	!	PUNCT
concept-2079	77	1	during	during	ADP
concept-2079	77	2	each	each	DET
concept-2079	77	3	iteration	iteration	NOUN
concept-2079	77	4	,	,	PUNCT
concept-2079	77	5	the	the	DET
concept-2079	77	6	curve	curve	NOUN
concept-2079	77	7	will	will	AUX
concept-2079	77	8	get	get	VERB
concept-2079	77	9	longer	long	ADJ
concept-2079	77	10	and	and	CCONJ
concept-2079	77	11	longer	long	ADV
concept-2079	77	12	over	over	ADP
concept-2079	77	13	time	time	NOUN
concept-2079	77	14	.	.	PUNCT
concept-2079	78	1	one	one	NUM
concept-2079	78	2	interesting	interesting	ADJ
concept-2079	78	3	result	result	NOUN
concept-2079	78	4	we	we	PRON
concept-2079	78	5	can	can	AUX
concept-2079	78	6	show	show	VERB
concept-2079	78	7	is	be	AUX
concept-2079	78	8	that	that	SCONJ
concept-2079	78	9	although	although	SCONJ
concept-2079	78	10	the	the	DET
concept-2079	78	11	koch	koch	PROPN
concept-2079	78	12	curve	curve	NOUN
concept-2079	78	13	has	have	VERB
concept-2079	78	14	infinite	infinite	ADJ
concept-2079	78	15	length	length	NOUN
concept-2079	78	16	,	,	PUNCT
concept-2079	78	17	the	the	DET
concept-2079	78	18	koch	koch	PROPN
concept-2079	78	19	snowflake	snowflake	NOUN
concept-2079	78	20	encompasses	encompass	VERB
concept-2079	78	21	an	an	DET
concept-2079	78	22	area	area	NOUN
concept-2079	78	23	that	that	PRON
concept-2079	78	24	is	be	AUX
concept-2079	78	25	finite	finite	ADJ
concept-2079	78	26	.	.	PUNCT
concept-2079	79	1	the	the	DET
concept-2079	79	2	koch	koch	PROPN
concept-2079	79	3	snowflake	snowflake	NOUN
concept-2079	79	4	is	be	AUX
concept-2079	79	5	a	a	DET
concept-2079	79	6	variation	variation	NOUN
concept-2079	79	7	of	of	ADP
concept-2079	79	8	the	the	DET
concept-2079	79	9	koch	koch	PROPN
concept-2079	79	10	curve	curve	NOUN
concept-2079	79	11	(	(	PUNCT
concept-2079	79	12	figure	figure	NOUN
concept-2079	79	13	2	2	NUM
concept-2079	79	14	)	)	PUNCT
concept-2079	79	15	.	.	PUNCT
concept-2079	80	1	we	we	PRON
concept-2079	80	2	first	first	ADV
concept-2079	80	3	start	start	VERB
concept-2079	80	4	out	out	ADP
concept-2079	80	5	by	by	ADP
concept-2079	80	6	finding	find	VERB
concept-2079	80	7	concept	concept	NOUN
concept-2079	80	8	,	,	PUNCT
concept-2079	80	9	vol	vol	NOUN
concept-2079	80	10	.	.	PUNCT
concept-2079	81	1	xxxix	xxxix	PROPN
concept-2079	81	2	(	(	PUNCT
concept-2079	81	3	2016	2016	NUM
concept-2079	81	4	)	)	PUNCT
concept-2079	81	5	5	5	NUM
concept-2079	81	6	the	the	DET
concept-2079	81	7	area	area	NOUN
concept-2079	81	8	of	of	ADP
concept-2079	81	9	an	an	DET
concept-2079	81	10	equilateral	equilateral	ADJ
concept-2079	81	11	triangle	triangle	NOUN
concept-2079	81	12	,	,	PUNCT
concept-2079	81	13	given	give	VERB
concept-2079	81	14	to	to	ADP
concept-2079	81	15	us	we	PRON
concept-2079	81	16	by	by	ADP
concept-2079	81	17	the	the	DET
concept-2079	81	18	formula	formula	NOUN
concept-2079	81	19	a	a	PRON
concept-2079	81	20	=	=	PUNCT
concept-2079	81	21	!	!	PUNCT
concept-2079	81	22	!	!	PUNCT
concept-2079	82	1	𝑠	𝑠	X
concept-2079	82	2	!	!	PUNCT
concept-2079	82	3	.	.	PUNCT
concept-2079	83	1	when	when	SCONJ
concept-2079	83	2	there	there	PRON
concept-2079	83	3	are	be	VERB
concept-2079	83	4	no	no	DET
concept-2079	83	5	iterations	iteration	NOUN
concept-2079	83	6	,	,	PUNCT
concept-2079	83	7	we	we	PRON
concept-2079	83	8	obtain	obtain	VERB
concept-2079	83	9	the	the	DET
concept-2079	83	10	area	area	NOUN
concept-2079	83	11	of	of	ADP
concept-2079	83	12	the	the	DET
concept-2079	83	13	original	original	ADJ
concept-2079	83	14	triangle	triangle	NOUN
concept-2079	83	15	which	which	PRON
concept-2079	83	16	is	be	AUX
concept-2079	83	17	given	give	VERB
concept-2079	83	18	to	to	ADP
concept-2079	83	19	us	we	PRON
concept-2079	83	20	by	by	ADP
concept-2079	83	21	!	!	PUNCT
concept-2079	83	22	!	!	PUNCT
concept-2079	84	1	𝑠	𝑠	X
concept-2079	84	2	!	!	PUNCT
concept-2079	84	3	,	,	PUNCT
concept-2079	84	4	then	then	ADV
concept-2079	84	5	for	for	ADP
concept-2079	84	6	the	the	DET
concept-2079	84	7	first	first	ADJ
concept-2079	84	8	iteration	iteration	NOUN
concept-2079	84	9	,	,	PUNCT
concept-2079	84	10	each	each	DET
concept-2079	84	11	side	side	NOUN
concept-2079	84	12	of	of	ADP
concept-2079	84	13	the	the	DET
concept-2079	84	14	three	three	NUM
concept-2079	84	15	new	new	ADJ
concept-2079	84	16	triangles	triangle	NOUN
concept-2079	84	17	is	be	AUX
concept-2079	84	18	cut	cut	VERB
concept-2079	84	19	into	into	ADP
concept-2079	84	20	thirds	third	NOUN
concept-2079	84	21	,	,	PUNCT
concept-2079	84	22	so	so	ADV
concept-2079	84	23	we	we	PRON
concept-2079	84	24	add	add	VERB
concept-2079	84	25	on	on	ADP
concept-2079	84	26	3	3	NUM
concept-2079	84	27	!	!	PUNCT
concept-2079	84	28	!	!	PUNCT
concept-2079	85	1	(	(	PUNCT
concept-2079	85	2	!	!	PUNCT
concept-2079	85	3	!	!	PUNCT
concept-2079	85	4	)	)	PUNCT
concept-2079	85	5	!	!	PUNCT
concept-2079	86	1	to	to	ADP
concept-2079	86	2	the	the	DET
concept-2079	86	3	area	area	NOUN
concept-2079	86	4	previously	previously	ADV
concept-2079	86	5	obtained	obtain	VERB
concept-2079	86	6	,	,	PUNCT
concept-2079	86	7	and	and	CCONJ
concept-2079	86	8	continue	continue	VERB
concept-2079	86	9	the	the	DET
concept-2079	86	10	process	process	NOUN
concept-2079	86	11	.	.	PUNCT
concept-2079	87	1	notice	notice	NOUN
concept-2079	87	2	,	,	PUNCT
concept-2079	87	3	there	there	PRON
concept-2079	87	4	is	be	VERB
concept-2079	87	5	a	a	DET
concept-2079	87	6	pattern	pattern	NOUN
concept-2079	87	7	regarding	regard	VERB
concept-2079	87	8	the	the	DET
concept-2079	87	9	new	new	ADJ
concept-2079	87	10	triangles	triangle	NOUN
concept-2079	87	11	added	add	VERB
concept-2079	87	12	on	on	ADP
concept-2079	87	13	to	to	ADP
concept-2079	87	14	base	base	NOUN
concept-2079	87	15	triangle	triangle	NOUN
concept-2079	87	16	,	,	PUNCT
concept-2079	87	17	3	3	NUM
concept-2079	87	18	,	,	PUNCT
concept-2079	87	19	12	12	NUM
concept-2079	87	20	,	,	PUNCT
concept-2079	87	21	48	48	NUM
concept-2079	87	22	,	,	PUNCT
concept-2079	87	23	...	...	PUNCT
concept-2079	88	1	=	=	PUNCT
concept-2079	89	1	3	3	NUM
concept-2079	89	2	*	*	SYM
concept-2079	89	3	4	4	NUM
concept-2079	89	4	!	!	PUNCT
concept-2079	89	5	!	!	PUNCT
concept-2079	89	6	!	!	PUNCT
concept-2079	89	7	.	.	PUNCT
concept-2079	90	1	written	write	VERB
concept-2079	90	2	out	out	ADP
concept-2079	90	3	,	,	PUNCT
concept-2079	90	4	the	the	DET
concept-2079	90	5	expanded	expand	VERB
concept-2079	90	6	area	area	NOUN
concept-2079	90	7	looks	look	VERB
concept-2079	90	8	like	like	ADP
concept-2079	90	9	:	:	PUNCT
concept-2079	90	10	!	!	PUNCT
concept-2079	90	11	!	!	PUNCT
concept-2079	91	1	𝑠	𝑠	X
concept-2079	91	2	!	!	PUNCT
concept-2079	92	1	+	+	CCONJ
concept-2079	92	2	3	3	X
concept-2079	92	3	!	!	PUNCT
concept-2079	92	4	!	!	PUNCT
concept-2079	93	1	(	(	PUNCT
concept-2079	93	2	!	!	PUNCT
concept-2079	93	3	!	!	PUNCT
concept-2079	93	4	)	)	PUNCT
concept-2079	93	5	!	!	PUNCT
concept-2079	94	1	+	+	CCONJ
concept-2079	94	2	12	12	NUM
concept-2079	94	3	!	!	PUNCT
concept-2079	94	4	!	!	PUNCT
concept-2079	95	1	(	(	PUNCT
concept-2079	95	2	!	!	PUNCT
concept-2079	95	3	!	!	PUNCT
concept-2079	95	4	)	)	PUNCT
concept-2079	95	5	!	!	PUNCT
concept-2079	96	1	+	+	CCONJ
concept-2079	96	2	48	48	NUM
concept-2079	96	3	!	!	PUNCT
concept-2079	96	4	!	!	PUNCT
concept-2079	97	1	(	(	PUNCT
concept-2079	97	2	!	!	PUNCT
concept-2079	97	3	!	!	PUNCT
concept-2079	97	4	"	"	PUNCT
concept-2079	97	5	)	)	PUNCT
concept-2079	97	6	!	!	PUNCT
concept-2079	98	1	+	+	X
concept-2079	98	2	...	...	PUNCT
concept-2079	98	3	=	=	PUNCT
concept-2079	98	4	!	!	PUNCT
concept-2079	98	5	!	!	PUNCT
concept-2079	98	6	 	 	SPACE
concept-2079	98	7	𝑠!(1	𝑠!(1	NOUN
concept-2079	98	8	+	+	CCONJ
concept-2079	98	9	!	!	PUNCT
concept-2079	98	10	!	!	PUNCT
concept-2079	99	1	+	+	CCONJ
concept-2079	99	2	!	!	PUNCT
concept-2079	100	1	∗	∗	NOUN
concept-2079	100	2	!	!	PUNCT
concept-2079	100	3	!	!	PUNCT
concept-2079	100	4	!	!	PUNCT
concept-2079	101	1	+	+	X
concept-2079	101	2	!	!	NOUN
concept-2079	101	3	∗	∗	NOUN
concept-2079	101	4	!	!	PUNCT
concept-2079	101	5	!	!	PUNCT
concept-2079	101	6	!	!	PUNCT
concept-2079	101	7	!	!	PUNCT
concept-2079	102	1	+	+	CCONJ
concept-2079	102	2	 	 	SPACE
concept-2079	102	3	…	…	PUNCT
concept-2079	102	4	)	)	PUNCT
concept-2079	102	5	=	=	PUNCT
concept-2079	102	6	!	!	PUNCT
concept-2079	102	7	!	!	PUNCT
concept-2079	102	8	 	 	SPACE
concept-2079	103	1	𝑠	𝑠	INTJ
concept-2079	103	2	!	!	PUNCT
concept-2079	104	1	(	(	PUNCT
concept-2079	104	2	1	1	NUM
concept-2079	104	3	+	+	NOUN
concept-2079	104	4	  	  	SPACE
concept-2079	104	5	!	!	PUNCT
concept-2079	105	1	∗	∗	NOUN
concept-2079	105	2	 	 	SPACE
concept-2079	105	3	!	!	PUNCT
concept-2079	105	4	!	!	PUNCT
concept-2079	105	5	!	!	PUNCT
concept-2079	105	6	!	!	PUNCT
concept-2079	105	7	!	!	PUNCT
concept-2079	105	8	!	!	PUNCT
concept-2079	105	9	!	!	PUNCT
concept-2079	105	10	!	!	PUNCT
concept-2079	105	11	!	!	PUNCT
concept-2079	105	12	!	!	PUNCT
concept-2079	105	13	)	)	PUNCT
concept-2079	105	14	.	.	PUNCT
concept-2079	106	1	now	now	ADV
concept-2079	106	2	using	use	VERB
concept-2079	106	3	the	the	DET
concept-2079	106	4	results	result	NOUN
concept-2079	106	5	from	from	ADP
concept-2079	106	6	calculus	calculus	NOUN
concept-2079	106	7	,	,	PUNCT
concept-2079	106	8	we	we	PRON
concept-2079	106	9	have	have	VERB
concept-2079	106	10	a	a	DET
concept-2079	106	11	geometric	geometric	ADJ
concept-2079	106	12	series	series	NOUN
concept-2079	106	13	that	that	PRON
concept-2079	106	14	converges	converge	VERB
concept-2079	106	15	to	to	ADP
concept-2079	106	16	!	!	PUNCT
concept-2079	106	17	!	!	PUNCT
concept-2079	106	18	!	!	PUNCT
concept-2079	106	19	!	!	PUNCT
concept-2079	107	1	=	=	PUNCT
concept-2079	107	2	!	!	PUNCT
concept-2079	107	3	!	!	PUNCT
concept-2079	107	4	!	!	PUNCT
concept-2079	107	5	!	!	PUNCT
concept-2079	107	6	!	!	PUNCT
concept-2079	107	7	!	!	PUNCT
concept-2079	108	1	=	=	PUNCT
concept-2079	108	2	!	!	PUNCT
concept-2079	108	3	!	!	PUNCT
concept-2079	108	4	!	!	PUNCT
concept-2079	108	5	!	!	PUNCT
concept-2079	109	1	=	=	PUNCT
concept-2079	109	2	!	!	PUNCT
concept-2079	109	3	!	!	PUNCT
concept-2079	110	1	and	and	CCONJ
concept-2079	110	2	since	since	SCONJ
concept-2079	110	3	we	we	PRON
concept-2079	110	4	shifted	shift	VERB
concept-2079	110	5	the	the	DET
concept-2079	110	6	series	series	NOUN
concept-2079	110	7	,	,	PUNCT
concept-2079	110	8	1	1	NUM
concept-2079	110	9	+	+	PUNCT
concept-2079	110	10	!	!	PUNCT
concept-2079	110	11	!	!	PUNCT
concept-2079	111	1	=	=	PUNCT
concept-2079	111	2	!	!	PUNCT
concept-2079	111	3	!	!	PUNCT
concept-2079	111	4	.	.	PUNCT
concept-2079	111	5	  	  	SPACE
concept-2079	112	1	this	this	PRON
concept-2079	112	2	implies	imply	VERB
concept-2079	112	3	that	that	SCONJ
concept-2079	112	4	the	the	DET
concept-2079	112	5	area	area	NOUN
concept-2079	112	6	for	for	ADP
concept-2079	112	7	the	the	DET
concept-2079	112	8	koch	koch	PROPN
concept-2079	112	9	snowflake	snowflake	NOUN
concept-2079	112	10	,	,	PUNCT
concept-2079	112	11	whose	whose	DET
concept-2079	112	12	construction	construction	NOUN
concept-2079	112	13	begins	begin	VERB
concept-2079	112	14	with	with	ADP
concept-2079	112	15	a	a	DET
concept-2079	112	16	triangle	triangle	NOUN
concept-2079	112	17	with	with	ADP
concept-2079	112	18	side	side	NOUN
concept-2079	112	19	length	length	NOUN
concept-2079	112	20	s	s	PART
concept-2079	112	21	is	be	AUX
concept-2079	112	22	equal	equal	ADJ
concept-2079	112	23	to	to	ADP
concept-2079	112	24	  	  	SPACE
concept-2079	112	25	!	!	PUNCT
concept-2079	112	26	!	!	PUNCT
concept-2079	112	27	 	 	SPACE
concept-2079	113	1	𝑠	𝑠	PROPN
concept-2079	113	2	!	!	PUNCT
concept-2079	113	3	!	!	PUNCT
concept-2079	113	4	!	!	PUNCT
concept-2079	114	1	=	=	PUNCT
concept-2079	114	2	  	  	SPACE
concept-2079	114	3	!	!	PUNCT
concept-2079	114	4	!	!	PUNCT
concept-2079	114	5	!	!	PUNCT
concept-2079	114	6	 	 	SPACE
concept-2079	115	1	𝑠	𝑠	PROPN
concept-2079	115	2	!	!	PROPN
concept-2079	115	3	,	,	PUNCT
concept-2079	115	4	has	have	VERB
concept-2079	115	5	a	a	DET
concept-2079	115	6	finite	finite	ADJ
concept-2079	115	7	area	area	NOUN
concept-2079	115	8	(	(	PUNCT
concept-2079	115	9	riddle	riddle	VERB
concept-2079	115	10	,	,	PUNCT
concept-2079	115	11	“	"	PUNCT
concept-2079	115	12	area	area	NOUN
concept-2079	115	13	of	of	ADP
concept-2079	115	14	the	the	DET
concept-2079	115	15	koch	koch	PROPN
concept-2079	115	16	snowflake	snowflake	NOUN
concept-2079	115	17	”	"	PUNCT
concept-2079	115	18	)	)	PUNCT
concept-2079	115	19	.	.	PUNCT
concept-2079	116	1	we	we	PRON
concept-2079	116	2	check	check	VERB
concept-2079	116	3	the	the	DET
concept-2079	116	4	hausdorff	hausdorff	NOUN
concept-2079	116	5	dimension	dimension	NOUN
concept-2079	116	6	to	to	PART
concept-2079	116	7	verify	verify	VERB
concept-2079	116	8	that	that	SCONJ
concept-2079	116	9	the	the	DET
concept-2079	116	10	koch	koch	PROPN
concept-2079	116	11	curve	curve	NOUN
concept-2079	116	12	is	be	AUX
concept-2079	116	13	a	a	DET
concept-2079	116	14	fractal	fractal	NOUN
concept-2079	116	15	:	:	PUNCT
concept-2079	116	16	there	there	PRON
concept-2079	116	17	are	be	VERB
concept-2079	116	18	four	four	NUM
concept-2079	116	19	self	self	NOUN
concept-2079	116	20	-	-	PUNCT
concept-2079	116	21	similar	similar	ADJ
concept-2079	116	22	pieces	piece	NOUN
concept-2079	116	23	after	after	ADP
concept-2079	116	24	the	the	DET
concept-2079	116	25	first	first	ADJ
concept-2079	116	26	iteration	iteration	NOUN
concept-2079	116	27	and	and	CCONJ
concept-2079	116	28	the	the	DET
concept-2079	116	29	curve	curve	NOUN
concept-2079	116	30	shrinks	shrink	VERB
concept-2079	116	31	by	by	ADP
concept-2079	116	32	a	a	DET
concept-2079	116	33	factor	factor	NOUN
concept-2079	116	34	of	of	ADP
concept-2079	116	35	one	one	NUM
concept-2079	116	36	third	third	NOUN
concept-2079	116	37	or	or	CCONJ
concept-2079	116	38	3	3	NUM
concept-2079	116	39	,	,	PUNCT
concept-2079	116	40	𝑑	𝑑	PROPN
concept-2079	116	41	=	=	NOUN
concept-2079	116	42	  	  	SPACE
concept-2079	116	43	!	!	PUNCT
concept-2079	116	44	"	"	PUNCT
concept-2079	116	45	!	!	PUNCT
concept-2079	116	46	!	!	PUNCT
concept-2079	116	47	"	"	PUNCT
concept-2079	116	48	!	!	PUNCT
concept-2079	117	1	=	=	PUNCT
concept-2079	117	2	1.26	1.26	NUM
concept-2079	117	3	,	,	PUNCT
concept-2079	117	4	 	 	SPACE
concept-2079	117	5	a	a	DET
concept-2079	117	6	fractional	fractional	ADJ
concept-2079	117	7	dimension	dimension	NOUN
concept-2079	117	8	!	!	PUNCT
concept-2079	118	1	figure	figure	NOUN
concept-2079	118	2	2	2	NUM
concept-2079	118	3	–	–	PUNCT
concept-2079	118	4	koch	koch	PROPN
concept-2079	118	5	snowflake	snowflake	VERB
concept-2079	118	6	another	another	DET
concept-2079	118	7	famous	famous	ADJ
concept-2079	118	8	example	example	NOUN
concept-2079	118	9	of	of	ADP
concept-2079	118	10	a	a	DET
concept-2079	118	11	fractal	fractal	NOUN
concept-2079	118	12	is	be	AUX
concept-2079	118	13	known	know	VERB
concept-2079	118	14	as	as	ADP
concept-2079	118	15	sierpiński	sierpiński	NOUN
concept-2079	118	16	's	's	PART
concept-2079	118	17	triangle	triangle	NOUN
concept-2079	118	18	created	create	VERB
concept-2079	118	19	by	by	ADP
concept-2079	118	20	wacław	wacław	ADJ
concept-2079	118	21	sierpiński	sierpiński	PROPN
concept-2079	118	22	.	.	PUNCT
concept-2079	119	1	in	in	ADP
concept-2079	119	2	order	order	NOUN
concept-2079	119	3	to	to	PART
concept-2079	119	4	construct	construct	VERB
concept-2079	119	5	the	the	DET
concept-2079	119	6	fractal	fractal	NOUN
concept-2079	119	7	,	,	PUNCT
concept-2079	119	8	first	first	ADV
concept-2079	119	9	create	create	VERB
concept-2079	119	10	a	a	DET
concept-2079	119	11	equilateral	equilateral	ADJ
concept-2079	119	12	triangle	triangle	NOUN
concept-2079	119	13	.	.	PUNCT
concept-2079	120	1	then	then	ADV
concept-2079	120	2	after	after	ADP
concept-2079	120	3	identifying	identify	VERB
concept-2079	120	4	the	the	DET
concept-2079	120	5	midpoints	midpoint	NOUN
concept-2079	120	6	of	of	ADP
concept-2079	120	7	each	each	DET
concept-2079	120	8	side	side	NOUN
concept-2079	120	9	,	,	PUNCT
concept-2079	120	10	connect	connect	VERB
concept-2079	120	11	those	those	DET
concept-2079	120	12	points	point	NOUN
concept-2079	120	13	to	to	ADP
concept-2079	120	14	concept	concept	NOUN
concept-2079	120	15	,	,	PUNCT
concept-2079	120	16	vol	vol	NOUN
concept-2079	120	17	.	.	PUNCT
concept-2079	121	1	xxxix	xxxix	PROPN
concept-2079	121	2	(	(	PUNCT
concept-2079	121	3	2016	2016	NUM
concept-2079	121	4	)	)	PUNCT
concept-2079	121	5	6	6	NUM
concept-2079	121	6	make	make	VERB
concept-2079	121	7	another	another	DET
concept-2079	121	8	triangle	triangle	NOUN
concept-2079	121	9	and	and	CCONJ
concept-2079	121	10	leave	leave	VERB
concept-2079	121	11	this	this	DET
concept-2079	121	12	triangle	triangle	NOUN
concept-2079	121	13	unshaded	unshaded	ADJ
concept-2079	121	14	while	while	SCONJ
concept-2079	121	15	shading	shade	VERB
concept-2079	121	16	in	in	ADP
concept-2079	121	17	the	the	DET
concept-2079	121	18	other	other	ADJ
concept-2079	121	19	triangles	triangle	NOUN
concept-2079	121	20	that	that	PRON
concept-2079	121	21	are	be	AUX
concept-2079	121	22	formed	form	VERB
concept-2079	121	23	.	.	PUNCT
concept-2079	122	1	then	then	ADV
concept-2079	122	2	iterate	iterate	VERB
concept-2079	122	3	the	the	DET
concept-2079	122	4	process	process	NOUN
concept-2079	122	5	a	a	DET
concept-2079	122	6	few	few	ADJ
concept-2079	122	7	times	time	NOUN
concept-2079	122	8	,	,	PUNCT
concept-2079	122	9	always	always	ADV
concept-2079	122	10	leaving	leave	VERB
concept-2079	122	11	the	the	DET
concept-2079	122	12	middle	middle	ADJ
concept-2079	122	13	triangle	triangle	NOUN
concept-2079	122	14	in	in	ADP
concept-2079	122	15	each	each	DET
concept-2079	122	16	larger	large	ADJ
concept-2079	122	17	triangle	triangle	NOUN
concept-2079	122	18	unshaded	unshaded	ADJ
concept-2079	122	19	.	.	PUNCT
concept-2079	123	1	notice	notice	NOUN
concept-2079	123	2	,	,	PUNCT
concept-2079	123	3	after	after	ADP
concept-2079	123	4	the	the	DET
concept-2079	123	5	first	first	ADJ
concept-2079	123	6	iteration	iteration	NOUN
concept-2079	123	7	,	,	PUNCT
concept-2079	123	8	there	there	PRON
concept-2079	123	9	are	be	VERB
concept-2079	123	10	four	four	NUM
concept-2079	123	11	triangles	triangle	NOUN
concept-2079	123	12	,	,	PUNCT
concept-2079	123	13	but	but	CCONJ
concept-2079	123	14	one	one	NUM
concept-2079	123	15	triangle	triangle	NOUN
concept-2079	123	16	of	of	ADP
concept-2079	123	17	half	half	ADJ
concept-2079	123	18	-	-	PUNCT
concept-2079	123	19	scale	scale	NOUN
concept-2079	123	20	,	,	PUNCT
concept-2079	123	21	or	or	CCONJ
concept-2079	123	22	,	,	PUNCT
concept-2079	123	23	an	an	DET
concept-2079	123	24	area	area	NOUN
concept-2079	123	25	of	of	ADP
concept-2079	123	26	one	one	NUM
concept-2079	123	27	-	-	PUNCT
concept-2079	123	28	fourth	fourth	NOUN
concept-2079	123	29	the	the	DET
concept-2079	123	30	original	original	ADJ
concept-2079	123	31	triangle	triangle	NOUN
concept-2079	123	32	,	,	PUNCT
concept-2079	123	33	is	be	AUX
concept-2079	123	34	unshaded	unshaded	ADJ
concept-2079	123	35	or	or	CCONJ
concept-2079	123	36	removed	remove	VERB
concept-2079	123	37	.	.	PUNCT
concept-2079	124	1	after	after	ADP
concept-2079	124	2	the	the	DET
concept-2079	124	3	second	second	ADJ
concept-2079	124	4	iteration	iteration	NOUN
concept-2079	124	5	,	,	PUNCT
concept-2079	124	6	there	there	PRON
concept-2079	124	7	are	be	VERB
concept-2079	124	8	three	three	NUM
concept-2079	124	9	additional	additional	ADJ
concept-2079	124	10	triangles	triangle	NOUN
concept-2079	124	11	at	at	ADP
concept-2079	124	12	one	one	NUM
concept-2079	124	13	-	-	PUNCT
concept-2079	124	14	fourth	fourth	NOUN
concept-2079	124	15	scale	scale	NOUN
concept-2079	124	16	,	,	PUNCT
concept-2079	124	17	or	or	CCONJ
concept-2079	124	18	one	one	NUM
concept-2079	124	19	-	-	PUNCT
concept-2079	124	20	sixteenth	sixteenth	NOUN
concept-2079	124	21	the	the	DET
concept-2079	124	22	area	area	NOUN
concept-2079	124	23	of	of	ADP
concept-2079	124	24	the	the	DET
concept-2079	124	25	original	original	ADJ
concept-2079	124	26	triangle	triangle	NOUN
concept-2079	124	27	being	be	AUX
concept-2079	124	28	removed	remove	VERB
concept-2079	124	29	(	(	PUNCT
concept-2079	124	30	figure	figure	NOUN
concept-2079	124	31	3	3	NUM
concept-2079	124	32	)	)	PUNCT
concept-2079	124	33	,	,	PUNCT
concept-2079	124	34	after	after	ADP
concept-2079	124	35	the	the	DET
concept-2079	124	36	nth	nth	NOUN
concept-2079	124	37	iteration	iteration	NOUN
concept-2079	124	38	,	,	PUNCT
concept-2079	124	39	triangles	triangle	NOUN
concept-2079	124	40	of	of	ADP
concept-2079	124	41	!	!	PUNCT
concept-2079	124	42	!	!	PUNCT
concept-2079	124	43	!	!	PUNCT
concept-2079	125	1	area	area	NOUN
concept-2079	125	2	will	will	AUX
concept-2079	125	3	be	be	AUX
concept-2079	125	4	removed	remove	VERB
concept-2079	125	5	;	;	PUNCT
concept-2079	125	6	in	in	ADP
concept-2079	125	7	other	other	ADJ
concept-2079	125	8	words	word	NOUN
concept-2079	125	9	,	,	PUNCT
concept-2079	125	10	the	the	DET
concept-2079	125	11	size	size	NOUN
concept-2079	125	12	of	of	ADP
concept-2079	125	13	the	the	DET
concept-2079	125	14	triangles	triangle	NOUN
concept-2079	125	15	being	be	AUX
concept-2079	125	16	removed	remove	VERB
concept-2079	125	17	is	be	AUX
concept-2079	125	18	getting	get	VERB
concept-2079	125	19	smaller	small	ADJ
concept-2079	125	20	and	and	CCONJ
concept-2079	125	21	smaller	small	ADJ
concept-2079	125	22	,	,	PUNCT
concept-2079	125	23	eventually	eventually	ADV
concept-2079	125	24	reaching	reach	VERB
concept-2079	125	25	an	an	DET
concept-2079	125	26	area	area	NOUN
concept-2079	125	27	of	of	ADP
concept-2079	125	28	zero	zero	NUM
concept-2079	125	29	as	as	ADP
concept-2079	125	30	n	n	NUM
concept-2079	125	31	approaches	approach	VERB
concept-2079	125	32	infinity	infinity	NOUN
concept-2079	125	33	.	.	PUNCT
concept-2079	126	1	you	you	PRON
concept-2079	126	2	should	should	AUX
concept-2079	126	3	also	also	ADV
concept-2079	126	4	notice	notice	VERB
concept-2079	126	5	that	that	SCONJ
concept-2079	126	6	there	there	PRON
concept-2079	126	7	is	be	VERB
concept-2079	126	8	a	a	DET
concept-2079	126	9	pattern	pattern	NOUN
concept-2079	126	10	with	with	ADP
concept-2079	126	11	the	the	DET
concept-2079	126	12	numbers	number	NOUN
concept-2079	126	13	of	of	ADP
concept-2079	126	14	triangles	triangle	NOUN
concept-2079	126	15	being	be	AUX
concept-2079	126	16	removed	remove	VERB
concept-2079	126	17	from	from	ADP
concept-2079	126	18	the	the	DET
concept-2079	126	19	original	original	ADJ
concept-2079	126	20	triangle	triangle	NOUN
concept-2079	126	21	:	:	PUNCT
concept-2079	126	22	1	1	NUM
concept-2079	126	23	,	,	PUNCT
concept-2079	126	24	3	3	NUM
concept-2079	126	25	,	,	PUNCT
concept-2079	126	26	9	9	NUM
concept-2079	126	27	,	,	PUNCT
concept-2079	126	28	27	27	NUM
concept-2079	126	29	...	...	SYM
concept-2079	126	30	3	3	X
concept-2079	126	31	!	!	X
concept-2079	126	32	triangles	triangle	NOUN
concept-2079	126	33	will	will	AUX
concept-2079	126	34	be	be	AUX
concept-2079	126	35	removed	remove	VERB
concept-2079	126	36	upon	upon	SCONJ
concept-2079	126	37	n	n	PRON
concept-2079	126	38	iterations	iteration	NOUN
concept-2079	126	39	.	.	PUNCT
concept-2079	127	1	it	it	PRON
concept-2079	127	2	appears	appear	VERB
concept-2079	127	3	that	that	SCONJ
concept-2079	127	4	if	if	SCONJ
concept-2079	127	5	this	this	DET
concept-2079	127	6	pattern	pattern	NOUN
concept-2079	127	7	continues	continue	VERB
concept-2079	127	8	,	,	PUNCT
concept-2079	127	9	we	we	PRON
concept-2079	127	10	will	will	AUX
concept-2079	127	11	have	have	VERB
concept-2079	127	12	an	an	DET
concept-2079	127	13	infinite	infinite	ADJ
concept-2079	127	14	number	number	NOUN
concept-2079	127	15	of	of	ADP
concept-2079	127	16	triangles	triangle	NOUN
concept-2079	127	17	in	in	ADP
concept-2079	127	18	a	a	DET
concept-2079	127	19	finite	finite	ADJ
concept-2079	127	20	region	region	NOUN
concept-2079	127	21	,	,	PUNCT
concept-2079	127	22	supporting	support	VERB
concept-2079	127	23	the	the	DET
concept-2079	127	24	idea	idea	NOUN
concept-2079	127	25	that	that	SCONJ
concept-2079	127	26	this	this	PRON
concept-2079	127	27	is	be	AUX
concept-2079	127	28	an	an	DET
concept-2079	127	29	example	example	NOUN
concept-2079	127	30	of	of	ADP
concept-2079	127	31	a	a	DET
concept-2079	127	32	fractal	fractal	NOUN
concept-2079	127	33	.	.	PUNCT
concept-2079	128	1	combining	combine	VERB
concept-2079	128	2	the	the	DET
concept-2079	128	3	observations	observation	NOUN
concept-2079	128	4	we	we	PRON
concept-2079	128	5	have	have	AUX
concept-2079	128	6	just	just	ADV
concept-2079	128	7	made	make	VERB
concept-2079	128	8	,	,	PUNCT
concept-2079	128	9	we	we	PRON
concept-2079	128	10	can	can	AUX
concept-2079	128	11	create	create	VERB
concept-2079	128	12	a	a	DET
concept-2079	128	13	geometric	geometric	ADJ
concept-2079	128	14	series	series	NOUN
concept-2079	128	15	that	that	PRON
concept-2079	128	16	describes	describe	VERB
concept-2079	128	17	the	the	DET
concept-2079	128	18	area	area	NOUN
concept-2079	128	19	removed	remove	VERB
concept-2079	128	20	from	from	ADP
concept-2079	128	21	the	the	DET
concept-2079	128	22	original	original	ADJ
concept-2079	128	23	triangle	triangle	NOUN
concept-2079	128	24	:	:	PUNCT
concept-2079	128	25	!	!	PUNCT
concept-2079	128	26	!	!	PUNCT
concept-2079	128	27	  	  	SPACE
concept-2079	128	28	!	!	PUNCT
concept-2079	128	29	!	!	PUNCT
concept-2079	128	30	!	!	PUNCT
concept-2079	129	1	∗	∗	NOUN
concept-2079	129	2	 	 	SPACE
concept-2079	129	3	3	3	NUM
concept-2079	129	4	!	!	PUNCT
concept-2079	129	5	=	=	PUNCT
concept-2079	129	6	!	!	PUNCT
concept-2079	129	7	!	!	PUNCT
concept-2079	129	8	!	!	PUNCT
concept-2079	129	9	!	!	PUNCT
concept-2079	129	10	!	!	PUNCT
concept-2079	129	11	!	!	PUNCT
concept-2079	130	1	∗	∗	NOUN
concept-2079	130	2	 	 	SPACE
concept-2079	130	3	3	3	NUM
concept-2079	130	4	!	!	PUNCT
concept-2079	130	5	=	=	PUNCT
concept-2079	130	6	!	!	PUNCT
concept-2079	130	7	!	!	PUNCT
concept-2079	130	8	!	!	PUNCT
concept-2079	130	9	!	!	PUNCT
concept-2079	130	10	!	!	PUNCT
concept-2079	131	1	∗	∗	NOUN
concept-2079	131	2	3	3	NUM
concept-2079	131	3	!	!	PUNCT
concept-2079	132	1	=	=	PUNCT
concept-2079	132	2	  	  	SPACE
concept-2079	132	3	!	!	PUNCT
concept-2079	132	4	!	!	PUNCT
concept-2079	132	5	!	!	PUNCT
concept-2079	132	6	!	!	PUNCT
concept-2079	132	7	!	!	PUNCT
concept-2079	132	8	!	!	PUNCT
concept-2079	132	9	!	!	PUNCT
concept-2079	133	1	𝑖	𝑖	X
concept-2079	133	2	!	!	PUNCT
concept-2079	133	3	!	!	PUNCT
concept-2079	133	4	!	!	PUNCT
concept-2079	134	1	𝑖	𝑖	X
concept-2079	134	2	!	!	PUNCT
concept-2079	134	3	!	!	PUNCT
concept-2079	134	4	 	 	SPACE
concept-2079	134	5	!	!	PUNCT
concept-2079	135	1	𝑖	𝑖	X
concept-2079	135	2	!	!	PUNCT
concept-2079	135	3	!	!	PUNCT
concept-2079	135	4	!	!	PUNCT
concept-2079	136	1	𝑖	𝑖	X
concept-2079	136	2	!	!	PUNCT
concept-2079	136	3	!	!	PUNCT
concept-2079	137	1	=	=	PUNCT
concept-2079	137	2	!	!	PUNCT
concept-2079	137	3	!	!	PUNCT
concept-2079	137	4	!	!	PUNCT
concept-2079	137	5	!	!	PUNCT
concept-2079	137	6	!	!	PUNCT
concept-2079	137	7	!	!	PUNCT
concept-2079	138	1	𝑖	𝑖	X
concept-2079	138	2	!	!	PUNCT
concept-2079	138	3	!	!	PUNCT
concept-2079	139	1	(	(	PUNCT
concept-2079	139	2	crilly	crilly	ADV
concept-2079	139	3	,	,	PUNCT
concept-2079	139	4	earnshaw	earnshaw	PROPN
concept-2079	139	5	,	,	PUNCT
concept-2079	139	6	jones	jones	PROPN
concept-2079	139	7	,	,	PUNCT
concept-2079	139	8	14	14	NUM
concept-2079	139	9	)	)	PUNCT
concept-2079	139	10	.	.	PUNCT
concept-2079	140	1	similar	similar	ADJ
concept-2079	140	2	to	to	ADP
concept-2079	140	3	the	the	DET
concept-2079	140	4	argument	argument	NOUN
concept-2079	140	5	for	for	ADP
concept-2079	140	6	the	the	DET
concept-2079	140	7	cantor	cantor	PROPN
concept-2079	140	8	set	set	NOUN
concept-2079	140	9	,	,	PUNCT
concept-2079	140	10	we	we	PRON
concept-2079	140	11	can	can	AUX
concept-2079	140	12	use	use	VERB
concept-2079	140	13	results	result	NOUN
concept-2079	140	14	from	from	ADP
concept-2079	140	15	calculus	calculus	NOUN
concept-2079	140	16	to	to	PART
concept-2079	140	17	find	find	VERB
concept-2079	140	18	where	where	SCONJ
concept-2079	140	19	this	this	DET
concept-2079	140	20	geometric	geometric	ADJ
concept-2079	140	21	series	series	NOUN
concept-2079	140	22	will	will	AUX
concept-2079	140	23	converge	converge	VERB
concept-2079	140	24	:	:	PUNCT
concept-2079	140	25	!	!	PUNCT
concept-2079	140	26	!	!	PUNCT
concept-2079	140	27	!	!	PUNCT
concept-2079	140	28	!	!	PUNCT
concept-2079	140	29	 	 	SPACE
concept-2079	141	1	=	=	SYM
concept-2079	141	2	  	  	SPACE
concept-2079	141	3	!	!	PUNCT
concept-2079	141	4	!	!	PUNCT
concept-2079	141	5	!	!	PUNCT
concept-2079	141	6	!	!	PUNCT
concept-2079	141	7	!	!	PUNCT
concept-2079	141	8	!	!	PUNCT
concept-2079	141	9	  	  	SPACE
concept-2079	142	1	=	=	PUNCT
concept-2079	142	2	!	!	PUNCT
concept-2079	142	3	!	!	PUNCT
concept-2079	142	4	!	!	PUNCT
concept-2079	142	5	!	!	PUNCT
concept-2079	143	1	=	=	PUNCT
concept-2079	143	2	 	 	SPACE
concept-2079	143	3	1	1	NUM
concept-2079	143	4	.	.	PUNCT
concept-2079	143	5	  	  	SPACE
concept-2079	143	6	this	this	PRON
concept-2079	143	7	suggests	suggest	VERB
concept-2079	143	8	the	the	DET
concept-2079	143	9	unshaded	unshaded	ADJ
concept-2079	143	10	regions	region	NOUN
concept-2079	143	11	will	will	AUX
concept-2079	143	12	eventually	eventually	ADV
concept-2079	143	13	take	take	VERB
concept-2079	143	14	over	over	ADP
concept-2079	143	15	the	the	DET
concept-2079	143	16	space	space	NOUN
concept-2079	143	17	of	of	ADP
concept-2079	143	18	the	the	DET
concept-2079	143	19	entire	entire	ADJ
concept-2079	143	20	triangle	triangle	NOUN
concept-2079	143	21	over	over	ADP
concept-2079	143	22	time	time	NOUN
concept-2079	143	23	.	.	PUNCT
concept-2079	144	1	finally	finally	ADV
concept-2079	144	2	,	,	PUNCT
concept-2079	144	3	to	to	PART
concept-2079	144	4	absolutely	absolutely	ADV
concept-2079	144	5	make	make	VERB
concept-2079	144	6	certain	certain	ADJ
concept-2079	144	7	the	the	DET
concept-2079	144	8	sierpiński	sierpiński	NOUN
concept-2079	144	9	triangle	triangle	NOUN
concept-2079	144	10	is	be	AUX
concept-2079	144	11	a	a	DET
concept-2079	144	12	fractal	fractal	NOUN
concept-2079	144	13	,	,	PUNCT
concept-2079	144	14	we	we	PRON
concept-2079	144	15	need	need	VERB
concept-2079	144	16	to	to	PART
concept-2079	144	17	identify	identify	VERB
concept-2079	144	18	the	the	DET
concept-2079	144	19	dimension	dimension	NOUN
concept-2079	144	20	.	.	PUNCT
concept-2079	145	1	using	use	VERB
concept-2079	145	2	the	the	DET
concept-2079	145	3	hausdorff	hausdorff	NOUN
concept-2079	145	4	dimension	dimension	PROPN
concept-2079	145	5	definition	definition	NOUN
concept-2079	145	6	,	,	PUNCT
concept-2079	145	7	we	we	PRON
concept-2079	145	8	see	see	VERB
concept-2079	145	9	that	that	SCONJ
concept-2079	145	10	there	there	PRON
concept-2079	145	11	are	be	VERB
concept-2079	145	12	three	three	NUM
concept-2079	145	13	self	self	NOUN
concept-2079	145	14	-	-	PUNCT
concept-2079	145	15	similar	similar	ADJ
concept-2079	145	16	pieces	piece	NOUN
concept-2079	145	17	of	of	ADP
concept-2079	145	18	the	the	DET
concept-2079	145	19	triangle	triangle	NOUN
concept-2079	145	20	after	after	ADP
concept-2079	145	21	the	the	DET
concept-2079	145	22	first	first	ADJ
concept-2079	145	23	iteration	iteration	NOUN
concept-2079	145	24	with	with	ADP
concept-2079	145	25	a	a	DET
concept-2079	145	26	magnification	magnification	NOUN
concept-2079	145	27	scale	scale	NOUN
concept-2079	145	28	of	of	ADP
concept-2079	145	29	two	two	NUM
concept-2079	145	30	(	(	PUNCT
concept-2079	145	31	half	half	ADJ
concept-2079	145	32	scale	scale	NOUN
concept-2079	145	33	)	)	PUNCT
concept-2079	145	34	.	.	PUNCT
concept-2079	146	1	this	this	PRON
concept-2079	146	2	gives	give	VERB
concept-2079	146	3	us	we	PRON
concept-2079	146	4	a	a	DET
concept-2079	146	5	fractional	fractional	ADJ
concept-2079	146	6	dimension	dimension	NOUN
concept-2079	146	7	of	of	ADP
concept-2079	146	8	!	!	PUNCT
concept-2079	146	9	"	"	PUNCT
concept-2079	146	10	!	!	PUNCT
concept-2079	146	11	!	!	PUNCT
concept-2079	146	12	"	"	PUNCT
concept-2079	146	13	!	!	PUNCT
concept-2079	147	1	=	=	NOUN
concept-2079	147	2	1.58	1.58	NUM
concept-2079	147	3	,	,	PUNCT
concept-2079	147	4	supporting	support	VERB
concept-2079	147	5	our	our	PRON
concept-2079	147	6	argument	argument	NOUN
concept-2079	147	7	regarding	regard	VERB
concept-2079	147	8	the	the	DET
concept-2079	147	9	fractal	fractal	ADJ
concept-2079	147	10	behavior	behavior	NOUN
concept-2079	147	11	of	of	ADP
concept-2079	147	12	this	this	DET
concept-2079	147	13	geometric	geometric	ADJ
concept-2079	147	14	structure	structure	NOUN
concept-2079	147	15	(	(	PUNCT
concept-2079	147	16	devaney	devaney	PROPN
concept-2079	147	17	,	,	PUNCT
concept-2079	147	18	“	"	PUNCT
concept-2079	147	19	the	the	DET
concept-2079	147	20	sierpiński	sierpiński	PROPN
concept-2079	147	21	triangle	triangle	NOUN
concept-2079	147	22	”	"	PUNCT
concept-2079	147	23	)	)	PUNCT
concept-2079	147	24	.	.	PUNCT
concept-2079	148	1	concept	concept	NOUN
concept-2079	148	2	,	,	PUNCT
concept-2079	148	3	vol	vol	NOUN
concept-2079	148	4	.	.	PUNCT
concept-2079	149	1	xxxix	xxxix	PROPN
concept-2079	149	2	(	(	PUNCT
concept-2079	149	3	2016	2016	NUM
concept-2079	149	4	)	)	PUNCT
concept-2079	149	5	7	7	NUM
concept-2079	149	6	figure	figure	NOUN
concept-2079	149	7	3	3	NUM
concept-2079	149	8	–	–	PUNCT
concept-2079	149	9	sierpiński	sierpiński	PROPN
concept-2079	149	10	’s	’s	PART
concept-2079	149	11	triangle	triangle	NOUN
concept-2079	149	12	our	our	PRON
concept-2079	149	13	next	next	ADJ
concept-2079	149	14	exploration	exploration	NOUN
concept-2079	149	15	of	of	ADP
concept-2079	149	16	fractal	fractal	ADJ
concept-2079	149	17	geometry	geometry	NOUN
concept-2079	149	18	will	will	AUX
concept-2079	149	19	involve	involve	VERB
concept-2079	149	20	discussion	discussion	NOUN
concept-2079	149	21	of	of	ADP
concept-2079	149	22	the	the	DET
concept-2079	149	23	julia	julia	PROPN
concept-2079	149	24	and	and	CCONJ
concept-2079	149	25	mandelbrot	mandelbrot	PROPN
concept-2079	149	26	sets	set	VERB
concept-2079	149	27	.	.	PUNCT
concept-2079	150	1	both	both	DET
concept-2079	150	2	sets	set	NOUN
concept-2079	150	3	exist	exist	VERB
concept-2079	150	4	within	within	ADP
concept-2079	150	5	the	the	DET
concept-2079	150	6	realm	realm	NOUN
concept-2079	150	7	of	of	ADP
concept-2079	150	8	the	the	DET
concept-2079	150	9	complex	complex	ADJ
concept-2079	150	10	plane	plane	NOUN
concept-2079	150	11	,	,	PUNCT
concept-2079	150	12	whose	whose	DET
concept-2079	150	13	subset	subset	NOUN
concept-2079	150	14	is	be	AUX
concept-2079	150	15	the	the	DET
concept-2079	150	16	real	real	ADJ
concept-2079	150	17	number	number	NOUN
concept-2079	150	18	line	line	NOUN
concept-2079	150	19	.	.	PUNCT
concept-2079	151	1	complex	complex	ADJ
concept-2079	151	2	numbers	number	NOUN
concept-2079	151	3	are	be	AUX
concept-2079	151	4	defined	define	VERB
concept-2079	151	5	as	as	ADP
concept-2079	151	6	z	z	NOUN
concept-2079	151	7	=	=	SYM
concept-2079	151	8	a+bi	a+bi	PROPN
concept-2079	151	9	,	,	PUNCT
concept-2079	151	10	where	where	SCONJ
concept-2079	151	11	a	a	PRON
concept-2079	151	12	is	be	AUX
concept-2079	151	13	a	a	DET
concept-2079	151	14	real	real	ADJ
concept-2079	151	15	number	number	NOUN
concept-2079	151	16	and	and	CCONJ
concept-2079	151	17	the	the	DET
concept-2079	151	18	b	b	NOUN
concept-2079	151	19	is	be	AUX
concept-2079	151	20	the	the	DET
concept-2079	151	21	imaginary	imaginary	ADJ
concept-2079	151	22	component	component	NOUN
concept-2079	151	23	.	.	PUNCT
concept-2079	152	1	the	the	DET
concept-2079	152	2	lower	low	ADJ
concept-2079	152	3	case	case	NOUN
concept-2079	152	4	i	i	PRON
concept-2079	152	5	is	be	AUX
concept-2079	152	6	notation	notation	NOUN
concept-2079	152	7	for	for	ADP
concept-2079	152	8	the	the	DET
concept-2079	152	9	square	square	ADJ
concept-2079	152	10	root	root	NOUN
concept-2079	152	11	of	of	ADP
concept-2079	152	12	negative	negative	ADJ
concept-2079	152	13	one	one	NOUN
concept-2079	152	14	,	,	PUNCT
concept-2079	152	15	a	a	DET
concept-2079	152	16	number	number	NOUN
concept-2079	152	17	that	that	PRON
concept-2079	152	18	does	do	AUX
concept-2079	152	19	not	not	PART
concept-2079	152	20	exist	exist	VERB
concept-2079	152	21	in	in	ADP
concept-2079	152	22	the	the	DET
concept-2079	152	23	set	set	NOUN
concept-2079	152	24	of	of	ADP
concept-2079	152	25	real	real	ADJ
concept-2079	152	26	numbers	number	NOUN
concept-2079	152	27	.	.	PUNCT
concept-2079	153	1	you	you	PRON
concept-2079	153	2	can	can	AUX
concept-2079	153	3	visualize	visualize	VERB
concept-2079	153	4	a	a	DET
concept-2079	153	5	complex	complex	ADJ
concept-2079	153	6	number	number	NOUN
concept-2079	153	7	on	on	ADP
concept-2079	153	8	an	an	DET
concept-2079	153	9	xy	xy	NOUN
concept-2079	153	10	-	-	PUNCT
concept-2079	153	11	coordinate	coordinate	NOUN
concept-2079	153	12	plane	plane	NOUN
concept-2079	153	13	,	,	PUNCT
concept-2079	153	14	where	where	SCONJ
concept-2079	153	15	the	the	DET
concept-2079	153	16	x	x	NOUN
concept-2079	153	17	-	-	NOUN
concept-2079	153	18	coordinate	coordinate	NOUN
concept-2079	153	19	represents	represent	VERB
concept-2079	153	20	the	the	DET
concept-2079	153	21	real	real	ADJ
concept-2079	153	22	number	number	NOUN
concept-2079	153	23	and	and	CCONJ
concept-2079	153	24	the	the	DET
concept-2079	153	25	y	y	NOUN
concept-2079	153	26	-	-	PUNCT
concept-2079	153	27	coordinate	coordinate	NOUN
concept-2079	153	28	represents	represent	VERB
concept-2079	153	29	the	the	DET
concept-2079	153	30	imaginary	imaginary	ADJ
concept-2079	153	31	component	component	NOUN
concept-2079	153	32	.	.	PUNCT
concept-2079	154	1	the	the	DET
concept-2079	154	2	mandelbrot	mandelbrot	PROPN
concept-2079	154	3	set	set	VERB
concept-2079	154	4	is	be	AUX
concept-2079	154	5	created	create	VERB
concept-2079	154	6	by	by	ADP
concept-2079	154	7	the	the	DET
concept-2079	154	8	rule	rule	NOUN
concept-2079	154	9	:	:	PUNCT
concept-2079	154	10	𝑧	𝑧	X
concept-2079	154	11	!	!	PUNCT
concept-2079	154	12	!	!	PUNCT
concept-2079	154	13	!	!	PUNCT
concept-2079	154	14	 	 	SPACE
concept-2079	155	1	→	→	PUNCT
concept-2079	155	2	𝑧	𝑧	NOUN
concept-2079	155	3	!	!	PUNCT
concept-2079	155	4	!	!	PUNCT
concept-2079	156	1	+	+	PUNCT
concept-2079	156	2	𝑐	𝑐	X
concept-2079	156	3	,	,	PUNCT
concept-2079	156	4	where	where	SCONJ
concept-2079	156	5	𝑧	𝑧	X
concept-2079	156	6	!	!	PROPN
concept-2079	156	7	is	be	AUX
concept-2079	156	8	a	a	DET
concept-2079	156	9	complex	complex	ADJ
concept-2079	156	10	number	number	NOUN
concept-2079	156	11	,	,	PUNCT
concept-2079	156	12	c	c	PROPN
concept-2079	156	13	is	be	AUX
concept-2079	156	14	a	a	DET
concept-2079	156	15	complex	complex	ADJ
concept-2079	156	16	number	number	NOUN
concept-2079	156	17	and	and	CCONJ
concept-2079	156	18	𝑧	𝑧	NOUN
concept-2079	156	19	!	!	PUNCT
concept-2079	156	20	!	!	PUNCT
concept-2079	156	21	!	!	PUNCT
concept-2079	157	1	represents	represent	VERB
concept-2079	157	2	the	the	DET
concept-2079	157	3	iterated	iterated	ADJ
concept-2079	157	4	complex	complex	ADJ
concept-2079	157	5	number	number	NOUN
concept-2079	157	6	.	.	PUNCT
concept-2079	158	1	in	in	ADP
concept-2079	158	2	order	order	NOUN
concept-2079	158	3	to	to	PART
concept-2079	158	4	use	use	VERB
concept-2079	158	5	this	this	DET
concept-2079	158	6	formula	formula	NOUN
concept-2079	158	7	,	,	PUNCT
concept-2079	158	8	you	you	PRON
concept-2079	158	9	take	take	VERB
concept-2079	158	10	𝑧	𝑧	ADV
concept-2079	158	11	!	!	NOUN
concept-2079	158	12	,	,	PUNCT
concept-2079	158	13	  	  	SPACE
concept-2079	158	14	square	square	VERB
concept-2079	158	15	the	the	DET
concept-2079	158	16	number	number	NOUN
concept-2079	158	17	and	and	CCONJ
concept-2079	158	18	add	add	VERB
concept-2079	158	19	c	c	NOUN
concept-2079	158	20	to	to	ADP
concept-2079	158	21	it	it	PRON
concept-2079	158	22	.	.	PUNCT
concept-2079	159	1	this	this	PRON
concept-2079	159	2	creates	create	VERB
concept-2079	159	3	a	a	DET
concept-2079	159	4	new	new	ADJ
concept-2079	159	5	complex	complex	ADJ
concept-2079	159	6	number	number	NOUN
concept-2079	159	7	,	,	PUNCT
concept-2079	159	8	𝑧	𝑧	PROPN
concept-2079	159	9	!	!	PUNCT
concept-2079	159	10	.	.	PUNCT
concept-2079	160	1	you	you	PRON
concept-2079	160	2	then	then	ADV
concept-2079	160	3	iterate	iterate	VERB
concept-2079	160	4	the	the	DET
concept-2079	160	5	process	process	NOUN
concept-2079	160	6	n	n	CCONJ
concept-2079	160	7	-	-	PUNCT
concept-2079	160	8	number	number	NOUN
concept-2079	160	9	of	of	ADP
concept-2079	160	10	times	time	NOUN
concept-2079	160	11	.	.	PUNCT
concept-2079	161	1	adding	add	VERB
concept-2079	161	2	the	the	DET
concept-2079	161	3	complex	complex	ADJ
concept-2079	161	4	number	number	NOUN
concept-2079	161	5	,	,	PUNCT
concept-2079	161	6	c	c	NOUN
concept-2079	161	7	,	,	PUNCT
concept-2079	161	8	to	to	ADP
concept-2079	161	9	your	your	PRON
concept-2079	161	10	original	original	ADJ
concept-2079	161	11	complex	complex	ADJ
concept-2079	161	12	number	number	NOUN
concept-2079	161	13	,	,	PUNCT
concept-2079	161	14	𝑧	𝑧	VERB
concept-2079	161	15	!	!	PROPN
concept-2079	161	16	,	,	PUNCT
concept-2079	161	17	allows	allow	VERB
concept-2079	161	18	us	we	PRON
concept-2079	161	19	to	to	PART
concept-2079	161	20	create	create	VERB
concept-2079	161	21	different	different	ADJ
concept-2079	161	22	fractal	fractal	ADJ
concept-2079	161	23	sets	set	NOUN
concept-2079	161	24	.	.	PUNCT
concept-2079	162	1	as	as	SCONJ
concept-2079	162	2	noted	note	VERB
concept-2079	162	3	above	above	ADV
concept-2079	162	4	,	,	PUNCT
concept-2079	162	5	each	each	DET
concept-2079	162	6	complex	complex	ADJ
concept-2079	162	7	number	number	NOUN
concept-2079	162	8	can	can	AUX
concept-2079	162	9	be	be	AUX
concept-2079	162	10	plotted	plot	VERB
concept-2079	162	11	as	as	ADP
concept-2079	162	12	a	a	DET
concept-2079	162	13	point	point	NOUN
concept-2079	162	14	so	so	SCONJ
concept-2079	162	15	this	this	DET
concept-2079	162	16	deterministic	deterministic	ADJ
concept-2079	162	17	rule	rule	NOUN
concept-2079	162	18	generates	generate	VERB
concept-2079	162	19	many	many	ADJ
concept-2079	162	20	points	point	NOUN
concept-2079	162	21	in	in	ADP
concept-2079	162	22	the	the	DET
concept-2079	162	23	plane	plane	NOUN
concept-2079	162	24	after	after	ADP
concept-2079	162	25	a	a	DET
concept-2079	162	26	few	few	ADJ
concept-2079	162	27	iterations	iteration	NOUN
concept-2079	162	28	.	.	PUNCT
concept-2079	163	1	if	if	SCONJ
concept-2079	163	2	you	you	PRON
concept-2079	163	3	iterate	iterate	VERB
concept-2079	163	4	this	this	DET
concept-2079	163	5	process	process	NOUN
concept-2079	163	6	,	,	PUNCT
concept-2079	163	7	you	you	PRON
concept-2079	163	8	will	will	AUX
concept-2079	163	9	find	find	VERB
concept-2079	163	10	that	that	SCONJ
concept-2079	163	11	the	the	DET
concept-2079	163	12	new	new	ADJ
concept-2079	163	13	points	point	NOUN
concept-2079	163	14	either	either	CCONJ
concept-2079	163	15	diverge	diverge	VERB
concept-2079	163	16	to	to	PART
concept-2079	163	17	infinity	infinity	VERB
concept-2079	163	18	or	or	CCONJ
concept-2079	163	19	remain	remain	VERB
concept-2079	163	20	bounded	bounded	ADJ
concept-2079	163	21	for	for	ADP
concept-2079	163	22	all	all	DET
concept-2079	163	23	time	time	NOUN
concept-2079	163	24	.	.	PUNCT
concept-2079	164	1	the	the	DET
concept-2079	164	2	julia	julia	PROPN
concept-2079	164	3	set	set	PROPN
concept-2079	164	4	is	be	AUX
concept-2079	164	5	actually	actually	ADV
concept-2079	164	6	the	the	DET
concept-2079	164	7	boundary	boundary	NOUN
concept-2079	164	8	between	between	ADP
concept-2079	164	9	the	the	DET
concept-2079	164	10	elements	element	NOUN
concept-2079	164	11	in	in	ADP
concept-2079	164	12	the	the	DET
concept-2079	164	13	orbit	orbit	NOUN
concept-2079	164	14	that	that	PRON
concept-2079	164	15	remain	remain	VERB
concept-2079	164	16	bounded	bounded	ADJ
concept-2079	164	17	and	and	CCONJ
concept-2079	164	18	those	those	PRON
concept-2079	164	19	that	that	PRON
concept-2079	164	20	diverge	diverge	VERB
concept-2079	164	21	to	to	PART
concept-2079	164	22	infinity	infinity	VERB
concept-2079	164	23	.	.	PUNCT
concept-2079	165	1	the	the	DET
concept-2079	165	2	julia	julia	PROPN
concept-2079	165	3	set	set	PROPN
concept-2079	165	4	can	can	AUX
concept-2079	165	5	be	be	AUX
concept-2079	165	6	created	create	VERB
concept-2079	165	7	by	by	ADP
concept-2079	165	8	iterating	iterate	VERB
concept-2079	165	9	points	point	NOUN
concept-2079	165	10	using	use	VERB
concept-2079	165	11	the	the	DET
concept-2079	165	12	same	same	ADJ
concept-2079	165	13	rule	rule	NOUN
concept-2079	165	14	as	as	SCONJ
concept-2079	165	15	the	the	DET
concept-2079	165	16	mandelbrot	mandelbrot	NOUN
concept-2079	165	17	set	set	VERB
concept-2079	165	18	:	:	PUNCT
concept-2079	165	19	 	 	SPACE
concept-2079	165	20	𝑧	𝑧	VERB
concept-2079	165	21	!	!	PUNCT
concept-2079	165	22	!	!	PUNCT
concept-2079	165	23	!	!	PUNCT
concept-2079	165	24	 	 	SPACE
concept-2079	166	1	=	=	PUNCT
concept-2079	166	2	𝑧	𝑧	VERB
concept-2079	166	3	!	!	PUNCT
concept-2079	166	4	!	!	PUNCT
concept-2079	167	1	+	+	CCONJ
concept-2079	167	2	𝑐.	𝑐.	VERB
concept-2079	167	3	the	the	DET
concept-2079	167	4	julia	julia	PROPN
concept-2079	167	5	set	set	PROPN
concept-2079	167	6	is	be	AUX
concept-2079	167	7	the	the	DET
concept-2079	167	8	set	set	NOUN
concept-2079	167	9	of	of	ADP
concept-2079	167	10	starting	start	VERB
concept-2079	167	11	values	value	NOUN
concept-2079	167	12	that	that	PRON
concept-2079	167	13	remain	remain	VERB
concept-2079	167	14	bounded	bounded	ADJ
concept-2079	167	15	under	under	ADP
concept-2079	167	16	iteration	iteration	NOUN
concept-2079	167	17	for	for	ADP
concept-2079	167	18	a	a	DET
concept-2079	167	19	fixed	fix	VERB
concept-2079	167	20	value	value	NOUN
concept-2079	167	21	of	of	ADP
concept-2079	167	22	c	c	NOUN
concept-2079	167	23	;	;	PUNCT
concept-2079	167	24	the	the	DET
concept-2079	167	25	mandelbrot	mandelbrot	NOUN
concept-2079	167	26	set	set	VERB
concept-2079	167	27	is	be	AUX
concept-2079	167	28	the	the	DET
concept-2079	167	29	set	set	NOUN
concept-2079	167	30	of	of	ADP
concept-2079	167	31	values	value	NOUN
concept-2079	167	32	of	of	ADP
concept-2079	167	33	c	c	PROPN
concept-2079	167	34	for	for	ADP
concept-2079	167	35	which	which	PRON
concept-2079	167	36	the	the	DET
concept-2079	167	37	iteration	iteration	NOUN
concept-2079	167	38	remains	remain	VERB
concept-2079	167	39	bounded	bound	VERB
concept-2079	167	40	when	when	SCONJ
concept-2079	167	41	starting	start	VERB
concept-2079	167	42	at	at	ADP
concept-2079	167	43	0	0	PROPN
concept-2079	167	44	(	(	PUNCT
concept-2079	167	45	crilly	crilly	ADV
concept-2079	167	46	,	,	PUNCT
concept-2079	167	47	earnshaw	earnshaw	PROPN
concept-2079	167	48	,	,	PUNCT
concept-2079	167	49	jones	jones	PROPN
concept-2079	167	50	,	,	PUNCT
concept-2079	167	51	22	22	NUM
concept-2079	167	52	-	-	SYM
concept-2079	167	53	23	23	NUM
concept-2079	167	54	)	)	PUNCT
concept-2079	167	55	.	.	PUNCT
concept-2079	168	1	computer	computer	NOUN
concept-2079	168	2	models	model	NOUN
concept-2079	168	3	gave	give	VERB
concept-2079	168	4	mandelbrot	mandelbrot	NOUN
concept-2079	168	5	,	,	PUNCT
concept-2079	168	6	and	and	CCONJ
concept-2079	168	7	later	later	ADJ
concept-2079	168	8	mathematicians	mathematician	NOUN
concept-2079	168	9	,	,	PUNCT
concept-2079	168	10	the	the	DET
concept-2079	168	11	ability	ability	NOUN
concept-2079	168	12	to	to	PART
concept-2079	168	13	create	create	VERB
concept-2079	168	14	rich	rich	ADJ
concept-2079	168	15	visual	visual	ADJ
concept-2079	168	16	representations	representation	NOUN
concept-2079	168	17	of	of	ADP
concept-2079	168	18	both	both	DET
concept-2079	168	19	sets	set	NOUN
concept-2079	168	20	.	.	PUNCT
concept-2079	169	1	first	first	ADV
concept-2079	169	2	,	,	PUNCT
concept-2079	169	3	we	we	PRON
concept-2079	169	4	will	will	AUX
concept-2079	169	5	discuss	discuss	VERB
concept-2079	169	6	how	how	SCONJ
concept-2079	169	7	the	the	DET
concept-2079	169	8	computer	computer	NOUN
concept-2079	169	9	can	can	AUX
concept-2079	169	10	be	be	AUX
concept-2079	169	11	used	use	VERB
concept-2079	169	12	to	to	PART
concept-2079	169	13	generate	generate	VERB
concept-2079	169	14	julia	julia	PROPN
concept-2079	169	15	sets	set	NOUN
concept-2079	169	16	and	and	CCONJ
concept-2079	169	17	then	then	ADV
concept-2079	169	18	mandelbrot	mandelbrot	PROPN
concept-2079	169	19	sets	set	VERB
concept-2079	169	20	.	.	PUNCT
concept-2079	170	1	the	the	DET
concept-2079	170	2	computer	computer	NOUN
concept-2079	170	3	recognizes	recognize	VERB
concept-2079	170	4	each	each	DET
concept-2079	170	5	iteration	iteration	NOUN
concept-2079	170	6	of	of	ADP
concept-2079	170	7	the	the	DET
concept-2079	170	8	rule	rule	NOUN
concept-2079	170	9	,	,	PUNCT
concept-2079	170	10	𝑧	𝑧	PROPN
concept-2079	170	11	!	!	PUNCT
concept-2079	170	12	!	!	PUNCT
concept-2079	170	13	!	!	PUNCT
concept-2079	170	14	 	 	SPACE
concept-2079	171	1	→	→	PUNCT
concept-2079	171	2	𝑧	𝑧	NOUN
concept-2079	171	3	!	!	PUNCT
concept-2079	171	4	!	!	PUNCT
concept-2079	172	1	+	+	PUNCT
concept-2079	173	1	𝑐	𝑐	X
concept-2079	173	2	,	,	PUNCT
concept-2079	173	3	as	as	ADP
concept-2079	173	4	a	a	DET
concept-2079	173	5	point	point	NOUN
concept-2079	173	6	or	or	CCONJ
concept-2079	173	7	pixel	pixel	NOUN
concept-2079	173	8	and	and	CCONJ
concept-2079	173	9	uses	use	VERB
concept-2079	173	10	the	the	DET
concept-2079	173	11	distance	distance	NOUN
concept-2079	173	12	formula	formula	NOUN
concept-2079	173	13	to	to	PART
concept-2079	173	14	determine	determine	VERB
concept-2079	173	15	if	if	SCONJ
concept-2079	173	16	the	the	DET
concept-2079	173	17	distance	distance	NOUN
concept-2079	173	18	between	between	ADP
concept-2079	173	19	the	the	DET
concept-2079	173	20	point	point	NOUN
concept-2079	173	21	and	and	CCONJ
concept-2079	173	22	the	the	DET
concept-2079	173	23	origin	origin	NOUN
concept-2079	173	24	is	be	AUX
concept-2079	173	25	greater	great	ADJ
concept-2079	173	26	than	than	ADP
concept-2079	173	27	or	or	CCONJ
concept-2079	173	28	less	less	ADJ
concept-2079	173	29	than	than	ADP
concept-2079	173	30	some	some	DET
concept-2079	173	31	pre	pre	ADJ
concept-2079	173	32	-	-	ADJ
concept-2079	173	33	specified	specified	ADJ
concept-2079	173	34	number	number	NOUN
concept-2079	173	35	.	.	PUNCT
concept-2079	174	1	if	if	SCONJ
concept-2079	174	2	the	the	DET
concept-2079	174	3	distance	distance	NOUN
concept-2079	174	4	is	be	AUX
concept-2079	174	5	larger	large	ADJ
concept-2079	174	6	than	than	ADP
concept-2079	174	7	the	the	DET
concept-2079	174	8	pre	pre	ADJ
concept-2079	174	9	-	-	ADJ
concept-2079	174	10	specified	specified	ADJ
concept-2079	174	11	number	number	NOUN
concept-2079	174	12	,	,	PUNCT
concept-2079	174	13	the	the	DET
concept-2079	174	14	point	point	NOUN
concept-2079	174	15	is	be	AUX
concept-2079	174	16	outside	outside	ADP
concept-2079	174	17	the	the	DET
concept-2079	174	18	julia	julia	PROPN
concept-2079	174	19	set	set	VERB
concept-2079	174	20	for	for	ADP
concept-2079	174	21	that	that	DET
concept-2079	174	22	c	c	PROPN
concept-2079	174	23	concept	concept	NOUN
concept-2079	174	24	,	,	PUNCT
concept-2079	174	25	vol	vol	NOUN
concept-2079	174	26	.	.	PUNCT
concept-2079	175	1	xxxix	xxxix	PROPN
concept-2079	175	2	(	(	PUNCT
concept-2079	175	3	2016	2016	NUM
concept-2079	175	4	)	)	PUNCT
concept-2079	175	5	8	8	NUM
concept-2079	175	6	value	value	NOUN
concept-2079	175	7	.	.	PUNCT
concept-2079	176	1	similarly	similarly	ADV
concept-2079	176	2	,	,	PUNCT
concept-2079	176	3	if	if	SCONJ
concept-2079	176	4	the	the	DET
concept-2079	176	5	distance	distance	NOUN
concept-2079	176	6	is	be	AUX
concept-2079	176	7	smaller	small	ADJ
concept-2079	176	8	than	than	ADP
concept-2079	176	9	the	the	DET
concept-2079	176	10	pre	pre	ADJ
concept-2079	176	11	-	-	ADJ
concept-2079	176	12	specified	specified	ADJ
concept-2079	176	13	number	number	NOUN
concept-2079	176	14	,	,	PUNCT
concept-2079	176	15	the	the	DET
concept-2079	176	16	point	point	NOUN
concept-2079	176	17	is	be	AUX
concept-2079	176	18	inside	inside	ADP
concept-2079	176	19	the	the	DET
concept-2079	176	20	julia	julia	PROPN
concept-2079	176	21	set	set	VERB
concept-2079	176	22	for	for	ADP
concept-2079	176	23	that	that	DET
concept-2079	176	24	c	c	NOUN
concept-2079	176	25	value	value	NOUN
concept-2079	176	26	.	.	PUNCT
concept-2079	177	1	computers	computer	NOUN
concept-2079	177	2	have	have	AUX
concept-2079	177	3	typically	typically	ADV
concept-2079	177	4	been	be	AUX
concept-2079	177	5	programmed	program	VERB
concept-2079	177	6	to	to	PART
concept-2079	177	7	produce	produce	VERB
concept-2079	177	8	different	different	ADJ
concept-2079	177	9	colors	color	NOUN
concept-2079	177	10	depending	depend	VERB
concept-2079	177	11	on	on	ADP
concept-2079	177	12	the	the	DET
concept-2079	177	13	distances	distance	NOUN
concept-2079	177	14	the	the	DET
concept-2079	177	15	iterated	iterated	ADJ
concept-2079	177	16	points	point	NOUN
concept-2079	177	17	are	be	AUX
concept-2079	177	18	from	from	ADP
concept-2079	177	19	the	the	DET
concept-2079	177	20	origin	origin	NOUN
concept-2079	177	21	.	.	PUNCT
concept-2079	178	1	other	other	ADJ
concept-2079	178	2	color	color	NOUN
concept-2079	178	3	effects	effect	NOUN
concept-2079	178	4	,	,	PUNCT
concept-2079	178	5	also	also	ADV
concept-2079	178	6	known	know	VERB
concept-2079	178	7	as	as	ADP
concept-2079	178	8	escape	escape	NOUN
concept-2079	178	9	value	value	NOUN
concept-2079	178	10	,	,	PUNCT
concept-2079	178	11	or	or	CCONJ
concept-2079	178	12	how	how	SCONJ
concept-2079	178	13	many	many	ADJ
concept-2079	178	14	iterations	iteration	NOUN
concept-2079	178	15	it	it	PRON
concept-2079	178	16	took	take	VERB
concept-2079	178	17	to	to	PART
concept-2079	178	18	end	end	VERB
concept-2079	178	19	up	up	ADP
concept-2079	178	20	outside	outside	ADP
concept-2079	178	21	a	a	DET
concept-2079	178	22	given	give	VERB
concept-2079	178	23	distance	distance	NOUN
concept-2079	178	24	from	from	ADP
concept-2079	178	25	the	the	DET
concept-2079	178	26	origin	origin	NOUN
concept-2079	178	27	,	,	PUNCT
concept-2079	178	28	can	can	AUX
concept-2079	178	29	produce	produce	VERB
concept-2079	178	30	even	even	ADV
concept-2079	178	31	more	more	ADJ
concept-2079	178	32	visual	visual	ADJ
concept-2079	178	33	effects	effect	NOUN
concept-2079	178	34	.	.	PUNCT
concept-2079	179	1	the	the	DET
concept-2079	179	2	c	c	PROPN
concept-2079	179	3	value	value	NOUN
concept-2079	179	4	used	use	VERB
concept-2079	179	5	for	for	ADP
concept-2079	179	6	calculations	calculation	NOUN
concept-2079	179	7	of	of	ADP
concept-2079	179	8	the	the	DET
concept-2079	179	9	julia	julia	PROPN
concept-2079	179	10	set	set	PROPN
concept-2079	179	11	,	,	PUNCT
concept-2079	179	12	will	will	AUX
concept-2079	179	13	give	give	VERB
concept-2079	179	14	your	your	PRON
concept-2079	179	15	visual	visual	ADJ
concept-2079	179	16	representation	representation	NOUN
concept-2079	179	17	various	various	ADJ
concept-2079	179	18	forms	form	NOUN
concept-2079	179	19	.	.	PUNCT
concept-2079	180	1	this	this	PRON
concept-2079	180	2	gives	give	VERB
concept-2079	180	3	us	we	PRON
concept-2079	180	4	some	some	DET
concept-2079	180	5	qualitative	qualitative	ADJ
concept-2079	180	6	support	support	NOUN
concept-2079	180	7	that	that	SCONJ
concept-2079	180	8	this	this	DET
concept-2079	180	9	mathematical	mathematical	ADJ
concept-2079	180	10	structure	structure	NOUN
concept-2079	180	11	has	have	AUX
concept-2079	180	12	chaotic	chaotic	ADJ
concept-2079	180	13	properties	property	NOUN
concept-2079	180	14	.	.	PUNCT
concept-2079	181	1	similarly	similarly	ADV
concept-2079	181	2	,	,	PUNCT
concept-2079	181	3	the	the	DET
concept-2079	181	4	c	c	PROPN
concept-2079	181	5	value	value	NOUN
concept-2079	181	6	also	also	ADV
concept-2079	181	7	determines	determine	VERB
concept-2079	181	8	if	if	SCONJ
concept-2079	181	9	the	the	DET
concept-2079	181	10	julia	julia	PROPN
concept-2079	181	11	set	set	PROPN
concept-2079	181	12	is	be	AUX
concept-2079	181	13	connected	connect	VERB
concept-2079	181	14	or	or	CCONJ
concept-2079	181	15	not	not	PART
concept-2079	181	16	.	.	PUNCT
concept-2079	182	1	a	a	DET
concept-2079	182	2	julia	julia	PROPN
concept-2079	182	3	set	set	NOUN
concept-2079	182	4	is	be	AUX
concept-2079	182	5	connected	connect	VERB
concept-2079	182	6	if	if	SCONJ
concept-2079	182	7	you	you	PRON
concept-2079	182	8	can	can	AUX
concept-2079	182	9	draw	draw	VERB
concept-2079	182	10	a	a	DET
concept-2079	182	11	line	line	NOUN
concept-2079	182	12	(	(	PUNCT
concept-2079	182	13	or	or	CCONJ
concept-2079	182	14	curve	curve	NOUN
concept-2079	182	15	)	)	PUNCT
concept-2079	182	16	between	between	ADP
concept-2079	182	17	any	any	DET
concept-2079	182	18	two	two	NUM
concept-2079	182	19	points	point	NOUN
concept-2079	182	20	in	in	ADP
concept-2079	182	21	the	the	DET
concept-2079	182	22	set	set	NOUN
concept-2079	182	23	with	with	ADP
concept-2079	182	24	the	the	DET
concept-2079	182	25	line	line	NOUN
concept-2079	182	26	remaining	remain	VERB
concept-2079	182	27	contained	contain	VERB
concept-2079	182	28	within	within	ADP
concept-2079	182	29	the	the	DET
concept-2079	182	30	set	set	NOUN
concept-2079	182	31	.	.	PUNCT
concept-2079	183	1	a	a	DET
concept-2079	183	2	julia	julia	PROPN
concept-2079	183	3	set	set	NOUN
concept-2079	183	4	is	be	AUX
concept-2079	183	5	considered	consider	VERB
concept-2079	183	6	disconnected	disconnected	ADJ
concept-2079	183	7	when	when	SCONJ
concept-2079	183	8	you	you	PRON
concept-2079	183	9	can	can	AUX
concept-2079	183	10	not	not	PART
concept-2079	183	11	do	do	VERB
concept-2079	183	12	this	this	PRON
concept-2079	183	13	;	;	PUNCT
concept-2079	183	14	visually	visually	ADV
concept-2079	183	15	it	it	PRON
concept-2079	183	16	appears	appear	VERB
concept-2079	183	17	to	to	PART
concept-2079	183	18	form	form	VERB
concept-2079	183	19	a	a	DET
concept-2079	183	20	“	"	PUNCT
concept-2079	183	21	dust	dust	NOUN
concept-2079	183	22	”	"	PUNCT
concept-2079	183	23	when	when	SCONJ
concept-2079	183	24	the	the	DET
concept-2079	183	25	julia	julia	PROPN
concept-2079	183	26	set	set	PROPN
concept-2079	183	27	is	be	AUX
concept-2079	183	28	disconnected	disconnect	VERB
concept-2079	183	29	.	.	PUNCT
concept-2079	184	1	the	the	DET
concept-2079	184	2	mandelbrot	mandelbrot	PROPN
concept-2079	184	3	set	set	VERB
concept-2079	184	4	is	be	AUX
concept-2079	184	5	formed	form	VERB
concept-2079	184	6	when	when	SCONJ
concept-2079	184	7	the	the	DET
concept-2079	184	8	julia	julia	PROPN
concept-2079	184	9	set	set	PROPN
concept-2079	184	10	is	be	AUX
concept-2079	184	11	connected	connect	VERB
concept-2079	184	12	(	(	PUNCT
concept-2079	184	13	crilly	crilly	ADV
concept-2079	184	14	,	,	PUNCT
concept-2079	184	15	earnshaw	earnshaw	PROPN
concept-2079	184	16	,	,	PUNCT
concept-2079	184	17	jones	jones	PROPN
concept-2079	184	18	,	,	PUNCT
concept-2079	184	19	22	22	NUM
concept-2079	184	20	-	-	SYM
concept-2079	184	21	23	23	NUM
concept-2079	184	22	)	)	PUNCT
concept-2079	184	23	.	.	PUNCT
concept-2079	185	1	figure	figure	NOUN
concept-2079	185	2	4	4	NUM
concept-2079	185	3	–	–	PUNCT
concept-2079	185	4	mandelbrot	mandelbrot	PROPN
concept-2079	185	5	set	set	VERB
concept-2079	185	6	in	in	ADP
concept-2079	185	7	1984	1984	NUM
concept-2079	185	8	,	,	PUNCT
concept-2079	185	9	mathematician	mathematician	NOUN
concept-2079	185	10	mitsuhiro	mitsuhiro	VERB
concept-2079	185	11	shishikura	shishikura	ADV
concept-2079	185	12	of	of	ADP
concept-2079	185	13	the	the	DET
concept-2079	185	14	tokyo	tokyo	PROPN
concept-2079	185	15	institute	institute	NOUN
concept-2079	185	16	of	of	ADP
concept-2079	185	17	technology	technology	PROPN
concept-2079	185	18	and	and	CCONJ
concept-2079	185	19	the	the	DET
concept-2079	185	20	state	state	NOUN
concept-2079	185	21	university	university	PROPN
concept-2079	185	22	of	of	ADP
concept-2079	185	23	new	new	PROPN
concept-2079	185	24	york	york	PROPN
concept-2079	185	25	at	at	ADP
concept-2079	185	26	stony	stony	PROPN
concept-2079	185	27	brook	brook	PROPN
concept-2079	185	28	,	,	PUNCT
concept-2079	185	29	proved	prove	VERB
concept-2079	185	30	that	that	SCONJ
concept-2079	185	31	the	the	DET
concept-2079	185	32	boundary	boundary	NOUN
concept-2079	185	33	of	of	ADP
concept-2079	185	34	the	the	DET
concept-2079	185	35	mandelbrot	mandelbrot	NOUN
concept-2079	185	36	set	set	NOUN
concept-2079	185	37	has	have	AUX
concept-2079	185	38	dimension	dimension	VERB
concept-2079	185	39	two	two	NUM
concept-2079	185	40	using	use	VERB
concept-2079	185	41	a	a	DET
concept-2079	185	42	proof	proof	NOUN
concept-2079	185	43	involving	involve	VERB
concept-2079	185	44	the	the	DET
concept-2079	185	45	concept	concept	NOUN
concept-2079	185	46	of	of	ADP
concept-2079	185	47	bifurcation	bifurcation	NOUN
concept-2079	185	48	of	of	ADP
concept-2079	185	49	parabolic	parabolic	ADJ
concept-2079	185	50	periodic	periodic	ADJ
concept-2079	185	51	points	point	NOUN
concept-2079	185	52	(	(	PUNCT
concept-2079	185	53	mandelbrot	mandelbrot	NOUN
concept-2079	185	54	,	,	PUNCT
concept-2079	185	55	111	111	NUM
concept-2079	185	56	)	)	PUNCT
concept-2079	185	57	.	.	PUNCT
concept-2079	186	1	a	a	DET
concept-2079	186	2	bifurcation	bifurcation	NOUN
concept-2079	186	3	occurs	occur	VERB
concept-2079	186	4	at	at	ADP
concept-2079	186	5	a	a	DET
concept-2079	186	6	parameter	parameter	NOUN
concept-2079	186	7	value	value	NOUN
concept-2079	186	8	at	at	ADP
concept-2079	186	9	which	which	PRON
concept-2079	186	10	some	some	DET
concept-2079	186	11	variation	variation	NOUN
concept-2079	186	12	induces	induce	VERB
concept-2079	186	13	dramatic	dramatic	ADJ
concept-2079	186	14	changes	change	NOUN
concept-2079	186	15	within	within	ADP
concept-2079	186	16	the	the	DET
concept-2079	186	17	dynamical	dynamical	ADJ
concept-2079	186	18	system	system	NOUN
concept-2079	186	19	.	.	PUNCT
concept-2079	187	1	an	an	DET
concept-2079	187	2	important	important	ADJ
concept-2079	187	3	idea	idea	NOUN
concept-2079	187	4	used	use	VERB
concept-2079	187	5	in	in	ADP
concept-2079	187	6	the	the	DET
concept-2079	187	7	proof	proof	NOUN
concept-2079	187	8	was	be	AUX
concept-2079	187	9	that	that	SCONJ
concept-2079	187	10	forming	form	VERB
concept-2079	187	11	a	a	DET
concept-2079	187	12	union	union	NOUN
concept-2079	187	13	of	of	ADP
concept-2079	187	14	all	all	DET
concept-2079	187	15	the	the	DET
concept-2079	187	16	connected	connected	ADJ
concept-2079	187	17	julia	julia	PROPN
concept-2079	187	18	sets	set	NOUN
concept-2079	187	19	could	could	AUX
concept-2079	187	20	create	create	VERB
concept-2079	187	21	mandelbrot	mandelbrot	NOUN
concept-2079	187	22	sets	set	NOUN
concept-2079	187	23	.	.	PUNCT
concept-2079	188	1	each	each	DET
concept-2079	188	2	connected	connect	VERB
concept-2079	188	3	julia	julia	PROPN
concept-2079	188	4	set	set	PROPN
concept-2079	188	5	represents	represent	VERB
concept-2079	188	6	a	a	DET
concept-2079	188	7	point	point	NOUN
concept-2079	188	8	in	in	ADP
concept-2079	188	9	the	the	DET
concept-2079	188	10	mandelbrot	mandelbrot	NOUN
concept-2079	188	11	set	set	VERB
concept-2079	188	12	.	.	PUNCT
concept-2079	189	1	shishikura	shishikura	ADV
concept-2079	189	2	shows	show	VERB
concept-2079	189	3	the	the	DET
concept-2079	189	4	dimension	dimension	NOUN
concept-2079	189	5	of	of	ADP
concept-2079	189	6	the	the	DET
concept-2079	189	7	mandelbrot	mandelbrot	NOUN
concept-2079	189	8	set	set	VERB
concept-2079	189	9	is	be	AUX
concept-2079	189	10	related	relate	VERB
concept-2079	189	11	to	to	ADP
concept-2079	189	12	the	the	DET
concept-2079	189	13	dimension	dimension	NOUN
concept-2079	189	14	of	of	ADP
concept-2079	189	15	the	the	DET
concept-2079	189	16	julia	julia	PROPN
concept-2079	189	17	sets	set	VERB
concept-2079	189	18	that	that	DET
concept-2079	189	19	concept	concept	NOUN
concept-2079	189	20	,	,	PUNCT
concept-2079	189	21	vol	vol	NOUN
concept-2079	189	22	.	.	PUNCT
concept-2079	190	1	xxxix	xxxix	PROPN
concept-2079	190	2	(	(	PUNCT
concept-2079	190	3	2016	2016	NUM
concept-2079	190	4	)	)	PUNCT
concept-2079	190	5	9	9	NUM
concept-2079	190	6	make	make	VERB
concept-2079	190	7	it	it	PRON
concept-2079	190	8	up	up	ADP
concept-2079	190	9	.	.	PUNCT
concept-2079	191	1	as	as	ADP
concept-2079	191	2	the	the	DET
concept-2079	191	3	dimension	dimension	NOUN
concept-2079	191	4	of	of	ADP
concept-2079	191	5	the	the	DET
concept-2079	191	6	julia	julia	PROPN
concept-2079	191	7	sets	set	VERB
concept-2079	191	8	increases	increase	NOUN
concept-2079	191	9	,	,	PUNCT
concept-2079	191	10	so	so	ADV
concept-2079	191	11	does	do	AUX
concept-2079	191	12	the	the	DET
concept-2079	191	13	dimension	dimension	NOUN
concept-2079	191	14	of	of	ADP
concept-2079	191	15	the	the	DET
concept-2079	191	16	mandelbrot	mandelbrot	NOUN
concept-2079	191	17	set	set	NOUN
concept-2079	191	18	,	,	PUNCT
concept-2079	191	19	eventually	eventually	ADV
concept-2079	191	20	reaching	reach	VERB
concept-2079	191	21	dimension	dimension	NOUN
concept-2079	191	22	two	two	NUM
concept-2079	191	23	(	(	PUNCT
concept-2079	191	24	brown	brown	ADJ
concept-2079	191	25	,	,	PUNCT
concept-2079	191	26	“	"	PUNCT
concept-2079	191	27	mandelbrot	mandelbrot	PROPN
concept-2079	191	28	set	set	VERB
concept-2079	191	29	is	be	AUX
concept-2079	191	30	as	as	ADV
concept-2079	191	31	complicated	complicated	ADJ
concept-2079	191	32	as	as	SCONJ
concept-2079	191	33	it	it	PRON
concept-2079	191	34	could	could	AUX
concept-2079	191	35	be	be	AUX
concept-2079	191	36	”	"	PUNCT
concept-2079	191	37	)	)	PUNCT
concept-2079	191	38	.	.	PUNCT
concept-2079	192	1	applications	application	NOUN
concept-2079	192	2	of	of	ADP
concept-2079	192	3	fractals	fractal	NOUN
concept-2079	192	4	our	our	PRON
concept-2079	192	5	exploration	exploration	NOUN
concept-2079	192	6	of	of	ADP
concept-2079	192	7	the	the	DET
concept-2079	192	8	mathematics	mathematic	NOUN
concept-2079	192	9	behind	behind	ADP
concept-2079	192	10	fractals	fractal	NOUN
concept-2079	192	11	has	have	AUX
concept-2079	192	12	helped	help	VERB
concept-2079	192	13	prepare	prepare	VERB
concept-2079	192	14	the	the	DET
concept-2079	192	15	way	way	NOUN
concept-2079	192	16	for	for	ADP
concept-2079	192	17	the	the	DET
concept-2079	192	18	second	second	ADJ
concept-2079	192	19	half	half	NOUN
concept-2079	192	20	of	of	ADP
concept-2079	192	21	our	our	PRON
concept-2079	192	22	journey	journey	NOUN
concept-2079	192	23	:	:	PUNCT
concept-2079	192	24	applications	application	NOUN
concept-2079	192	25	of	of	ADP
concept-2079	192	26	fractals	fractal	NOUN
concept-2079	192	27	to	to	ADP
concept-2079	192	28	the	the	DET
concept-2079	192	29	real	real	ADJ
concept-2079	192	30	world	world	NOUN
concept-2079	192	31	.	.	PUNCT
concept-2079	193	1	you	you	PRON
concept-2079	193	2	may	may	AUX
concept-2079	193	3	be	be	AUX
concept-2079	193	4	wondering	wonder	VERB
concept-2079	193	5	how	how	SCONJ
concept-2079	193	6	this	this	DET
concept-2079	193	7	knowledge	knowledge	NOUN
concept-2079	193	8	of	of	ADP
concept-2079	193	9	fractals	fractal	NOUN
concept-2079	193	10	could	could	AUX
concept-2079	193	11	be	be	AUX
concept-2079	193	12	useful	useful	ADJ
concept-2079	193	13	to	to	PART
concept-2079	193	14	stem	stem	VERB
concept-2079	193	15	professionals	professional	NOUN
concept-2079	193	16	?	?	PUNCT
concept-2079	194	1	fractals	fractal	NOUN
concept-2079	194	2	have	have	AUX
concept-2079	194	3	been	be	AUX
concept-2079	194	4	useful	useful	ADJ
concept-2079	194	5	in	in	ADP
concept-2079	194	6	helping	help	VERB
concept-2079	194	7	quantify	quantify	VERB
concept-2079	194	8	and	and	CCONJ
concept-2079	194	9	explain	explain	VERB
concept-2079	194	10	brownian	brownian	ADJ
concept-2079	194	11	motion	motion	NOUN
concept-2079	194	12	,	,	PUNCT
concept-2079	194	13	applications	application	NOUN
concept-2079	194	14	in	in	ADP
concept-2079	194	15	biology	biology	NOUN
concept-2079	194	16	,	,	PUNCT
concept-2079	194	17	the	the	DET
concept-2079	194	18	stock	stock	NOUN
concept-2079	194	19	market	market	NOUN
concept-2079	194	20	,	,	PUNCT
concept-2079	194	21	and	and	CCONJ
concept-2079	194	22	used	use	VERB
concept-2079	194	23	in	in	ADP
concept-2079	194	24	various	various	ADJ
concept-2079	194	25	technologies	technology	NOUN
concept-2079	194	26	.	.	PUNCT
concept-2079	195	1	we	we	PRON
concept-2079	195	2	will	will	AUX
concept-2079	195	3	also	also	ADV
concept-2079	195	4	explore	explore	VERB
concept-2079	195	5	how	how	SCONJ
concept-2079	195	6	secondary	secondary	ADJ
concept-2079	195	7	mathematics	mathematics	NOUN
concept-2079	195	8	teachers	teacher	NOUN
concept-2079	195	9	may	may	AUX
concept-2079	195	10	introduce	introduce	VERB
concept-2079	195	11	students	student	NOUN
concept-2079	195	12	to	to	ADP
concept-2079	195	13	fractals	fractal	NOUN
concept-2079	195	14	,	,	PUNCT
concept-2079	195	15	possibly	possibly	ADV
concept-2079	195	16	piquing	pique	VERB
concept-2079	195	17	their	their	PRON
concept-2079	195	18	overall	overall	ADJ
concept-2079	195	19	interest	interest	NOUN
concept-2079	195	20	in	in	ADP
concept-2079	195	21	mathematics	mathematic	NOUN
concept-2079	195	22	,	,	PUNCT
concept-2079	195	23	and	and	CCONJ
concept-2079	195	24	challenging	challenge	VERB
concept-2079	195	25	some	some	DET
concept-2079	195	26	negative	negative	ADJ
concept-2079	195	27	cultural	cultural	ADJ
concept-2079	195	28	stereotypes	stereotype	NOUN
concept-2079	195	29	.	.	PUNCT
concept-2079	196	1	brownian	brownian	ADJ
concept-2079	196	2	motion	motion	NOUN
concept-2079	196	3	in	in	ADP
concept-2079	196	4	1827	1827	NUM
concept-2079	196	5	,	,	PUNCT
concept-2079	196	6	robert	robert	PROPN
concept-2079	196	7	brown	brown	PROPN
concept-2079	196	8	discovered	discover	VERB
concept-2079	196	9	that	that	SCONJ
concept-2079	196	10	particles	particle	NOUN
concept-2079	196	11	of	of	ADP
concept-2079	196	12	a	a	DET
concept-2079	196	13	substance	substance	NOUN
concept-2079	196	14	,	,	PUNCT
concept-2079	196	15	suspended	suspend	VERB
concept-2079	196	16	in	in	ADP
concept-2079	196	17	liquid	liquid	NOUN
concept-2079	196	18	,	,	PUNCT
concept-2079	196	19	would	would	AUX
concept-2079	196	20	continue	continue	VERB
concept-2079	196	21	to	to	PART
concept-2079	196	22	move	move	VERB
concept-2079	196	23	.	.	PUNCT
concept-2079	197	1	this	this	DET
concept-2079	197	2	phenomenon	phenomenon	NOUN
concept-2079	197	3	would	would	AUX
concept-2079	197	4	later	later	ADV
concept-2079	197	5	be	be	AUX
concept-2079	197	6	known	know	VERB
concept-2079	197	7	and	and	CCONJ
concept-2079	197	8	studied	study	VERB
concept-2079	197	9	as	as	ADP
concept-2079	197	10	brownian	brownian	ADJ
concept-2079	197	11	motion	motion	NOUN
concept-2079	197	12	(	(	PUNCT
concept-2079	197	13	gordon	gordon	PROPN
concept-2079	197	14	,	,	PUNCT
concept-2079	197	15	clarke	clarke	PROPN
concept-2079	197	16	,	,	PUNCT
concept-2079	197	17	mandelbrot	mandelbrot	PROPN
concept-2079	197	18	,	,	PUNCT
concept-2079	197	19	et	et	PROPN
concept-2079	197	20	al	al	PROPN
concept-2079	197	21	.	.	PROPN
concept-2079	197	22	,	,	PUNCT
concept-2079	197	23	11	11	NUM
concept-2079	197	24	)	)	PUNCT
concept-2079	197	25	.	.	PUNCT
concept-2079	198	1	in	in	ADP
concept-2079	198	2	1908	1908	NUM
concept-2079	198	3	,	,	PUNCT
concept-2079	198	4	einstein	einstein	PROPN
concept-2079	198	5	took	take	VERB
concept-2079	198	6	his	his	PRON
concept-2079	198	7	work	work	NOUN
concept-2079	198	8	further	far	ADV
concept-2079	198	9	when	when	SCONJ
concept-2079	198	10	he	he	PRON
concept-2079	198	11	was	be	AUX
concept-2079	198	12	studying	study	VERB
concept-2079	198	13	how	how	SCONJ
concept-2079	198	14	particles	particle	NOUN
concept-2079	198	15	of	of	ADP
concept-2079	198	16	a	a	DET
concept-2079	198	17	substance	substance	NOUN
concept-2079	198	18	behave	behave	VERB
concept-2079	198	19	when	when	SCONJ
concept-2079	198	20	exposed	expose	VERB
concept-2079	198	21	to	to	ADP
concept-2079	198	22	heat	heat	VERB
concept-2079	198	23	and	and	CCONJ
concept-2079	198	24	suspended	suspend	VERB
concept-2079	198	25	in	in	ADP
concept-2079	198	26	a	a	DET
concept-2079	198	27	liquid	liquid	NOUN
concept-2079	198	28	.	.	PUNCT
concept-2079	199	1	he	he	PRON
concept-2079	199	2	was	be	AUX
concept-2079	199	3	able	able	ADJ
concept-2079	199	4	to	to	PART
concept-2079	199	5	use	use	VERB
concept-2079	199	6	the	the	DET
concept-2079	199	7	mathematics	mathematic	NOUN
concept-2079	199	8	of	of	ADP
concept-2079	199	9	physics	physics	PROPN
concept-2079	199	10	to	to	PART
concept-2079	199	11	quantify	quantify	VERB
concept-2079	199	12	what	what	PRON
concept-2079	199	13	he	he	PRON
concept-2079	199	14	observed	observe	VERB
concept-2079	199	15	(	(	PUNCT
concept-2079	199	16	kinetic	kinetic	NOUN
concept-2079	199	17	-	-	PUNCT
concept-2079	199	18	molecular	molecular	ADJ
concept-2079	199	19	theory	theory	NOUN
concept-2079	199	20	of	of	ADP
concept-2079	199	21	heat	heat	NOUN
concept-2079	199	22	)	)	PUNCT
concept-2079	199	23	in	in	ADP
concept-2079	199	24	an	an	DET
concept-2079	199	25	experiment	experiment	NOUN
concept-2079	199	26	.	.	PUNCT
concept-2079	200	1	ultimately	ultimately	ADV
concept-2079	200	2	the	the	DET
concept-2079	200	3	findings	finding	NOUN
concept-2079	200	4	of	of	ADP
concept-2079	200	5	his	his	PRON
concept-2079	200	6	experiment	experiment	NOUN
concept-2079	200	7	lead	lead	VERB
concept-2079	200	8	him	he	PRON
concept-2079	200	9	to	to	PART
concept-2079	200	10	believe	believe	VERB
concept-2079	200	11	that	that	SCONJ
concept-2079	200	12	the	the	DET
concept-2079	200	13	behavior	behavior	NOUN
concept-2079	200	14	of	of	ADP
concept-2079	200	15	the	the	DET
concept-2079	200	16	particles	particle	NOUN
concept-2079	200	17	could	could	AUX
concept-2079	200	18	be	be	AUX
concept-2079	200	19	predicted	predict	VERB
concept-2079	200	20	to	to	ADP
concept-2079	200	21	some	some	DET
concept-2079	200	22	degree	degree	NOUN
concept-2079	200	23	(	(	PUNCT
concept-2079	200	24	lee	lee	PROPN
concept-2079	200	25	and	and	CCONJ
concept-2079	200	26	hoon	hoon	PROPN
concept-2079	200	27	,	,	PUNCT
concept-2079	200	28	“	"	PUNCT
concept-2079	200	29	brownian	brownian	ADJ
concept-2079	200	30	motion	motion	NOUN
concept-2079	200	31	”	"	PUNCT
concept-2079	200	32	)	)	PUNCT
concept-2079	200	33	.	.	PUNCT
concept-2079	201	1	figure	figure	NOUN
concept-2079	201	2	5	5	NUM
concept-2079	201	3	–	–	PUNCT
concept-2079	201	4	brownian	brownian	ADJ
concept-2079	201	5	motion	motion	NOUN
concept-2079	201	6	concept	concept	NOUN
concept-2079	201	7	,	,	PUNCT
concept-2079	201	8	vol	vol	NOUN
concept-2079	201	9	.	.	PUNCT
concept-2079	202	1	xxxix	xxxix	PROPN
concept-2079	202	2	(	(	PUNCT
concept-2079	202	3	2016	2016	NUM
concept-2079	202	4	)	)	PUNCT
concept-2079	202	5	10	10	NUM
concept-2079	202	6	brownian	brownian	ADJ
concept-2079	202	7	motion	motion	NOUN
concept-2079	202	8	of	of	ADP
concept-2079	202	9	a	a	DET
concept-2079	202	10	particle	particle	NOUN
concept-2079	202	11	,	,	PUNCT
concept-2079	202	12	under	under	ADP
concept-2079	202	13	a	a	DET
concept-2079	202	14	microscope	microscope	NOUN
concept-2079	202	15	,	,	PUNCT
concept-2079	202	16	is	be	AUX
concept-2079	202	17	said	say	VERB
concept-2079	202	18	to	to	PART
concept-2079	202	19	have	have	VERB
concept-2079	202	20	a	a	DET
concept-2079	202	21	fractional	fractional	ADJ
concept-2079	202	22	dimension	dimension	NOUN
concept-2079	202	23	of	of	ADP
concept-2079	202	24	two	two	NUM
concept-2079	202	25	.	.	PUNCT
concept-2079	203	1	this	this	PRON
concept-2079	203	2	is	be	AUX
concept-2079	203	3	because	because	SCONJ
concept-2079	203	4	if	if	SCONJ
concept-2079	203	5	you	you	PRON
concept-2079	203	6	try	try	VERB
concept-2079	203	7	to	to	PART
concept-2079	203	8	predict	predict	VERB
concept-2079	203	9	the	the	DET
concept-2079	203	10	movement	movement	NOUN
concept-2079	203	11	of	of	ADP
concept-2079	203	12	a	a	DET
concept-2079	203	13	particular	particular	ADJ
concept-2079	203	14	particle	particle	NOUN
concept-2079	203	15	from	from	ADP
concept-2079	203	16	one	one	NUM
concept-2079	203	17	location	location	NOUN
concept-2079	203	18	to	to	ADP
concept-2079	203	19	some	some	DET
concept-2079	203	20	other	other	ADJ
concept-2079	203	21	location	location	NOUN
concept-2079	203	22	under	under	ADP
concept-2079	203	23	the	the	DET
concept-2079	203	24	microscope	microscope	NOUN
concept-2079	203	25	,	,	PUNCT
concept-2079	203	26	you	you	PRON
concept-2079	203	27	will	will	AUX
concept-2079	203	28	find	find	VERB
concept-2079	203	29	it	it	PRON
concept-2079	203	30	will	will	AUX
concept-2079	203	31	most	most	ADV
concept-2079	203	32	likely	likely	ADV
concept-2079	203	33	have	have	VERB
concept-2079	203	34	to	to	PART
concept-2079	203	35	take	take	VERB
concept-2079	203	36	a	a	DET
concept-2079	203	37	path	path	NOUN
concept-2079	203	38	that	that	PRON
concept-2079	203	39	fills	fill	VERB
concept-2079	203	40	the	the	DET
concept-2079	203	41	entire	entire	ADJ
concept-2079	203	42	space	space	NOUN
concept-2079	203	43	before	before	ADP
concept-2079	203	44	reaching	reach	VERB
concept-2079	203	45	the	the	DET
concept-2079	203	46	desired	desire	VERB
concept-2079	203	47	“	"	PUNCT
concept-2079	203	48	stopping	stop	VERB
concept-2079	203	49	”	"	PUNCT
concept-2079	203	50	point	point	NOUN
concept-2079	203	51	.	.	PUNCT
concept-2079	204	1	fractals	fractal	NOUN
concept-2079	204	2	are	be	AUX
concept-2079	204	3	involved	involve	VERB
concept-2079	204	4	in	in	ADP
concept-2079	204	5	fractional	fractional	ADJ
concept-2079	204	6	brownian	brownian	ADJ
concept-2079	204	7	motion	motion	NOUN
concept-2079	204	8	models	model	NOUN
concept-2079	204	9	;	;	PUNCT
concept-2079	204	10	utilizing	utilize	VERB
concept-2079	204	11	a	a	DET
concept-2079	204	12	random	random	ADJ
concept-2079	204	13	walk	walk	NOUN
concept-2079	204	14	(	(	PUNCT
concept-2079	204	15	a	a	DET
concept-2079	204	16	mathematical	mathematical	ADJ
concept-2079	204	17	representation	representation	NOUN
concept-2079	204	18	of	of	ADP
concept-2079	204	19	the	the	DET
concept-2079	204	20	random	random	ADJ
concept-2079	204	21	behavior	behavior	NOUN
concept-2079	204	22	that	that	PRON
concept-2079	204	23	occurs	occur	VERB
concept-2079	204	24	)	)	PUNCT
concept-2079	204	25	and	and	CCONJ
concept-2079	204	26	a	a	DET
concept-2079	204	27	random	random	ADJ
concept-2079	204	28	iteration	iteration	NOUN
concept-2079	204	29	algorithm	algorithm	NOUN
concept-2079	204	30	(	(	PUNCT
concept-2079	204	31	a	a	DET
concept-2079	204	32	deterministic	deterministic	ADJ
concept-2079	204	33	rule	rule	NOUN
concept-2079	204	34	that	that	PRON
concept-2079	204	35	produces	produce	VERB
concept-2079	204	36	a	a	DET
concept-2079	204	37	“	"	PUNCT
concept-2079	204	38	random	random	ADJ
concept-2079	204	39	”	"	PUNCT
concept-2079	204	40	pattern	pattern	NOUN
concept-2079	204	41	)	)	PUNCT
concept-2079	204	42	,	,	PUNCT
concept-2079	204	43	(	(	PUNCT
concept-2079	204	44	lee	lee	PROPN
concept-2079	204	45	and	and	CCONJ
concept-2079	204	46	hoon	hoon	PROPN
concept-2079	204	47	,	,	PUNCT
concept-2079	204	48	“	"	PUNCT
concept-2079	204	49	brownian	brownian	ADJ
concept-2079	204	50	motion	motion	NOUN
concept-2079	204	51	”	"	PUNCT
concept-2079	204	52	)	)	PUNCT
concept-2079	204	53	.	.	PUNCT
concept-2079	205	1	fractal	fractal	ADJ
concept-2079	205	2	geometry	geometry	NOUN
concept-2079	205	3	and	and	CCONJ
concept-2079	205	4	brownian	brownian	ADJ
concept-2079	205	5	motion	motion	NOUN
concept-2079	205	6	have	have	AUX
concept-2079	205	7	helped	help	VERB
concept-2079	205	8	medical	medical	ADJ
concept-2079	205	9	imaging	imaging	NOUN
concept-2079	205	10	technologists	technologist	NOUN
concept-2079	205	11	make	make	VERB
concept-2079	205	12	more	more	ADV
concept-2079	205	13	accurate	accurate	ADJ
concept-2079	205	14	diagnostic	diagnostic	ADJ
concept-2079	205	15	test	test	NOUN
concept-2079	205	16	readings	reading	NOUN
concept-2079	205	17	through	through	ADP
concept-2079	205	18	two	two	NUM
concept-2079	205	19	primary	primary	ADJ
concept-2079	205	20	avenues	avenue	NOUN
concept-2079	205	21	:	:	PUNCT
concept-2079	205	22	classification	classification	NOUN
concept-2079	205	23	and	and	CCONJ
concept-2079	205	24	edge	edge	NOUN
concept-2079	205	25	enhancement	enhancement	NOUN
concept-2079	205	26	for	for	ADP
concept-2079	205	27	ultrasonic	ultrasonic	ADJ
concept-2079	205	28	liver	liver	NOUN
concept-2079	205	29	images	image	NOUN
concept-2079	205	30	.	.	PUNCT
concept-2079	206	1	classification	classification	NOUN
concept-2079	206	2	is	be	AUX
concept-2079	206	3	when	when	SCONJ
concept-2079	206	4	you	you	PRON
concept-2079	206	5	use	use	VERB
concept-2079	206	6	brownian	brownian	ADJ
concept-2079	206	7	fractional	fractional	ADJ
concept-2079	206	8	motion	motion	NOUN
concept-2079	206	9	to	to	PART
concept-2079	206	10	produce	produce	VERB
concept-2079	206	11	a	a	DET
concept-2079	206	12	motion	motion	NOUN
concept-2079	206	13	vector	vector	NOUN
concept-2079	206	14	that	that	PRON
concept-2079	206	15	will	will	AUX
concept-2079	206	16	accurately	accurately	ADV
concept-2079	206	17	portray	portray	VERB
concept-2079	206	18	the	the	DET
concept-2079	206	19	surface	surface	NOUN
concept-2079	206	20	of	of	ADP
concept-2079	206	21	the	the	DET
concept-2079	206	22	liver	liver	NOUN
concept-2079	206	23	.	.	PUNCT
concept-2079	207	1	edge	edge	NOUN
concept-2079	207	2	enhancement	enhancement	NOUN
concept-2079	207	3	is	be	AUX
concept-2079	207	4	when	when	SCONJ
concept-2079	207	5	you	you	PRON
concept-2079	207	6	take	take	VERB
concept-2079	207	7	each	each	DET
concept-2079	207	8	individual	individual	ADJ
concept-2079	207	9	pixel	pixel	NOUN
concept-2079	207	10	from	from	ADP
concept-2079	207	11	the	the	DET
concept-2079	207	12	current	current	ADJ
concept-2079	207	13	image	image	NOUN
concept-2079	207	14	of	of	ADP
concept-2079	207	15	the	the	DET
concept-2079	207	16	liver	liver	NOUN
concept-2079	207	17	and	and	CCONJ
concept-2079	207	18	calculate	calculate	VERB
concept-2079	207	19	its	its	PRON
concept-2079	207	20	fractional	fractional	ADJ
concept-2079	207	21	dimension	dimension	NOUN
concept-2079	207	22	in	in	ADP
concept-2079	207	23	comparison	comparison	NOUN
concept-2079	207	24	to	to	ADP
concept-2079	207	25	the	the	DET
concept-2079	207	26	whole	whole	ADJ
concept-2079	207	27	image	image	NOUN
concept-2079	207	28	.	.	PUNCT
concept-2079	208	1	doing	do	VERB
concept-2079	208	2	these	these	DET
concept-2079	208	3	types	type	NOUN
concept-2079	208	4	of	of	ADP
concept-2079	208	5	calculations	calculation	NOUN
concept-2079	208	6	helps	help	VERB
concept-2079	208	7	the	the	DET
concept-2079	208	8	medical	medical	ADJ
concept-2079	208	9	imaging	imaging	NOUN
concept-2079	208	10	technologists	technologist	NOUN
concept-2079	208	11	obtain	obtain	VERB
concept-2079	208	12	a	a	DET
concept-2079	208	13	better	well	ADJ
concept-2079	208	14	picture	picture	NOUN
concept-2079	208	15	of	of	ADP
concept-2079	208	16	what	what	PRON
concept-2079	208	17	is	be	AUX
concept-2079	208	18	happening	happen	VERB
concept-2079	208	19	to	to	ADP
concept-2079	208	20	the	the	DET
concept-2079	208	21	liver	liver	NOUN
concept-2079	208	22	without	without	ADP
concept-2079	208	23	an	an	DET
concept-2079	208	24	actual	actual	ADJ
concept-2079	208	25	physical	physical	ADJ
concept-2079	208	26	procedure	procedure	NOUN
concept-2079	208	27	—	—	PUNCT
concept-2079	208	28	reducing	reduce	VERB
concept-2079	208	29	unnecessary	unnecessary	ADJ
concept-2079	208	30	risk	risk	NOUN
concept-2079	208	31	and	and	CCONJ
concept-2079	208	32	time	time	NOUN
concept-2079	208	33	.	.	PUNCT
concept-2079	209	1	medical	medical	ADJ
concept-2079	209	2	researchers	researcher	NOUN
concept-2079	209	3	basu	basu	PROPN
concept-2079	209	4	,	,	PUNCT
concept-2079	209	5	barba	barba	PROPN
concept-2079	209	6	and	and	CCONJ
concept-2079	209	7	chan	chan	PROPN
concept-2079	209	8	(	(	PUNCT
concept-2079	209	9	“	"	PUNCT
concept-2079	209	10	texture	texture	ADJ
concept-2079	209	11	analysis	analysis	NOUN
concept-2079	209	12	in	in	ADP
concept-2079	209	13	cytology	cytology	NOUN
concept-2079	209	14	using	use	VERB
concept-2079	209	15	fractals	fractal	NOUN
concept-2079	209	16	”	"	PUNCT
concept-2079	209	17	)	)	PUNCT
concept-2079	209	18	show	show	VERB
concept-2079	209	19	how	how	SCONJ
concept-2079	209	20	fractional	fractional	ADJ
concept-2079	209	21	dimension	dimension	NOUN
concept-2079	209	22	can	can	AUX
concept-2079	209	23	be	be	AUX
concept-2079	209	24	used	use	VERB
concept-2079	209	25	to	to	PART
concept-2079	209	26	try	try	VERB
concept-2079	209	27	to	to	PART
concept-2079	209	28	distinguish	distinguish	VERB
concept-2079	209	29	between	between	ADP
concept-2079	209	30	healthy	healthy	ADJ
concept-2079	209	31	and	and	CCONJ
concept-2079	209	32	malignant	malignant	ADJ
concept-2079	209	33	cells	cell	NOUN
concept-2079	209	34	after	after	ADP
concept-2079	209	35	noticing	notice	VERB
concept-2079	209	36	that	that	SCONJ
concept-2079	209	37	malignant	malignant	ADJ
concept-2079	209	38	cells	cell	NOUN
concept-2079	209	39	consistently	consistently	ADV
concept-2079	209	40	have	have	VERB
concept-2079	209	41	a	a	DET
concept-2079	209	42	different	different	ADJ
concept-2079	209	43	fractional	fractional	ADJ
concept-2079	209	44	dimension	dimension	NOUN
concept-2079	209	45	compared	compare	VERB
concept-2079	209	46	to	to	ADP
concept-2079	209	47	the	the	DET
concept-2079	209	48	healthy	healthy	ADJ
concept-2079	209	49	cells	cell	NOUN
concept-2079	209	50	,	,	PUNCT
concept-2079	209	51	independent	independent	ADJ
concept-2079	209	52	of	of	ADP
concept-2079	209	53	the	the	DET
concept-2079	209	54	type	type	NOUN
concept-2079	209	55	of	of	ADP
concept-2079	209	56	cell	cell	NOUN
concept-2079	209	57	:	:	PUNCT
concept-2079	209	58	breast	breast	NOUN
concept-2079	209	59	,	,	PUNCT
concept-2079	209	60	bronchial	bronchial	ADJ
concept-2079	209	61	,	,	PUNCT
concept-2079	209	62	ovarian	ovarian	ADJ
concept-2079	209	63	,	,	PUNCT
concept-2079	209	64	and	and	CCONJ
concept-2079	209	65	uterine	uterine	NOUN
concept-2079	209	66	.	.	PUNCT
concept-2079	210	1	similarly	similarly	ADV
concept-2079	210	2	,	,	PUNCT
concept-2079	210	3	smith	smith	PROPN
concept-2079	210	4	,	,	PUNCT
concept-2079	210	5	lange	lange	NOUN
concept-2079	210	6	,	,	PUNCT
concept-2079	210	7	and	and	CCONJ
concept-2079	210	8	marks	mark	NOUN
concept-2079	210	9	(	(	PUNCT
concept-2079	210	10	“	"	PUNCT
concept-2079	210	11	fractal	fractal	ADJ
concept-2079	210	12	methods	method	NOUN
concept-2079	210	13	and	and	CCONJ
concept-2079	210	14	results	result	NOUN
concept-2079	210	15	in	in	ADP
concept-2079	210	16	cellular	cellular	ADJ
concept-2079	210	17	morphology	morphology	NOUN
concept-2079	210	18	...	...	PUNCT
concept-2079	210	19	”	"	PUNCT
concept-2079	210	20	)	)	PUNCT
concept-2079	210	21	give	give	VERB
concept-2079	210	22	us	we	PRON
concept-2079	210	23	insight	insight	NOUN
concept-2079	210	24	into	into	ADP
concept-2079	210	25	the	the	DET
concept-2079	210	26	methods	method	NOUN
concept-2079	210	27	in	in	ADP
concept-2079	210	28	which	which	PRON
concept-2079	210	29	biologists	biologist	NOUN
concept-2079	210	30	are	be	AUX
concept-2079	210	31	using	use	VERB
concept-2079	210	32	mathematical	mathematical	ADJ
concept-2079	210	33	techniques	technique	NOUN
concept-2079	210	34	to	to	PART
concept-2079	210	35	better	well	ADV
concept-2079	210	36	understand	understand	VERB
concept-2079	210	37	cell	cell	NOUN
concept-2079	210	38	morphology	morphology	NOUN
concept-2079	210	39	,	,	PUNCT
concept-2079	210	40	relating	relate	VERB
concept-2079	210	41	to	to	ADP
concept-2079	210	42	the	the	DET
concept-2079	210	43	overall	overall	ADJ
concept-2079	210	44	physical	physical	ADJ
concept-2079	210	45	characteristics	characteristic	NOUN
concept-2079	210	46	of	of	ADP
concept-2079	210	47	cells	cell	NOUN
concept-2079	210	48	.	.	PUNCT
concept-2079	211	1	there	there	PRON
concept-2079	211	2	exist	exist	VERB
concept-2079	211	3	two	two	NUM
concept-2079	211	4	major	major	ADJ
concept-2079	211	5	methods	method	NOUN
concept-2079	211	6	of	of	ADP
concept-2079	211	7	calculating	calculate	VERB
concept-2079	211	8	fractional	fractional	ADJ
concept-2079	211	9	dimension	dimension	NOUN
concept-2079	211	10	of	of	ADP
concept-2079	211	11	these	these	DET
concept-2079	211	12	cells	cell	NOUN
concept-2079	211	13	:	:	PUNCT
concept-2079	211	14	using	use	VERB
concept-2079	211	15	length	length	NOUN
concept-2079	211	16	(	(	PUNCT
concept-2079	211	17	previously	previously	ADV
concept-2079	211	18	discussed	discuss	VERB
concept-2079	211	19	with	with	ADP
concept-2079	211	20	the	the	DET
concept-2079	211	21	rulers	ruler	NOUN
concept-2079	211	22	example	example	NOUN
concept-2079	211	23	in	in	ADP
concept-2079	211	24	the	the	DET
concept-2079	211	25	introduction	introduction	NOUN
concept-2079	211	26	)	)	PUNCT
concept-2079	211	27	or	or	CCONJ
concept-2079	211	28	the	the	DET
concept-2079	211	29	mass	mass	NOUN
concept-2079	211	30	of	of	ADP
concept-2079	211	31	an	an	DET
concept-2079	211	32	object	object	NOUN
concept-2079	211	33	.	.	PUNCT
concept-2079	212	1	the	the	DET
concept-2079	212	2	mass	mass	NOUN
concept-2079	212	3	method	method	NOUN
concept-2079	212	4	involves	involve	VERB
concept-2079	212	5	“	"	PUNCT
concept-2079	212	6	counting	counting	NOUN
concept-2079	212	7	of	of	ADP
concept-2079	212	8	border	border	NOUN
concept-2079	212	9	pixels	pixel	NOUN
concept-2079	212	10	in	in	ADP
concept-2079	212	11	a	a	DET
concept-2079	212	12	sampling	sample	VERB
concept-2079	212	13	region	region	NOUN
concept-2079	212	14	,	,	PUNCT
concept-2079	212	15	such	such	ADJ
concept-2079	212	16	as	as	ADP
concept-2079	212	17	disc	disc	NOUN
concept-2079	212	18	diameters	diameter	NOUN
concept-2079	212	19	,	,	PUNCT
concept-2079	212	20	as	as	ADP
concept-2079	212	21	a	a	DET
concept-2079	212	22	function	function	NOUN
concept-2079	212	23	of	of	ADP
concept-2079	212	24	the	the	DET
concept-2079	212	25	sizes	size	NOUN
concept-2079	212	26	of	of	ADP
concept-2079	212	27	the	the	DET
concept-2079	212	28	sample	sample	NOUN
concept-2079	212	29	regions	region	NOUN
concept-2079	212	30	”	"	PUNCT
concept-2079	212	31	when	when	SCONJ
concept-2079	212	32	given	give	VERB
concept-2079	212	33	a	a	DET
concept-2079	212	34	digital	digital	ADJ
concept-2079	212	35	representation	representation	NOUN
concept-2079	212	36	of	of	ADP
concept-2079	212	37	the	the	DET
concept-2079	212	38	image	image	NOUN
concept-2079	212	39	(	(	PUNCT
concept-2079	212	40	smith	smith	PROPN
concept-2079	212	41	,	,	PUNCT
concept-2079	212	42	lange	lange	NOUN
concept-2079	212	43	,	,	PUNCT
concept-2079	212	44	and	and	CCONJ
concept-2079	212	45	marks	mark	NOUN
concept-2079	212	46	,	,	PUNCT
concept-2079	212	47	“	"	PUNCT
concept-2079	212	48	fractal	fractal	ADJ
concept-2079	212	49	methods	method	NOUN
concept-2079	212	50	...	...	PUNCT
concept-2079	212	51	”	"	PUNCT
concept-2079	212	52	)	)	PUNCT
concept-2079	212	53	.	.	PUNCT
concept-2079	213	1	the	the	DET
concept-2079	213	2	computer	computer	NOUN
concept-2079	213	3	is	be	AUX
concept-2079	213	4	then	then	ADV
concept-2079	213	5	programmed	program	VERB
concept-2079	213	6	to	to	PART
concept-2079	213	7	count	count	VERB
concept-2079	213	8	the	the	DET
concept-2079	213	9	number	number	NOUN
concept-2079	213	10	of	of	ADP
concept-2079	213	11	pixels	pixel	NOUN
concept-2079	213	12	contained	contain	VERB
concept-2079	213	13	in	in	ADP
concept-2079	213	14	these	these	DET
concept-2079	213	15	round	round	ADJ
concept-2079	213	16	or	or	CCONJ
concept-2079	213	17	box	box	NOUN
concept-2079	213	18	regions	region	NOUN
concept-2079	213	19	placed	place	VERB
concept-2079	213	20	randomly	randomly	ADV
concept-2079	213	21	all	all	ADV
concept-2079	213	22	around	around	ADP
concept-2079	213	23	the	the	DET
concept-2079	213	24	border	border	NOUN
concept-2079	213	25	of	of	ADP
concept-2079	213	26	the	the	DET
concept-2079	213	27	image	image	NOUN
concept-2079	213	28	.	.	PUNCT
concept-2079	214	1	typically	typically	ADV
concept-2079	214	2	,	,	PUNCT
concept-2079	214	3	the	the	DET
concept-2079	214	4	scientists	scientist	NOUN
concept-2079	214	5	will	will	AUX
concept-2079	214	6	plot	plot	VERB
concept-2079	214	7	a	a	DET
concept-2079	214	8	diagram	diagram	NOUN
concept-2079	214	9	comparing	compare	VERB
concept-2079	214	10	the	the	DET
concept-2079	214	11	log	log	NOUN
concept-2079	214	12	of	of	ADP
concept-2079	214	13	the	the	DET
concept-2079	214	14	pixels	pixel	NOUN
concept-2079	214	15	within	within	ADP
concept-2079	214	16	each	each	DET
concept-2079	214	17	box	box	NOUN
concept-2079	214	18	vs.	vs.	ADP
concept-2079	214	19	the	the	DET
concept-2079	214	20	log	log	NOUN
concept-2079	214	21	the	the	DET
concept-2079	214	22	measuring	measure	VERB
concept-2079	214	23	unit	unit	NOUN
concept-2079	214	24	length	length	NOUN
concept-2079	214	25	.	.	PUNCT
concept-2079	215	1	the	the	DET
concept-2079	215	2	power	power	NOUN
concept-2079	215	3	law	law	NOUN
concept-2079	215	4	describing	describe	VERB
concept-2079	215	5	this	this	DET
concept-2079	215	6	behavior	behavior	NOUN
concept-2079	215	7	can	can	AUX
concept-2079	215	8	be	be	AUX
concept-2079	215	9	represented	represent	VERB
concept-2079	215	10	mathematically	mathematically	ADV
concept-2079	215	11	as	as	ADP
concept-2079	215	12	:	:	PUNCT
concept-2079	215	13	µ(r	µ(r	NUM
concept-2079	215	14	)	)	PUNCT
concept-2079	215	15	=	=	VERB
concept-2079	215	16	a𝑟𝑑	a𝑟𝑑	PROPN
concept-2079	215	17	,	,	PUNCT
concept-2079	215	18	where	where	SCONJ
concept-2079	215	19	µ(r	µ(r	NOUN
concept-2079	215	20	)	)	PUNCT
concept-2079	215	21	is	be	AUX
concept-2079	215	22	the	the	DET
concept-2079	215	23	number	number	NOUN
concept-2079	215	24	of	of	ADP
concept-2079	215	25	pixels	pixel	NOUN
concept-2079	215	26	(	(	PUNCT
concept-2079	215	27	considered	consider	VERB
concept-2079	215	28	mass	mass	NOUN
concept-2079	215	29	)	)	PUNCT
concept-2079	215	30	,	,	PUNCT
concept-2079	215	31	r	r	NOUN
concept-2079	215	32	is	be	AUX
concept-2079	215	33	the	the	DET
concept-2079	215	34	length	length	NOUN
concept-2079	215	35	of	of	ADP
concept-2079	215	36	the	the	DET
concept-2079	215	37	edge	edge	NOUN
concept-2079	215	38	of	of	ADP
concept-2079	215	39	the	the	DET
concept-2079	215	40	boxes	box	NOUN
concept-2079	215	41	or	or	CCONJ
concept-2079	215	42	circle	circle	NOUN
concept-2079	215	43	diameter	diameter	NOUN
concept-2079	215	44	,	,	PUNCT
concept-2079	215	45	a	a	PRON
concept-2079	215	46	is	be	AUX
concept-2079	215	47	a	a	DET
concept-2079	215	48	pre	pre	ADJ
concept-2079	215	49	-	-	NOUN
concept-2079	215	50	factor	factor	NOUN
concept-2079	215	51	(	(	PUNCT
concept-2079	215	52	a	a	DET
concept-2079	215	53	concept	concept	NOUN
concept-2079	215	54	,	,	PUNCT
concept-2079	215	55	vol	vol	NOUN
concept-2079	215	56	.	.	PUNCT
concept-2079	216	1	xxxix	xxxix	PROPN
concept-2079	216	2	(	(	PUNCT
concept-2079	216	3	2016	2016	NUM
concept-2079	216	4	)	)	PUNCT
concept-2079	216	5	11	11	NUM
concept-2079	216	6	periodic	periodic	ADJ
concept-2079	216	7	function	function	NOUN
concept-2079	216	8	whose	whose	DET
concept-2079	216	9	period	period	NOUN
concept-2079	216	10	is	be	AUX
concept-2079	216	11	independent	independent	ADJ
concept-2079	216	12	of	of	ADP
concept-2079	216	13	the	the	DET
concept-2079	216	14	fractal	fractal	ADJ
concept-2079	216	15	dimension	dimension	NOUN
concept-2079	216	16	)	)	PUNCT
concept-2079	216	17	,	,	PUNCT
concept-2079	216	18	d	d	X
concept-2079	216	19	is	be	AUX
concept-2079	216	20	the	the	DET
concept-2079	216	21	mass	mass	ADJ
concept-2079	216	22	fractional	fractional	ADJ
concept-2079	216	23	dimension	dimension	NOUN
concept-2079	216	24	or	or	CCONJ
concept-2079	216	25	slope	slope	NOUN
concept-2079	216	26	of	of	ADP
concept-2079	216	27	the	the	DET
concept-2079	216	28	plot	plot	NOUN
concept-2079	216	29	of	of	ADP
concept-2079	216	30	log	log	NOUN
concept-2079	216	31	µ(r	µ(r	NUM
concept-2079	216	32	)	)	PUNCT
concept-2079	216	33	vs.	vs.	CCONJ
concept-2079	216	34	log	log	PROPN
concept-2079	216	35	r.	r.	PROPN
concept-2079	216	36	(	(	PUNCT
concept-2079	216	37	smith	smith	PROPN
concept-2079	216	38	,	,	PUNCT
concept-2079	216	39	lange	lange	NOUN
concept-2079	216	40	,	,	PUNCT
concept-2079	216	41	and	and	CCONJ
concept-2079	216	42	marks	mark	NOUN
concept-2079	216	43	,	,	PUNCT
concept-2079	216	44	“	"	PUNCT
concept-2079	216	45	fractal	fractal	ADJ
concept-2079	216	46	methods	method	NOUN
concept-2079	216	47	...	...	PUNCT
concept-2079	216	48	”	"	PUNCT
concept-2079	216	49	)	)	PUNCT
concept-2079	216	50	.	.	PUNCT
concept-2079	217	1	scientists	scientist	NOUN
concept-2079	217	2	must	must	AUX
concept-2079	217	3	also	also	ADV
concept-2079	217	4	account	account	VERB
concept-2079	217	5	for	for	ADP
concept-2079	217	6	lacunarity	lacunarity	NOUN
concept-2079	217	7	when	when	SCONJ
concept-2079	217	8	trying	try	VERB
concept-2079	217	9	to	to	PART
concept-2079	217	10	use	use	VERB
concept-2079	217	11	fractals	fractal	NOUN
concept-2079	217	12	to	to	PART
concept-2079	217	13	measure	measure	VERB
concept-2079	217	14	the	the	DET
concept-2079	217	15	dimensions	dimension	NOUN
concept-2079	217	16	of	of	ADP
concept-2079	217	17	cells	cell	NOUN
concept-2079	217	18	.	.	PUNCT
concept-2079	218	1	lacunarity	lacunarity	NOUN
concept-2079	218	2	is	be	AUX
concept-2079	218	3	a	a	DET
concept-2079	218	4	measure	measure	NOUN
concept-2079	218	5	of	of	ADP
concept-2079	218	6	“	"	PUNCT
concept-2079	218	7	non	non	ADJ
concept-2079	218	8	-	-	NOUN
concept-2079	218	9	uniformity	uniformity	NOUN
concept-2079	218	10	of	of	ADP
concept-2079	218	11	structure	structure	NOUN
concept-2079	218	12	or	or	CCONJ
concept-2079	218	13	the	the	DET
concept-2079	218	14	degree	degree	NOUN
concept-2079	218	15	of	of	ADP
concept-2079	218	16	structural	structural	ADJ
concept-2079	218	17	variance	variance	NOUN
concept-2079	218	18	within	within	ADP
concept-2079	218	19	an	an	DET
concept-2079	218	20	object	object	NOUN
concept-2079	218	21	;	;	PUNCT
concept-2079	218	22	”	"	PUNCT
concept-2079	218	23	a	a	DET
concept-2079	218	24	fractal	fractal	ADJ
concept-2079	218	25	structure	structure	NOUN
concept-2079	218	26	that	that	PRON
concept-2079	218	27	has	have	VERB
concept-2079	218	28	high	high	ADJ
concept-2079	218	29	lacunarity	lacunarity	NOUN
concept-2079	218	30	may	may	AUX
concept-2079	218	31	have	have	VERB
concept-2079	218	32	large	large	ADJ
concept-2079	218	33	gaps	gap	NOUN
concept-2079	218	34	or	or	CCONJ
concept-2079	218	35	holes	hole	NOUN
concept-2079	218	36	in	in	ADP
concept-2079	218	37	its	its	PRON
concept-2079	218	38	design	design	NOUN
concept-2079	218	39	and/or	and/or	CCONJ
concept-2079	218	40	loses	lose	VERB
concept-2079	218	41	selfsimilarity	selfsimilarity	NOUN
concept-2079	218	42	when	when	SCONJ
concept-2079	218	43	rotated	rotate	VERB
concept-2079	218	44	90	90	NUM
concept-2079	218	45	degrees	degree	NOUN
concept-2079	218	46	(	(	PUNCT
concept-2079	218	47	smith	smith	PROPN
concept-2079	218	48	,	,	PUNCT
concept-2079	218	49	lange	lange	NOUN
concept-2079	218	50	,	,	PUNCT
concept-2079	218	51	and	and	CCONJ
concept-2079	218	52	marks	mark	NOUN
concept-2079	218	53	,	,	PUNCT
concept-2079	218	54	“	"	PUNCT
concept-2079	218	55	fractal	fractal	ADJ
concept-2079	218	56	methods	method	NOUN
concept-2079	218	57	...	...	PUNCT
concept-2079	218	58	”	"	PUNCT
concept-2079	218	59	)	)	PUNCT
concept-2079	218	60	.	.	PUNCT
concept-2079	219	1	lacunarity	lacunarity	NOUN
concept-2079	219	2	is	be	AUX
concept-2079	219	3	used	use	VERB
concept-2079	219	4	to	to	PART
concept-2079	219	5	determine	determine	VERB
concept-2079	219	6	the	the	DET
concept-2079	219	7	differences	difference	NOUN
concept-2079	219	8	in	in	ADP
concept-2079	219	9	objects	object	NOUN
concept-2079	219	10	with	with	ADP
concept-2079	219	11	similar	similar	ADJ
concept-2079	219	12	fractional	fractional	ADJ
concept-2079	219	13	dimensions	dimension	NOUN
concept-2079	219	14	(	(	PUNCT
concept-2079	219	15	gould	gould	PROPN
concept-2079	219	16	,	,	PUNCT
concept-2079	219	17	vadakkan	vadakkan	PROPN
concept-2079	219	18	,	,	PUNCT
concept-2079	219	19	poche	poche	PROPN
concept-2079	219	20	,	,	PUNCT
concept-2079	219	21	dickinson	dickinson	PROPN
concept-2079	219	22	,	,	PUNCT
concept-2079	219	23	“	"	PUNCT
concept-2079	219	24	multifractal	multifractal	ADJ
concept-2079	219	25	and	and	CCONJ
concept-2079	219	26	lacunarity	lacunarity	NOUN
concept-2079	219	27	analysis	analysis	NOUN
concept-2079	219	28	of	of	ADP
concept-2079	219	29	microvascular	microvascular	ADJ
concept-2079	219	30	morphology	morphology	NOUN
concept-2079	219	31	and	and	CCONJ
concept-2079	219	32	remodeling	remodeling	NOUN
concept-2079	219	33	”	"	PUNCT
concept-2079	219	34	)	)	PUNCT
concept-2079	219	35	.	.	PUNCT
concept-2079	220	1	we	we	PRON
concept-2079	220	2	calculate	calculate	VERB
concept-2079	220	3	lacunarity	lacunarity	NOUN
concept-2079	220	4	,	,	PUNCT
concept-2079	220	5	or	or	CCONJ
concept-2079	220	6	l	l	NOUN
concept-2079	220	7	,	,	PUNCT
concept-2079	220	8	by	by	ADP
concept-2079	220	9	calculating	calculate	VERB
concept-2079	220	10	the	the	DET
concept-2079	220	11	mean	mean	ADJ
concept-2079	220	12	and	and	CCONJ
concept-2079	220	13	standard	standard	ADJ
concept-2079	220	14	deviation	deviation	NOUN
concept-2079	220	15	of	of	ADP
concept-2079	220	16	either	either	CCONJ
concept-2079	220	17	the	the	DET
concept-2079	220	18	length	length	NOUN
concept-2079	220	19	or	or	CCONJ
concept-2079	220	20	mass	mass	NOUN
concept-2079	220	21	of	of	ADP
concept-2079	220	22	the	the	DET
concept-2079	220	23	desired	desire	VERB
concept-2079	220	24	portion	portion	NOUN
concept-2079	220	25	of	of	ADP
concept-2079	220	26	the	the	DET
concept-2079	220	27	image	image	NOUN
concept-2079	220	28	,	,	PUNCT
concept-2079	220	29	then	then	ADV
concept-2079	220	30	normalizing	normalize	VERB
concept-2079	220	31	those	those	DET
concept-2079	220	32	two	two	NUM
concept-2079	220	33	values	value	NOUN
concept-2079	220	34	by	by	ADP
concept-2079	220	35	dividing	divide	VERB
concept-2079	220	36	the	the	DET
concept-2079	220	37	variance	variance	NOUN
concept-2079	220	38	by	by	ADP
concept-2079	220	39	the	the	DET
concept-2079	220	40	square	square	NOUN
concept-2079	220	41	of	of	ADP
concept-2079	220	42	the	the	DET
concept-2079	220	43	mean	mean	NOUN
concept-2079	220	44	of	of	ADP
concept-2079	220	45	all	all	DET
concept-2079	220	46	box	box	NOUN
concept-2079	220	47	or	or	CCONJ
concept-2079	220	48	disc	disc	NOUN
concept-2079	220	49	regions	region	NOUN
concept-2079	220	50	surveyed	survey	VERB
concept-2079	220	51	in	in	ADP
concept-2079	220	52	the	the	DET
concept-2079	220	53	image	image	NOUN
concept-2079	220	54	(	(	PUNCT
concept-2079	220	55	smith	smith	PROPN
concept-2079	220	56	,	,	PUNCT
concept-2079	220	57	lange	lange	NOUN
concept-2079	220	58	,	,	PUNCT
concept-2079	220	59	and	and	CCONJ
concept-2079	220	60	marks	mark	NOUN
concept-2079	220	61	,	,	PUNCT
concept-2079	220	62	“	"	PUNCT
concept-2079	220	63	fractal	fractal	ADJ
concept-2079	220	64	methods	method	NOUN
concept-2079	220	65	...	...	PUNCT
concept-2079	220	66	”	"	PUNCT
concept-2079	220	67	)	)	PUNCT
concept-2079	220	68	.	.	PUNCT
concept-2079	221	1	a	a	DET
concept-2079	221	2	similar	similar	ADJ
concept-2079	221	3	method	method	NOUN
concept-2079	221	4	to	to	PART
concept-2079	221	5	calculate	calculate	VERB
concept-2079	221	6	l	l	NOUN
concept-2079	221	7	is	be	AUX
concept-2079	221	8	dividing	divide	VERB
concept-2079	221	9	the	the	DET
concept-2079	221	10	standard	standard	ADJ
concept-2079	221	11	deviation	deviation	NOUN
concept-2079	221	12	by	by	ADP
concept-2079	221	13	the	the	DET
concept-2079	221	14	mean	mean	NOUN
concept-2079	221	15	of	of	ADP
concept-2079	221	16	all	all	DET
concept-2079	221	17	boxes	box	NOUN
concept-2079	221	18	or	or	CCONJ
concept-2079	221	19	discs	disc	NOUN
concept-2079	221	20	used	use	VERB
concept-2079	221	21	,	,	PUNCT
concept-2079	221	22	a	a	DET
concept-2079	221	23	statistical	statistical	ADJ
concept-2079	221	24	calculation	calculation	NOUN
concept-2079	221	25	,	,	PUNCT
concept-2079	221	26	also	also	ADV
concept-2079	221	27	known	know	VERB
concept-2079	221	28	as	as	ADP
concept-2079	221	29	the	the	DET
concept-2079	221	30	coefficient	coefficient	NOUN
concept-2079	221	31	of	of	ADP
concept-2079	221	32	variation	variation	NOUN
concept-2079	221	33	.	.	PUNCT
concept-2079	222	1	multifractals	multifractal	NOUN
concept-2079	222	2	,	,	PUNCT
concept-2079	222	3	or	or	CCONJ
concept-2079	222	4	“	"	PUNCT
concept-2079	222	5	objects	object	NOUN
concept-2079	222	6	whose	whose	DET
concept-2079	222	7	fractal	fractal	ADJ
concept-2079	222	8	dimension	dimension	NOUN
concept-2079	222	9	varies	vary	VERB
concept-2079	222	10	as	as	ADP
concept-2079	222	11	a	a	DET
concept-2079	222	12	function	function	NOUN
concept-2079	222	13	of	of	ADP
concept-2079	222	14	location	location	NOUN
concept-2079	222	15	within	within	ADP
concept-2079	222	16	in	in	ADP
concept-2079	222	17	a	a	DET
concept-2079	222	18	set	set	NOUN
concept-2079	222	19	(	(	PUNCT
concept-2079	222	20	image	image	NOUN
concept-2079	222	21	,	,	PUNCT
concept-2079	222	22	frame	frame	NOUN
concept-2079	222	23	)	)	PUNCT
concept-2079	222	24	”	"	PUNCT
concept-2079	222	25	(	(	PUNCT
concept-2079	222	26	smith	smith	PROPN
concept-2079	222	27	,	,	PUNCT
concept-2079	222	28	lange	lange	NOUN
concept-2079	222	29	,	,	PUNCT
concept-2079	222	30	and	and	CCONJ
concept-2079	222	31	marks	mark	NOUN
concept-2079	222	32	,	,	PUNCT
concept-2079	222	33	“	"	PUNCT
concept-2079	222	34	fractal	fractal	ADJ
concept-2079	222	35	methods	method	NOUN
concept-2079	222	36	...	...	PUNCT
concept-2079	222	37	”	"	PUNCT
concept-2079	222	38	)	)	PUNCT
concept-2079	222	39	,	,	PUNCT
concept-2079	222	40	were	be	AUX
concept-2079	222	41	introduced	introduce	VERB
concept-2079	222	42	to	to	ADP
concept-2079	222	43	the	the	DET
concept-2079	222	44	author	author	NOUN
concept-2079	222	45	via	via	ADP
concept-2079	222	46	the	the	DET
concept-2079	222	47	context	context	NOUN
concept-2079	222	48	of	of	ADP
concept-2079	222	49	a	a	DET
concept-2079	222	50	biological	biological	ADJ
concept-2079	222	51	application	application	NOUN
concept-2079	222	52	of	of	ADP
concept-2079	222	53	fractal	fractal	ADJ
concept-2079	222	54	dimension	dimension	NOUN
concept-2079	222	55	but	but	CCONJ
concept-2079	222	56	also	also	ADV
concept-2079	222	57	have	have	VERB
concept-2079	222	58	connections	connection	NOUN
concept-2079	222	59	to	to	ADP
concept-2079	222	60	the	the	DET
concept-2079	222	61	financial	financial	ADJ
concept-2079	222	62	stock	stock	NOUN
concept-2079	222	63	market	market	NOUN
concept-2079	222	64	as	as	ADV
concept-2079	222	65	well	well	ADV
concept-2079	222	66	.	.	PUNCT
concept-2079	223	1	previously	previously	ADV
concept-2079	223	2	,	,	PUNCT
concept-2079	223	3	brownian	brownian	ADJ
concept-2079	223	4	motion	motion	NOUN
concept-2079	223	5	models	model	NOUN
concept-2079	223	6	utilizing	utilize	VERB
concept-2079	223	7	a	a	DET
concept-2079	223	8	random	random	ADJ
concept-2079	223	9	walk	walk	NOUN
concept-2079	223	10	and	and	CCONJ
concept-2079	223	11	statistical	statistical	ADJ
concept-2079	223	12	distributions	distribution	NOUN
concept-2079	223	13	have	have	AUX
concept-2079	223	14	been	be	AUX
concept-2079	223	15	used	use	VERB
concept-2079	223	16	to	to	PART
concept-2079	223	17	try	try	VERB
concept-2079	223	18	to	to	PART
concept-2079	223	19	make	make	VERB
concept-2079	223	20	accurate	accurate	ADJ
concept-2079	223	21	predictions	prediction	NOUN
concept-2079	223	22	about	about	ADP
concept-2079	223	23	financial	financial	ADJ
concept-2079	223	24	systems	system	NOUN
concept-2079	223	25	.	.	PUNCT
concept-2079	224	1	however	however	ADV
concept-2079	224	2	,	,	PUNCT
concept-2079	224	3	real	real	ADJ
concept-2079	224	4	world	world	NOUN
concept-2079	224	5	events	event	NOUN
concept-2079	224	6	,	,	PUNCT
concept-2079	224	7	such	such	ADJ
concept-2079	224	8	as	as	ADP
concept-2079	224	9	the	the	DET
concept-2079	224	10	global	global	ADJ
concept-2079	224	11	stock	stock	NOUN
concept-2079	224	12	market	market	NOUN
concept-2079	224	13	crisis	crisis	NOUN
concept-2079	224	14	of	of	ADP
concept-2079	224	15	2008	2008	NUM
concept-2079	224	16	,	,	PUNCT
concept-2079	224	17	have	have	AUX
concept-2079	224	18	revealed	reveal	VERB
concept-2079	224	19	the	the	DET
concept-2079	224	20	flaws	flaw	NOUN
concept-2079	224	21	of	of	ADP
concept-2079	224	22	using	use	VERB
concept-2079	224	23	brownian	brownian	ADJ
concept-2079	224	24	motion	motion	NOUN
concept-2079	224	25	modeling	modeling	NOUN
concept-2079	224	26	systems	system	NOUN
concept-2079	224	27	,	,	PUNCT
concept-2079	224	28	primarily	primarily	ADV
concept-2079	224	29	with	with	ADP
concept-2079	224	30	the	the	DET
concept-2079	224	31	inability	inability	NOUN
concept-2079	224	32	to	to	PART
concept-2079	224	33	account	account	VERB
concept-2079	224	34	for	for	ADP
concept-2079	224	35	large	large	ADJ
concept-2079	224	36	spikes	spike	NOUN
concept-2079	224	37	of	of	ADP
concept-2079	224	38	sales	sale	NOUN
concept-2079	224	39	or	or	CCONJ
concept-2079	224	40	losses	loss	NOUN
concept-2079	224	41	within	within	ADP
concept-2079	224	42	the	the	DET
concept-2079	224	43	system	system	NOUN
concept-2079	224	44	within	within	ADP
concept-2079	224	45	a	a	DET
concept-2079	224	46	short	short	ADJ
concept-2079	224	47	period	period	NOUN
concept-2079	224	48	of	of	ADP
concept-2079	224	49	time	time	NOUN
concept-2079	224	50	(	(	PUNCT
concept-2079	224	51	clarke	clarke	PROPN
concept-2079	224	52	,	,	PUNCT
concept-2079	224	53	mandelbrot	mandelbrot	PROPN
concept-2079	224	54	,	,	PUNCT
concept-2079	224	55	stewart	stewart	PROPN
concept-2079	224	56	,	,	PUNCT
concept-2079	224	57	et	et	PROPN
concept-2079	224	58	.	.	PUNCT
concept-2079	225	1	al	al	PROPN
concept-2079	225	2	.	.	PROPN
concept-2079	225	3	,	,	PUNCT
concept-2079	225	4	127	127	NUM
concept-2079	225	5	)	)	PUNCT
concept-2079	225	6	.	.	PUNCT
concept-2079	226	1	financial	financial	ADJ
concept-2079	226	2	market	market	NOUN
concept-2079	226	3	modeling	modeling	NOUN
concept-2079	226	4	using	use	VERB
concept-2079	226	5	fractals	fractal	NOUN
concept-2079	226	6	financial	financial	ADJ
concept-2079	226	7	systems	system	NOUN
concept-2079	226	8	are	be	AUX
concept-2079	226	9	good	good	ADJ
concept-2079	226	10	candidates	candidate	NOUN
concept-2079	226	11	to	to	PART
concept-2079	226	12	be	be	AUX
concept-2079	226	13	modeled	model	VERB
concept-2079	226	14	by	by	ADP
concept-2079	226	15	fractals	fractal	NOUN
concept-2079	226	16	because	because	SCONJ
concept-2079	226	17	the	the	DET
concept-2079	226	18	graphical	graphical	ADJ
concept-2079	226	19	representations	representation	NOUN
concept-2079	226	20	of	of	ADP
concept-2079	226	21	the	the	DET
concept-2079	226	22	rise	rise	NOUN
concept-2079	226	23	and	and	CCONJ
concept-2079	226	24	fall	fall	NOUN
concept-2079	226	25	of	of	ADP
concept-2079	226	26	stocks	stock	NOUN
concept-2079	226	27	look	look	VERB
concept-2079	226	28	similar	similar	ADJ
concept-2079	226	29	on	on	ADP
concept-2079	226	30	different	different	ADJ
concept-2079	226	31	scales	scale	NOUN
concept-2079	226	32	when	when	SCONJ
concept-2079	226	33	comparing	compare	VERB
concept-2079	226	34	price	price	NOUN
concept-2079	226	35	vs.	vs.	ADP
concept-2079	226	36	time	time	NOUN
concept-2079	226	37	(	(	PUNCT
concept-2079	226	38	idea	idea	NOUN
concept-2079	226	39	of	of	ADP
concept-2079	226	40	self	self	NOUN
concept-2079	226	41	-	-	PUNCT
concept-2079	226	42	similarity	similarity	NOUN
concept-2079	226	43	)	)	PUNCT
concept-2079	226	44	.	.	PUNCT
concept-2079	227	1	mathematicians	mathematician	NOUN
concept-2079	227	2	can	can	AUX
concept-2079	227	3	replicate	replicate	VERB
concept-2079	227	4	stock	stock	NOUN
concept-2079	227	5	market	market	NOUN
concept-2079	227	6	prices	price	NOUN
concept-2079	227	7	using	use	VERB
concept-2079	227	8	an	an	DET
concept-2079	227	9	initiator	initiator	NOUN
concept-2079	227	10	/	/	SYM
concept-2079	227	11	generator	generator	NOUN
concept-2079	227	12	model	model	NOUN
concept-2079	227	13	.	.	PUNCT
concept-2079	228	1	in	in	ADP
concept-2079	228	2	order	order	NOUN
concept-2079	228	3	to	to	PART
concept-2079	228	4	construct	construct	VERB
concept-2079	228	5	this	this	DET
concept-2079	228	6	model	model	NOUN
concept-2079	228	7	,	,	PUNCT
concept-2079	228	8	first	first	ADV
concept-2079	228	9	start	start	VERB
concept-2079	228	10	out	out	ADP
concept-2079	228	11	with	with	ADP
concept-2079	228	12	the	the	DET
concept-2079	228	13	trend	trend	NOUN
concept-2079	228	14	line	line	NOUN
concept-2079	228	15	called	call	VERB
concept-2079	228	16	the	the	DET
concept-2079	228	17	initiator	initiator	NOUN
concept-2079	228	18	.	.	PUNCT
concept-2079	229	1	next	next	ADV
concept-2079	229	2	,	,	PUNCT
concept-2079	229	3	pick	pick	VERB
concept-2079	229	4	an	an	DET
concept-2079	229	5	interval	interval	NOUN
concept-2079	229	6	of	of	ADP
concept-2079	229	7	the	the	DET
concept-2079	229	8	graph	graph	NOUN
concept-2079	229	9	you	you	PRON
concept-2079	229	10	are	be	AUX
concept-2079	229	11	interested	interested	ADJ
concept-2079	229	12	in	in	ADP
concept-2079	229	13	studying	study	VERB
concept-2079	229	14	and	and	CCONJ
concept-2079	229	15	apply	apply	VERB
concept-2079	229	16	the	the	DET
concept-2079	229	17	generator	generator	NOUN
concept-2079	229	18	to	to	ADP
concept-2079	229	19	that	that	DET
concept-2079	229	20	portion	portion	NOUN
concept-2079	229	21	.	.	PUNCT
concept-2079	230	1	the	the	DET
concept-2079	230	2	generator	generator	NOUN
concept-2079	230	3	is	be	AUX
concept-2079	230	4	a	a	DET
concept-2079	230	5	modification	modification	NOUN
concept-2079	230	6	much	much	ADJ
concept-2079	230	7	like	like	ADP
concept-2079	230	8	the	the	DET
concept-2079	230	9	replacement	replacement	NOUN
concept-2079	230	10	algorithm	algorithm	NOUN
concept-2079	230	11	in	in	ADP
concept-2079	230	12	the	the	DET
concept-2079	230	13	koch	koch	PROPN
concept-2079	230	14	curve	curve	NOUN
concept-2079	230	15	in	in	ADP
concept-2079	230	16	which	which	PRON
concept-2079	230	17	each	each	DET
concept-2079	230	18	segment	segment	NOUN
concept-2079	230	19	is	be	AUX
concept-2079	230	20	replaced	replace	VERB
concept-2079	230	21	by	by	ADP
concept-2079	230	22	a	a	DET
concept-2079	230	23	modified	modify	VERB
concept-2079	230	24	concept	concept	NOUN
concept-2079	230	25	,	,	PUNCT
concept-2079	230	26	vol	vol	NOUN
concept-2079	230	27	.	.	PUNCT
concept-2079	230	28	xxxix	xxxix	PROPN
concept-2079	230	29	(	(	PUNCT
concept-2079	230	30	2016	2016	NUM
concept-2079	230	31	)	)	PUNCT
concept-2079	230	32	12	12	NUM
concept-2079	230	33	curve	curve	NOUN
concept-2079	230	34	(	(	PUNCT
concept-2079	230	35	with	with	ADP
concept-2079	230	36	four	four	NUM
concept-2079	230	37	segments	segment	NOUN
concept-2079	230	38	in	in	ADP
concept-2079	230	39	the	the	DET
concept-2079	230	40	case	case	NOUN
concept-2079	230	41	of	of	ADP
concept-2079	230	42	the	the	DET
concept-2079	230	43	koch	koch	PROPN
concept-2079	230	44	curve	curve	NOUN
concept-2079	230	45	)	)	PUNCT
concept-2079	230	46	.	.	PUNCT
concept-2079	231	1	however	however	ADV
concept-2079	231	2	,	,	PUNCT
concept-2079	231	3	on	on	ADP
concept-2079	231	4	a	a	DET
concept-2079	231	5	different	different	ADJ
concept-2079	231	6	portion	portion	NOUN
concept-2079	231	7	of	of	ADP
concept-2079	231	8	the	the	DET
concept-2079	231	9	same	same	ADJ
concept-2079	231	10	interval	interval	NOUN
concept-2079	231	11	,	,	PUNCT
concept-2079	231	12	you	you	PRON
concept-2079	231	13	will	will	AUX
concept-2079	231	14	iterate	iterate	VERB
concept-2079	231	15	an	an	DET
concept-2079	231	16	inverted	inverted	ADJ
concept-2079	231	17	version	version	NOUN
concept-2079	231	18	of	of	ADP
concept-2079	231	19	the	the	DET
concept-2079	231	20	generator	generator	NOUN
concept-2079	231	21	.	.	PUNCT
concept-2079	232	1	(	(	PUNCT
concept-2079	232	2	imagine	imagine	VERB
concept-2079	232	3	the	the	DET
concept-2079	232	4	koch	koch	PROPN
concept-2079	232	5	substitution	substitution	NOUN
concept-2079	232	6	with	with	ADP
concept-2079	232	7	the	the	DET
concept-2079	232	8	added	add	VERB
concept-2079	232	9	triangular	triangular	NOUN
concept-2079	232	10	piece	piece	NOUN
concept-2079	232	11	not	not	PART
concept-2079	232	12	symmetric	symmetric	ADJ
concept-2079	232	13	.	.	PUNCT
concept-2079	233	1	on	on	ADP
concept-2079	233	2	one	one	NUM
concept-2079	233	3	interval	interval	NOUN
concept-2079	233	4	,	,	PUNCT
concept-2079	233	5	substitute	substitute	VERB
concept-2079	233	6	the	the	DET
concept-2079	233	7	original	original	ADJ
concept-2079	233	8	,	,	PUNCT
concept-2079	233	9	and	and	CCONJ
concept-2079	233	10	on	on	ADP
concept-2079	233	11	the	the	DET
concept-2079	233	12	other	other	ADJ
concept-2079	233	13	,	,	PUNCT
concept-2079	233	14	substitute	substitute	VERB
concept-2079	233	15	the	the	DET
concept-2079	233	16	flipped	flip	VERB
concept-2079	233	17	version	version	NOUN
concept-2079	233	18	.	.	PUNCT
concept-2079	233	19	)	)	PUNCT
concept-2079	234	1	note	note	VERB
concept-2079	234	2	:	:	PUNCT
concept-2079	234	3	the	the	DET
concept-2079	234	4	points	point	NOUN
concept-2079	234	5	on	on	ADP
concept-2079	234	6	the	the	DET
concept-2079	234	7	generator	generator	NOUN
concept-2079	234	8	must	must	AUX
concept-2079	234	9	satisfy	satisfy	VERB
concept-2079	234	10	the	the	DET
concept-2079	234	11	conditions	condition	NOUN
concept-2079	234	12	:	:	PUNCT
concept-2079	235	1	|dyi|	|dyi|	ADV
concept-2079	235	2	=	=	PUNCT
concept-2079	235	3	(	(	PUNCT
concept-2079	235	4	dti)1/2	dti)1/2	INTJ
concept-2079	235	5	,	,	PUNCT
concept-2079	235	6	where	where	SCONJ
concept-2079	235	7	|dyi|	|dyi|	PRON
concept-2079	235	8	is	be	AUX
concept-2079	235	9	the	the	DET
concept-2079	235	10	height	height	NOUN
concept-2079	235	11	of	of	ADP
concept-2079	235	12	some	some	DET
concept-2079	235	13	point	point	NOUN
concept-2079	235	14	(	(	PUNCT
concept-2079	235	15	typically	typically	ADV
concept-2079	235	16	representing	represent	VERB
concept-2079	235	17	cost	cost	NOUN
concept-2079	235	18	of	of	ADP
concept-2079	235	19	the	the	DET
concept-2079	235	20	stock	stock	NOUN
concept-2079	235	21	in	in	ADP
concept-2079	235	22	a	a	DET
concept-2079	235	23	financial	financial	ADJ
concept-2079	235	24	setting	setting	NOUN
concept-2079	235	25	)	)	PUNCT
concept-2079	235	26	and	and	CCONJ
concept-2079	235	27	(	(	PUNCT
concept-2079	235	28	dti)1/2	dti)1/2	PROPN
concept-2079	235	29	is	be	AUX
concept-2079	235	30	the	the	DET
concept-2079	235	31	distance	distance	NOUN
concept-2079	235	32	that	that	PRON
concept-2079	235	33	point	point	NOUN
concept-2079	235	34	travels	travel	VERB
concept-2079	235	35	on	on	ADP
concept-2079	235	36	the	the	DET
concept-2079	235	37	t	t	NOUN
concept-2079	235	38	axis	axis	NOUN
concept-2079	235	39	or	or	CCONJ
concept-2079	235	40	time	time	NOUN
concept-2079	235	41	(	(	PUNCT
concept-2079	235	42	brennan	brennan	NOUN
concept-2079	235	43	,	,	PUNCT
concept-2079	235	44	“	"	PUNCT
concept-2079	235	45	fractals	fractal	NOUN
concept-2079	235	46	and	and	CCONJ
concept-2079	235	47	financial	financial	ADJ
concept-2079	235	48	risk	risk	NOUN
concept-2079	235	49	”	"	PUNCT
concept-2079	235	50	)	)	PUNCT
concept-2079	235	51	.	.	PUNCT
concept-2079	236	1	as	as	SCONJ
concept-2079	236	2	you	you	PRON
concept-2079	236	3	continue	continue	VERB
concept-2079	236	4	to	to	PART
concept-2079	236	5	break	break	VERB
concept-2079	236	6	the	the	DET
concept-2079	236	7	interval	interval	NOUN
concept-2079	236	8	up	up	ADP
concept-2079	236	9	using	use	VERB
concept-2079	236	10	more	more	ADJ
concept-2079	236	11	and	and	CCONJ
concept-2079	236	12	more	more	ADJ
concept-2079	236	13	initiators	initiator	NOUN
concept-2079	236	14	,	,	PUNCT
concept-2079	236	15	it	it	PRON
concept-2079	236	16	produces	produce	VERB
concept-2079	236	17	a	a	DET
concept-2079	236	18	graph	graph	NOUN
concept-2079	236	19	that	that	PRON
concept-2079	236	20	more	more	ADV
concept-2079	236	21	accurately	accurately	ADV
concept-2079	236	22	represents	represent	VERB
concept-2079	236	23	the	the	DET
concept-2079	236	24	fluctuations	fluctuation	NOUN
concept-2079	236	25	than	than	ADP
concept-2079	236	26	just	just	ADV
concept-2079	236	27	a	a	DET
concept-2079	236	28	brownian	brownian	ADJ
concept-2079	236	29	motion	motion	NOUN
concept-2079	236	30	model	model	NOUN
concept-2079	236	31	,	,	PUNCT
concept-2079	236	32	primarily	primarily	ADV
concept-2079	236	33	due	due	ADP
concept-2079	236	34	to	to	ADP
concept-2079	236	35	the	the	DET
concept-2079	236	36	inverted	inverted	ADJ
concept-2079	236	37	generator	generator	NOUN
concept-2079	236	38	.	.	PUNCT
concept-2079	237	1	an	an	DET
concept-2079	237	2	even	even	ADV
concept-2079	237	3	better	well	ADJ
concept-2079	237	4	representation	representation	NOUN
concept-2079	237	5	of	of	ADP
concept-2079	237	6	financial	financial	ADJ
concept-2079	237	7	markets	market	NOUN
concept-2079	237	8	lies	lie	VERB
concept-2079	237	9	within	within	ADP
concept-2079	237	10	a	a	DET
concept-2079	237	11	multi	multi	ADJ
concept-2079	237	12	-	-	ADJ
concept-2079	237	13	fractal	fractal	ADJ
concept-2079	237	14	initiator	initiator	NOUN
concept-2079	237	15	/	/	SYM
concept-2079	237	16	generator	generator	NOUN
concept-2079	237	17	model	model	NOUN
concept-2079	237	18	according	accord	VERB
concept-2079	237	19	to	to	ADP
concept-2079	237	20	mandelbrot	mandelbrot	PROPN
concept-2079	237	21	.	.	PUNCT
concept-2079	238	1	the	the	DET
concept-2079	238	2	multi	multi	ADJ
concept-2079	238	3	-	-	ADJ
concept-2079	238	4	fractal	fractal	ADJ
concept-2079	238	5	model	model	NOUN
concept-2079	238	6	allows	allow	VERB
concept-2079	238	7	the	the	DET
concept-2079	238	8	financial	financial	ADJ
concept-2079	238	9	analysts	analyst	NOUN
concept-2079	238	10	to	to	PART
concept-2079	238	11	incorporate	incorporate	VERB
concept-2079	238	12	the	the	DET
concept-2079	238	13	fact	fact	NOUN
concept-2079	238	14	that	that	SCONJ
concept-2079	238	15	many	many	ADJ
concept-2079	238	16	people	people	NOUN
concept-2079	238	17	will	will	AUX
concept-2079	238	18	be	be	AUX
concept-2079	238	19	buying	buy	VERB
concept-2079	238	20	stocks	stock	NOUN
concept-2079	238	21	at	at	ADP
concept-2079	238	22	different	different	ADJ
concept-2079	238	23	times	time	NOUN
concept-2079	238	24	and	and	CCONJ
concept-2079	238	25	at	at	ADP
concept-2079	238	26	different	different	ADJ
concept-2079	238	27	rates	rate	NOUN
concept-2079	238	28	.	.	PUNCT
concept-2079	239	1	budinski	budinski	ADJ
concept-2079	239	2	-	-	PUNCT
concept-2079	239	3	petkovic	petkovic	ADJ
concept-2079	239	4	,	,	PUNCT
concept-2079	239	5	loncarevic	loncarevic	ADJ
concept-2079	239	6	,	,	PUNCT
concept-2079	239	7	jasksic	jasksic	NOUN
concept-2079	239	8	and	and	CCONJ
concept-2079	239	9	vrhovac	vrhovac	NOUN
concept-2079	239	10	(	(	PUNCT
concept-2079	239	11	“	"	PUNCT
concept-2079	239	12	fractal	fractal	ADJ
concept-2079	239	13	properties	property	NOUN
concept-2079	239	14	of	of	ADP
concept-2079	239	15	financial	financial	ADJ
concept-2079	239	16	markets	market	NOUN
concept-2079	239	17	”	"	PUNCT
concept-2079	239	18	)	)	PUNCT
concept-2079	239	19	demonstrated	demonstrate	VERB
concept-2079	239	20	that	that	SCONJ
concept-2079	239	21	the	the	DET
concept-2079	239	22	u.s	u.s	PROPN
concept-2079	239	23	.	.	PROPN
concept-2079	239	24	s&p	s&p	PROPN
concept-2079	239	25	500	500	NUM
concept-2079	239	26	financial	financial	ADJ
concept-2079	239	27	bubbles	bubble	NOUN
concept-2079	239	28	in	in	ADP
concept-2079	239	29	1987	1987	NUM
concept-2079	239	30	,	,	PUNCT
concept-2079	239	31	2000	2000	NUM
concept-2079	239	32	,	,	PUNCT
concept-2079	239	33	and	and	CCONJ
concept-2079	239	34	2007	2007	NUM
concept-2079	239	35	could	could	AUX
concept-2079	239	36	be	be	AUX
concept-2079	239	37	well	well	ADV
concept-2079	239	38	modeled	model	VERB
concept-2079	239	39	by	by	ADP
concept-2079	239	40	the	the	DET
concept-2079	239	41	besicovitch	besicovitch	PROPN
concept-2079	239	42	-	-	PUNCT
concept-2079	239	43	ursell	ursell	NOUN
concept-2079	239	44	(	(	PUNCT
concept-2079	239	45	b	b	NOUN
concept-2079	239	46	-	-	PUNCT
concept-2079	239	47	u	u	NOUN
concept-2079	239	48	)	)	PUNCT
concept-2079	239	49	fractal	fractal	ADJ
concept-2079	239	50	model	model	NOUN
concept-2079	239	51	.	.	PUNCT
concept-2079	240	1	a	a	DET
concept-2079	240	2	financial	financial	ADJ
concept-2079	240	3	bubble	bubble	NOUN
concept-2079	240	4	is	be	AUX
concept-2079	240	5	a	a	DET
concept-2079	240	6	period	period	NOUN
concept-2079	240	7	of	of	ADP
concept-2079	240	8	extreme	extreme	ADJ
concept-2079	240	9	growth	growth	NOUN
concept-2079	240	10	(	(	PUNCT
concept-2079	240	11	generally	generally	ADV
concept-2079	240	12	exponential	exponential	ADJ
concept-2079	240	13	in	in	ADP
concept-2079	240	14	nature	nature	NOUN
concept-2079	240	15	)	)	PUNCT
concept-2079	240	16	,	,	PUNCT
concept-2079	240	17	sometimes	sometimes	ADV
concept-2079	240	18	followed	follow	VERB
concept-2079	240	19	by	by	ADP
concept-2079	240	20	a	a	DET
concept-2079	240	21	cataclysmic	cataclysmic	ADJ
concept-2079	240	22	drop	drop	NOUN
concept-2079	240	23	in	in	ADP
concept-2079	240	24	stock	stock	NOUN
concept-2079	240	25	prices	price	NOUN
concept-2079	240	26	,	,	PUNCT
concept-2079	240	27	or	or	CCONJ
concept-2079	240	28	crash	crash	NOUN
concept-2079	240	29	.	.	PUNCT
concept-2079	241	1	one	one	NUM
concept-2079	241	2	method	method	NOUN
concept-2079	241	3	econophysicists	econophysicist	NOUN
concept-2079	241	4	use	use	VERB
concept-2079	241	5	to	to	PART
concept-2079	241	6	determine	determine	VERB
concept-2079	241	7	trends	trend	NOUN
concept-2079	241	8	and	and	CCONJ
concept-2079	241	9	make	make	VERB
concept-2079	241	10	predictions	prediction	NOUN
concept-2079	241	11	about	about	ADP
concept-2079	241	12	crashes	crash	NOUN
concept-2079	241	13	is	be	AUX
concept-2079	241	14	by	by	ADP
concept-2079	241	15	fitting	fit	VERB
concept-2079	241	16	the	the	DET
concept-2079	241	17	financial	financial	ADJ
concept-2079	241	18	data	datum	NOUN
concept-2079	241	19	to	to	ADP
concept-2079	241	20	the	the	DET
concept-2079	241	21	log	log	NOUN
concept-2079	241	22	-	-	PUNCT
concept-2079	241	23	periodic	periodic	NOUN
concept-2079	241	24	power	power	NOUN
concept-2079	241	25	law	law	NOUN
concept-2079	241	26	using	use	VERB
concept-2079	241	27	log	log	NOUN
concept-2079	241	28	-	-	PUNCT
concept-2079	241	29	bylog	bylog	NOUN
concept-2079	241	30	plots	plot	NOUN
concept-2079	241	31	.	.	PUNCT
concept-2079	242	1	the	the	DET
concept-2079	242	2	researchers	researcher	NOUN
concept-2079	242	3	in	in	ADP
concept-2079	242	4	the	the	DET
concept-2079	242	5	paper	paper	NOUN
concept-2079	242	6	first	first	ADV
concept-2079	242	7	defined	define	VERB
concept-2079	242	8	a	a	DET
concept-2079	242	9	saw	saw	NOUN
concept-2079	242	10	-	-	PUNCT
concept-2079	242	11	tooth	tooth	NOUN
concept-2079	242	12	,	,	PUNCT
concept-2079	242	13	or	or	CCONJ
concept-2079	242	14	tent	tent	NOUN
concept-2079	242	15	map	map	NOUN
concept-2079	242	16	f(x	f(x	PROPN
concept-2079	242	17	)	)	PUNCT
concept-2079	242	18	and	and	CCONJ
concept-2079	242	19	an	an	DET
concept-2079	242	20	another	another	DET
concept-2079	242	21	function	function	NOUN
concept-2079	242	22	,	,	PUNCT
concept-2079	242	23	g(x	g(x	NOUN
concept-2079	242	24	)	)	PUNCT
concept-2079	242	25	,	,	PUNCT
concept-2079	242	26	to	to	PART
concept-2079	242	27	derive	derive	VERB
concept-2079	242	28	h(x	h(x	PROPN
concept-2079	242	29	)	)	PUNCT
concept-2079	242	30	,	,	PUNCT
concept-2079	242	31	a	a	DET
concept-2079	242	32	b	b	X
concept-2079	242	33	-	-	PUNCT
concept-2079	242	34	u	u	NOUN
concept-2079	242	35	function	function	NOUN
concept-2079	242	36	.	.	PUNCT
concept-2079	243	1	the	the	DET
concept-2079	243	2	b	b	X
concept-2079	243	3	-	-	PUNCT
concept-2079	243	4	u	u	NOUN
concept-2079	243	5	function	function	NOUN
concept-2079	243	6	is	be	AUX
concept-2079	243	7	a	a	DET
concept-2079	243	8	type	type	NOUN
concept-2079	243	9	of	of	ADP
concept-2079	243	10	dynamical	dynamical	ADJ
concept-2079	243	11	system	system	NOUN
concept-2079	243	12	that	that	PRON
concept-2079	243	13	behaves	behave	VERB
concept-2079	243	14	as	as	ADP
concept-2079	243	15	a	a	DET
concept-2079	243	16	fractal	fractal	NOUN
concept-2079	243	17	since	since	SCONJ
concept-2079	243	18	it	it	PRON
concept-2079	243	19	has	have	VERB
concept-2079	243	20	a	a	DET
concept-2079	243	21	dimension	dimension	NOUN
concept-2079	243	22	of	of	ADP
concept-2079	243	23	at	at	ADV
concept-2079	243	24	most	most	ADV
concept-2079	243	25	two	two	NUM
concept-2079	243	26	and	and	CCONJ
concept-2079	243	27	it	it	PRON
concept-2079	243	28	has	have	AUX
concept-2079	243	29	“	"	PUNCT
concept-2079	243	30	almost	almost	ADV
concept-2079	243	31	periodicity”behaving	periodicity”behaving	NOUN
concept-2079	243	32	similarly	similarly	ADV
concept-2079	243	33	but	but	CCONJ
concept-2079	243	34	not	not	PART
concept-2079	243	35	exactly	exactly	ADV
concept-2079	243	36	the	the	DET
concept-2079	243	37	same	same	ADJ
concept-2079	243	38	upon	upon	SCONJ
concept-2079	243	39	each	each	DET
concept-2079	243	40	iteration	iteration	NOUN
concept-2079	243	41	.	.	PUNCT
concept-2079	244	1	the	the	DET
concept-2079	244	2	researchers	researcher	NOUN
concept-2079	244	3	used	use	VERB
concept-2079	244	4	a	a	DET
concept-2079	244	5	non	non	ADJ
concept-2079	244	6	-	-	ADJ
concept-2079	244	7	linear	linear	ADJ
concept-2079	244	8	fitting	fitting	ADJ
concept-2079	244	9	algorithm	algorithm	NOUN
concept-2079	244	10	in	in	ADP
concept-2079	244	11	matlab	matlab	PROPN
concept-2079	244	12	to	to	PART
concept-2079	244	13	show	show	VERB
concept-2079	244	14	the	the	DET
concept-2079	244	15	b	b	NOUN
concept-2079	244	16	-	-	PUNCT
concept-2079	244	17	u	u	NOUN
concept-2079	244	18	function	function	NOUN
concept-2079	244	19	produced	produce	VERB
concept-2079	244	20	relatively	relatively	ADV
concept-2079	244	21	small	small	ADJ
concept-2079	244	22	regression	regression	NOUN
concept-2079	244	23	errors	error	NOUN
concept-2079	244	24	.	.	PUNCT
concept-2079	245	1	this	this	PRON
concept-2079	245	2	gives	give	VERB
concept-2079	245	3	further	further	ADJ
concept-2079	245	4	support	support	NOUN
concept-2079	245	5	to	to	ADP
concept-2079	245	6	the	the	DET
concept-2079	245	7	argument	argument	NOUN
concept-2079	245	8	mandelbrot	mandelbrot	NOUN
concept-2079	245	9	had	have	AUX
concept-2079	245	10	made	make	VERB
concept-2079	245	11	regarding	regard	VERB
concept-2079	245	12	the	the	DET
concept-2079	245	13	use	use	NOUN
concept-2079	245	14	of	of	ADP
concept-2079	245	15	fractals	fractal	NOUN
concept-2079	245	16	in	in	ADP
concept-2079	245	17	making	make	VERB
concept-2079	245	18	financial	financial	ADJ
concept-2079	245	19	predictions	prediction	NOUN
concept-2079	245	20	.	.	PUNCT
concept-2079	246	1	practical	practical	ADJ
concept-2079	246	2	applications	application	NOUN
concept-2079	246	3	of	of	ADP
concept-2079	246	4	fractals	fractal	NOUN
concept-2079	246	5	in	in	ADP
concept-2079	246	6	technology	technology	NOUN
concept-2079	246	7	cell	cell	NOUN
concept-2079	246	8	phone	phone	NOUN
concept-2079	246	9	technology	technology	NOUN
concept-2079	246	10	also	also	ADV
concept-2079	246	11	has	have	AUX
concept-2079	246	12	benefited	benefit	VERB
concept-2079	246	13	from	from	ADP
concept-2079	246	14	this	this	DET
concept-2079	246	15	area	area	NOUN
concept-2079	246	16	of	of	ADP
concept-2079	246	17	mathematics	mathematic	NOUN
concept-2079	246	18	.	.	PUNCT
concept-2079	247	1	in	in	ADP
concept-2079	247	2	1999	1999	NUM
concept-2079	247	3	,	,	PUNCT
concept-2079	247	4	dwight	dwight	PROPN
concept-2079	247	5	jaggard	jaggard	PROPN
concept-2079	247	6	and	and	CCONJ
concept-2079	247	7	douglas	douglas	PROPN
concept-2079	247	8	werner	werner	PROPN
concept-2079	247	9	found	find	VERB
concept-2079	247	10	cell	cell	NOUN
concept-2079	247	11	phone	phone	NOUN
concept-2079	247	12	antennas	antenna	NOUN
concept-2079	247	13	arranged	arrange	VERB
concept-2079	247	14	in	in	ADP
concept-2079	247	15	a	a	DET
concept-2079	247	16	fractal	fractal	ADJ
concept-2079	247	17	pattern	pattern	NOUN
concept-2079	247	18	were	be	AUX
concept-2079	247	19	superior	superior	ADJ
concept-2079	247	20	in	in	ADP
concept-2079	247	21	transmitting	transmit	VERB
concept-2079	247	22	radio	radio	NOUN
concept-2079	247	23	signals	signal	NOUN
concept-2079	247	24	over	over	ADP
concept-2079	247	25	other	other	ADJ
concept-2079	247	26	arrangements	arrangement	NOUN
concept-2079	247	27	of	of	ADP
concept-2079	247	28	the	the	DET
concept-2079	247	29	antenna	antenna	NOUN
concept-2079	247	30	(	(	PUNCT
concept-2079	247	31	stewart	stewart	PROPN
concept-2079	247	32	,	,	PUNCT
concept-2079	247	33	clark	clark	PROPN
concept-2079	247	34	,	,	PUNCT
concept-2079	247	35	mandelbrot	mandelbrot	PROPN
concept-2079	247	36	,	,	PUNCT
concept-2079	247	37	et	et	PROPN
concept-2079	247	38	al	al	PROPN
concept-2079	247	39	.	.	PROPN
concept-2079	247	40	,	,	PUNCT
concept-2079	247	41	21	21	NUM
concept-2079	247	42	)	)	PUNCT
concept-2079	247	43	.	.	PUNCT
concept-2079	248	1	other	other	ADJ
concept-2079	248	2	researchers	researcher	NOUN
concept-2079	248	3	,	,	PUNCT
concept-2079	248	4	nathan	nathan	PROPN
concept-2079	248	5	cohen	cohen	PROPN
concept-2079	248	6	and	and	CCONJ
concept-2079	248	7	robert	robert	PROPN
concept-2079	248	8	hohfeld	hohfeld	PROPN
concept-2079	248	9	,	,	PUNCT
concept-2079	248	10	proved	prove	VERB
concept-2079	248	11	antenna	antenna	NOUN
concept-2079	248	12	designs	design	NOUN
concept-2079	248	13	that	that	PRON
concept-2079	248	14	had	have	VERB
concept-2079	248	15	self	self	NOUN
concept-2079	248	16	-	-	PUNCT
concept-2079	248	17	similarity	similarity	NOUN
concept-2079	248	18	and	and	CCONJ
concept-2079	248	19	symmetry	symmetry	NOUN
concept-2079	248	20	properties	property	NOUN
concept-2079	248	21	(	(	PUNCT
concept-2079	248	22	both	both	PRON
concept-2079	248	23	of	of	ADP
concept-2079	248	24	which	which	PRON
concept-2079	248	25	are	be	AUX
concept-2079	248	26	found	find	VERB
concept-2079	248	27	in	in	ADP
concept-2079	248	28	most	most	ADJ
concept-2079	248	29	fractals	fractal	NOUN
concept-2079	248	30	)	)	PUNCT
concept-2079	248	31	performed	perform	VERB
concept-2079	248	32	well	well	ADV
concept-2079	248	33	at	at	ADP
concept-2079	248	34	various	various	ADJ
concept-2079	248	35	frequencies	frequency	NOUN
concept-2079	248	36	.	.	PUNCT
concept-2079	249	1	fractals	fractal	NOUN
concept-2079	249	2	are	be	AUX
concept-2079	249	3	also	also	ADV
concept-2079	249	4	useful	useful	ADJ
concept-2079	249	5	in	in	ADP
concept-2079	249	6	computational	computational	ADJ
concept-2079	249	7	applications	application	NOUN
concept-2079	249	8	such	such	ADJ
concept-2079	249	9	as	as	ADP
concept-2079	249	10	concept	concept	NOUN
concept-2079	249	11	,	,	PUNCT
concept-2079	249	12	vol	vol	NOUN
concept-2079	249	13	.	.	PUNCT
concept-2079	250	1	xxxix	xxxix	PROPN
concept-2079	250	2	(	(	PUNCT
concept-2079	250	3	2016	2016	NUM
concept-2079	250	4	)	)	PUNCT
concept-2079	250	5	13	13	NUM
concept-2079	250	6	image	image	NOUN
concept-2079	250	7	and	and	CCONJ
concept-2079	250	8	data	datum	NOUN
concept-2079	250	9	compression	compression	NOUN
concept-2079	250	10	,	,	PUNCT
concept-2079	250	11	as	as	ADV
concept-2079	250	12	well	well	ADV
concept-2079	250	13	as	as	ADP
concept-2079	250	14	data	data	NOUN
concept-2079	250	15	mining	mining	NOUN
concept-2079	250	16	(	(	PUNCT
concept-2079	250	17	barnsley	barnsley	NOUN
concept-2079	250	18	,	,	PUNCT
concept-2079	250	19	saupe	saupe	PROPN
concept-2079	250	20	,	,	PUNCT
concept-2079	250	21	and	and	CCONJ
concept-2079	250	22	vrscay	vrscay	NOUN
concept-2079	250	23	,	,	PUNCT
concept-2079	250	24	2	2	NUM
concept-2079	250	25	-	-	SYM
concept-2079	250	26	9	9	NUM
concept-2079	250	27	)	)	PUNCT
concept-2079	250	28	.	.	PUNCT
concept-2079	251	1	the	the	DET
concept-2079	251	2	internet	internet	NOUN
concept-2079	251	3	also	also	ADV
concept-2079	251	4	behaves	behave	VERB
concept-2079	251	5	in	in	ADP
concept-2079	251	6	fractal	fractal	ADJ
concept-2079	251	7	-	-	PUNCT
concept-2079	251	8	like	like	ADJ
concept-2079	251	9	ways	way	NOUN
concept-2079	251	10	when	when	SCONJ
concept-2079	251	11	looking	look	VERB
concept-2079	251	12	at	at	ADP
concept-2079	251	13	how	how	SCONJ
concept-2079	251	14	websites	website	NOUN
concept-2079	251	15	,	,	PUNCT
concept-2079	251	16	search	search	NOUN
concept-2079	251	17	engines	engine	NOUN
concept-2079	251	18	,	,	PUNCT
concept-2079	251	19	and	and	CCONJ
concept-2079	251	20	users	user	NOUN
concept-2079	251	21	interact	interact	VERB
concept-2079	251	22	with	with	ADP
concept-2079	251	23	each	each	DET
concept-2079	251	24	other	other	ADJ
concept-2079	251	25	.	.	PUNCT
concept-2079	252	1	the	the	DET
concept-2079	252	2	following	follow	VERB
concept-2079	252	3	observations	observation	NOUN
concept-2079	252	4	help	help	VERB
concept-2079	252	5	us	we	PRON
concept-2079	252	6	see	see	VERB
concept-2079	252	7	some	some	DET
concept-2079	252	8	patterns	pattern	NOUN
concept-2079	252	9	with	with	ADP
concept-2079	252	10	information	information	NOUN
concept-2079	252	11	transfer	transfer	NOUN
concept-2079	252	12	across	across	ADP
concept-2079	252	13	the	the	DET
concept-2079	252	14	internet	internet	NOUN
concept-2079	252	15	:	:	PUNCT
concept-2079	253	1	1	1	X
concept-2079	253	2	.	.	X
concept-2079	254	1	as	as	ADP
concept-2079	254	2	a	a	DET
concept-2079	254	3	page	page	NOUN
concept-2079	254	4	’s	’s	PART
concept-2079	254	5	connectedness	connectedness	NOUN
concept-2079	254	6	(	(	PUNCT
concept-2079	254	7	linking	link	VERB
concept-2079	254	8	of	of	ADP
concept-2079	254	9	one	one	NUM
concept-2079	254	10	page	page	NOUN
concept-2079	254	11	to	to	ADP
concept-2079	254	12	another	another	PRON
concept-2079	254	13	)	)	PUNCT
concept-2079	254	14	increases	increase	NOUN
concept-2079	254	15	,	,	PUNCT
concept-2079	254	16	traffic	traffic	NOUN
concept-2079	254	17	to	to	ADP
concept-2079	254	18	the	the	DET
concept-2079	254	19	website	website	NOUN
concept-2079	254	20	also	also	ADV
concept-2079	254	21	increases	increase	VERB
concept-2079	254	22	.	.	PUNCT
concept-2079	255	1	2	2	X
concept-2079	255	2	.	.	X
concept-2079	255	3	the	the	DET
concept-2079	255	4	more	more	ADJ
concept-2079	255	5	traffic	traffic	NOUN
concept-2079	255	6	that	that	PRON
concept-2079	255	7	a	a	DET
concept-2079	255	8	page	page	NOUN
concept-2079	255	9	generates	generate	VERB
concept-2079	255	10	,	,	PUNCT
concept-2079	255	11	the	the	PRON
concept-2079	255	12	greater	great	ADJ
concept-2079	255	13	its	its	PRON
concept-2079	255	14	connections	connection	NOUN
concept-2079	255	15	to	to	ADP
concept-2079	255	16	other	other	ADJ
concept-2079	255	17	websites	website	NOUN
concept-2079	255	18	.	.	PUNCT
concept-2079	256	1	3	3	X
concept-2079	256	2	.	.	X
concept-2079	256	3	the	the	PRON
concept-2079	256	4	greater	great	ADJ
concept-2079	256	5	a	a	DET
concept-2079	256	6	page	page	NOUN
concept-2079	256	7	’s	’s	PART
concept-2079	256	8	rank	rank	NOUN
concept-2079	256	9	(	(	PUNCT
concept-2079	256	10	where	where	SCONJ
concept-2079	256	11	it	it	PRON
concept-2079	256	12	appears	appear	VERB
concept-2079	256	13	on	on	ADP
concept-2079	256	14	a	a	DET
concept-2079	256	15	search	search	NOUN
concept-2079	256	16	engine	engine	NOUN
concept-2079	256	17	search	search	NOUN
concept-2079	256	18	)	)	PUNCT
concept-2079	256	19	,	,	PUNCT
concept-2079	256	20	the	the	PRON
concept-2079	256	21	greater	great	ADJ
concept-2079	256	22	its	its	PRON
concept-2079	256	23	traffic	traffic	NOUN
concept-2079	256	24	.	.	PUNCT
concept-2079	257	1	4	4	X
concept-2079	257	2	.	.	X
concept-2079	257	3	the	the	PRON
concept-2079	257	4	greater	great	ADJ
concept-2079	257	5	a	a	DET
concept-2079	257	6	page	page	NOUN
concept-2079	257	7	’s	’s	PART
concept-2079	257	8	rank	rank	NOUN
concept-2079	257	9	,	,	PUNCT
concept-2079	257	10	the	the	PRON
concept-2079	257	11	greater	great	ADJ
concept-2079	257	12	its	its	PRON
concept-2079	257	13	connectedness	connectedness	NOUN
concept-2079	257	14	.	.	PUNCT
concept-2079	258	1	5	5	X
concept-2079	258	2	.	.	X
concept-2079	258	3	as	as	ADP
concept-2079	258	4	the	the	DET
concept-2079	258	5	traffic	traffic	NOUN
concept-2079	258	6	increases	increase	NOUN
concept-2079	258	7	,	,	PUNCT
concept-2079	258	8	so	so	ADV
concept-2079	258	9	does	do	VERB
concept-2079	258	10	the	the	DET
concept-2079	258	11	page	page	NOUN
concept-2079	258	12	’s	’s	PART
concept-2079	258	13	rank	rank	NOUN
concept-2079	258	14	.	.	PUNCT
concept-2079	259	1	6	6	X
concept-2079	259	2	.	.	X
concept-2079	259	3	similarly	similarly	ADV
concept-2079	259	4	,	,	PUNCT
concept-2079	259	5	as	as	SCONJ
concept-2079	259	6	the	the	DET
concept-2079	259	7	page	page	NOUN
concept-2079	259	8	increases	increase	VERB
concept-2079	259	9	its	its	PRON
concept-2079	259	10	number	number	NOUN
concept-2079	259	11	of	of	ADP
concept-2079	259	12	connections	connection	NOUN
concept-2079	259	13	,	,	PUNCT
concept-2079	259	14	the	the	DET
concept-2079	259	15	ranking	ranking	NOUN
concept-2079	259	16	of	of	ADP
concept-2079	259	17	the	the	DET
concept-2079	259	18	page	page	NOUN
concept-2079	259	19	also	also	ADV
concept-2079	259	20	increases	increase	VERB
concept-2079	259	21	(	(	PUNCT
concept-2079	259	22	stewart	stewart	PROPN
concept-2079	259	23	,	,	PUNCT
concept-2079	259	24	clark	clark	PROPN
concept-2079	259	25	,	,	PUNCT
concept-2079	259	26	mandelbrot	mandelbrot	PROPN
concept-2079	259	27	,	,	PUNCT
concept-2079	259	28	et	et	PROPN
concept-2079	259	29	al	al	PROPN
concept-2079	259	30	.	.	PROPN
concept-2079	259	31	,	,	PUNCT
concept-2079	259	32	93	93	NUM
concept-2079	259	33	)	)	PUNCT
concept-2079	259	34	.	.	PUNCT
concept-2079	260	1	expanding	expand	VERB
concept-2079	260	2	on	on	ADP
concept-2079	260	3	these	these	DET
concept-2079	260	4	observations	observation	NOUN
concept-2079	260	5	to	to	PART
concept-2079	260	6	form	form	VERB
concept-2079	260	7	a	a	DET
concept-2079	260	8	type	type	NOUN
concept-2079	260	9	of	of	ADP
concept-2079	260	10	system	system	NOUN
concept-2079	260	11	,	,	PUNCT
concept-2079	260	12	you	you	PRON
concept-2079	260	13	can	can	AUX
concept-2079	260	14	see	see	VERB
concept-2079	260	15	that	that	SCONJ
concept-2079	260	16	the	the	DET
concept-2079	260	17	internet	internet	NOUN
concept-2079	260	18	can	can	AUX
concept-2079	260	19	produce	produce	VERB
concept-2079	260	20	patterns	pattern	NOUN
concept-2079	260	21	that	that	PRON
concept-2079	260	22	are	be	AUX
concept-2079	260	23	self	self	NOUN
concept-2079	260	24	-	-	PUNCT
concept-2079	260	25	organizing	organize	VERB
concept-2079	260	26	,	,	PUNCT
concept-2079	260	27	and	and	CCONJ
concept-2079	260	28	give	give	VERB
concept-2079	260	29	the	the	DET
concept-2079	260	30	overall	overall	ADJ
concept-2079	260	31	system	system	NOUN
concept-2079	260	32	some	some	DET
concept-2079	260	33	sense	sense	NOUN
concept-2079	260	34	of	of	ADP
concept-2079	260	35	predictability	predictability	NOUN
concept-2079	260	36	and	and	CCONJ
concept-2079	260	37	order	order	NOUN
concept-2079	260	38	.	.	PUNCT
concept-2079	261	1	researchers	researcher	NOUN
concept-2079	261	2	have	have	AUX
concept-2079	261	3	determined	determine	VERB
concept-2079	261	4	patterns	pattern	NOUN
concept-2079	261	5	of	of	ADP
concept-2079	261	6	self	self	NOUN
concept-2079	261	7	-	-	PUNCT
concept-2079	261	8	organization	organization	NOUN
concept-2079	261	9	within	within	ADP
concept-2079	261	10	hyperlinks	hyperlink	NOUN
concept-2079	261	11	,	,	PUNCT
concept-2079	261	12	physical	physical	ADJ
concept-2079	261	13	connections	connection	NOUN
concept-2079	261	14	providing	provide	VERB
concept-2079	261	15	access	access	NOUN
concept-2079	261	16	to	to	ADP
concept-2079	261	17	the	the	DET
concept-2079	261	18	internet	internet	NOUN
concept-2079	261	19	,	,	PUNCT
concept-2079	261	20	the	the	DET
concept-2079	261	21	information	information	NOUN
concept-2079	261	22	being	be	AUX
concept-2079	261	23	exchanged	exchange	VERB
concept-2079	261	24	on	on	ADP
concept-2079	261	25	the	the	DET
concept-2079	261	26	internet	internet	NOUN
concept-2079	261	27	,	,	PUNCT
concept-2079	261	28	in	in	ADP
concept-2079	261	29	the	the	DET
concept-2079	261	30	form	form	NOUN
concept-2079	261	31	of	of	ADP
concept-2079	261	32	files	file	NOUN
concept-2079	261	33	,	,	PUNCT
concept-2079	261	34	traffic	traffic	NOUN
concept-2079	261	35	patterns	pattern	NOUN
concept-2079	261	36	of	of	ADP
concept-2079	261	37	data	datum	NOUN
concept-2079	261	38	transmitted	transmit	VERB
concept-2079	261	39	,	,	PUNCT
concept-2079	261	40	and	and	CCONJ
concept-2079	261	41	the	the	DET
concept-2079	261	42	ways	way	NOUN
concept-2079	261	43	in	in	ADP
concept-2079	261	44	which	which	PRON
concept-2079	261	45	people	people	NOUN
concept-2079	261	46	are	be	AUX
concept-2079	261	47	accessing	access	VERB
concept-2079	261	48	the	the	DET
concept-2079	261	49	data	datum	NOUN
concept-2079	261	50	(	(	PUNCT
concept-2079	261	51	stewart	stewart	PROPN
concept-2079	261	52	,	,	PUNCT
concept-2079	261	53	clark	clark	PROPN
concept-2079	261	54	,	,	PUNCT
concept-2079	261	55	mandelbrot	mandelbrot	PROPN
concept-2079	261	56	,	,	PUNCT
concept-2079	261	57	et	et	PROPN
concept-2079	261	58	al	al	PROPN
concept-2079	261	59	.	.	PROPN
concept-2079	261	60	,	,	PUNCT
concept-2079	261	61	94	94	NUM
concept-2079	261	62	)	)	PUNCT
concept-2079	261	63	.	.	PUNCT
concept-2079	262	1	computer	computer	NOUN
concept-2079	262	2	scientists	scientist	NOUN
concept-2079	262	3	use	use	VERB
concept-2079	262	4	a	a	DET
concept-2079	262	5	power	power	NOUN
concept-2079	262	6	-	-	PUNCT
concept-2079	262	7	law	law	NOUN
concept-2079	262	8	distribution	distribution	NOUN
concept-2079	262	9	to	to	PART
concept-2079	262	10	study	study	VERB
concept-2079	262	11	these	these	DET
concept-2079	262	12	types	type	NOUN
concept-2079	262	13	of	of	ADP
concept-2079	262	14	phenomenon	phenomenon	NOUN
concept-2079	262	15	,	,	PUNCT
concept-2079	262	16	similar	similar	ADJ
concept-2079	262	17	to	to	ADP
concept-2079	262	18	the	the	DET
concept-2079	262	19	techniques	technique	NOUN
concept-2079	262	20	of	of	ADP
concept-2079	262	21	the	the	DET
concept-2079	262	22	econophysicists	econophysicist	NOUN
concept-2079	262	23	.	.	PUNCT
concept-2079	263	1	they	they	PRON
concept-2079	263	2	discovered	discover	VERB
concept-2079	263	3	that	that	SCONJ
concept-2079	263	4	when	when	SCONJ
concept-2079	263	5	looking	look	VERB
concept-2079	263	6	at	at	ADP
concept-2079	263	7	data	data	NOUN
concept-2079	263	8	traffic	traffic	NOUN
concept-2079	263	9	,	,	PUNCT
concept-2079	263	10	regardless	regardless	ADV
concept-2079	263	11	of	of	ADP
concept-2079	263	12	the	the	DET
concept-2079	263	13	time	time	NOUN
concept-2079	263	14	scale	scale	NOUN
concept-2079	263	15	,	,	PUNCT
concept-2079	263	16	self	self	NOUN
concept-2079	263	17	-	-	PUNCT
concept-2079	263	18	similarity	similarity	NOUN
concept-2079	263	19	emerges	emerge	NOUN
concept-2079	263	20	.	.	PUNCT
concept-2079	264	1	most	most	ADJ
concept-2079	264	2	of	of	ADP
concept-2079	264	3	the	the	DET
concept-2079	264	4	internet	internet	NOUN
concept-2079	264	5	traffic	traffic	NOUN
concept-2079	264	6	is	be	AUX
concept-2079	264	7	small	small	ADJ
concept-2079	264	8	,	,	PUNCT
concept-2079	264	9	checking	check	VERB
concept-2079	264	10	an	an	DET
concept-2079	264	11	email	email	NOUN
concept-2079	264	12	,	,	PUNCT
concept-2079	264	13	or	or	CCONJ
concept-2079	264	14	browsing	browse	VERB
concept-2079	264	15	a	a	DET
concept-2079	264	16	website	website	NOUN
concept-2079	264	17	.	.	PUNCT
concept-2079	265	1	however	however	ADV
concept-2079	265	2	,	,	PUNCT
concept-2079	265	3	this	this	DET
concept-2079	265	4	trend	trend	NOUN
concept-2079	265	5	is	be	AUX
concept-2079	265	6	often	often	ADV
concept-2079	265	7	interrupted	interrupt	VERB
concept-2079	265	8	by	by	ADP
concept-2079	265	9	spikes	spike	NOUN
concept-2079	265	10	of	of	ADP
concept-2079	265	11	high	high	ADJ
concept-2079	265	12	data	datum	NOUN
concept-2079	265	13	transfers	transfer	NOUN
concept-2079	265	14	,	,	PUNCT
concept-2079	265	15	such	such	ADJ
concept-2079	265	16	as	as	ADP
concept-2079	265	17	when	when	SCONJ
concept-2079	265	18	someone	someone	PRON
concept-2079	265	19	streams	stream	VERB
concept-2079	265	20	video	video	NOUN
concept-2079	265	21	on	on	ADP
concept-2079	265	22	netflix	netflix	PROPN
concept-2079	265	23	.	.	PUNCT
concept-2079	266	1	mathematically	mathematically	ADV
concept-2079	266	2	,	,	PUNCT
concept-2079	266	3	the	the	DET
concept-2079	266	4	self	self	NOUN
concept-2079	266	5	-	-	PUNCT
concept-2079	266	6	similarity	similarity	NOUN
concept-2079	266	7	and	and	CCONJ
concept-2079	266	8	self	self	NOUN
concept-2079	266	9	-	-	PUNCT
concept-2079	266	10	organizing	organize	VERB
concept-2079	266	11	results	result	NOUN
concept-2079	266	12	are	be	AUX
concept-2079	266	13	due	due	ADJ
concept-2079	266	14	to	to	ADP
concept-2079	266	15	the	the	DET
concept-2079	266	16	power	power	NOUN
concept-2079	266	17	law	law	NOUN
concept-2079	266	18	,	,	PUNCT
concept-2079	266	19	which	which	PRON
concept-2079	266	20	states	state	VERB
concept-2079	266	21	,	,	PUNCT
concept-2079	266	22	“	"	PUNCT
concept-2079	266	23	the	the	DET
concept-2079	266	24	frequency	frequency	NOUN
concept-2079	266	25	of	of	ADP
concept-2079	266	26	an	an	DET
concept-2079	266	27	item	item	NOUN
concept-2079	266	28	of	of	ADP
concept-2079	266	29	size	size	NOUN
concept-2079	266	30	x	x	X
concept-2079	266	31	is	be	AUX
concept-2079	266	32	proportional	proportional	ADJ
concept-2079	266	33	to	to	ADP
concept-2079	266	34	x	x	NOUN
concept-2079	266	35	-	-	PUNCT
concept-2079	266	36	b	b	NOUN
concept-2079	266	37	,	,	PUNCT
concept-2079	266	38	where	where	SCONJ
concept-2079	266	39	b	b	NOUN
concept-2079	266	40	is	be	AUX
concept-2079	266	41	a	a	DET
concept-2079	266	42	constant	constant	ADJ
concept-2079	266	43	”	"	PUNCT
concept-2079	266	44	(	(	PUNCT
concept-2079	266	45	stewart	stewart	PROPN
concept-2079	266	46	,	,	PUNCT
concept-2079	266	47	clark	clark	PROPN
concept-2079	266	48	,	,	PUNCT
concept-2079	266	49	mandelbrot	mandelbrot	PROPN
concept-2079	266	50	,	,	PUNCT
concept-2079	266	51	et	et	PROPN
concept-2079	266	52	al	al	PROPN
concept-2079	266	53	.	.	PROPN
concept-2079	266	54	,	,	PUNCT
concept-2079	266	55	96	96	NUM
concept-2079	266	56	)	)	PUNCT
concept-2079	266	57	.	.	PUNCT
concept-2079	267	1	the	the	DET
concept-2079	267	2	power	power	NOUN
concept-2079	267	3	law	law	NOUN
concept-2079	267	4	,	,	PUNCT
concept-2079	267	5	also	also	ADV
concept-2079	267	6	known	know	VERB
concept-2079	267	7	as	as	ADP
concept-2079	267	8	the	the	DET
concept-2079	267	9	power	power	NOUN
concept-2079	267	10	law	law	NOUN
concept-2079	267	11	distribution	distribution	NOUN
concept-2079	267	12	,	,	PUNCT
concept-2079	267	13	is	be	AUX
concept-2079	267	14	called	call	VERB
concept-2079	267	15	heavy	heavy	ADV
concept-2079	267	16	-	-	PUNCT
concept-2079	267	17	tailed	tailed	ADJ
concept-2079	267	18	because	because	SCONJ
concept-2079	267	19	the	the	DET
concept-2079	267	20	right	right	ADJ
concept-2079	267	21	side	side	NOUN
concept-2079	267	22	of	of	ADP
concept-2079	267	23	the	the	DET
concept-2079	267	24	distribution	distribution	NOUN
concept-2079	267	25	contains	contain	VERB
concept-2079	267	26	more	more	ADJ
concept-2079	267	27	data	datum	NOUN
concept-2079	267	28	points	point	NOUN
concept-2079	267	29	than	than	ADP
concept-2079	267	30	the	the	DET
concept-2079	267	31	other	other	ADJ
concept-2079	267	32	parts	part	NOUN
concept-2079	267	33	of	of	ADP
concept-2079	267	34	the	the	DET
concept-2079	267	35	distribution	distribution	NOUN
concept-2079	267	36	(	(	PUNCT
concept-2079	267	37	in	in	ADP
concept-2079	267	38	comparison	comparison	NOUN
concept-2079	267	39	to	to	ADP
concept-2079	267	40	the	the	DET
concept-2079	267	41	gaussian	gaussian	NOUN
concept-2079	267	42	or	or	CCONJ
concept-2079	267	43	normal	normal	ADJ
concept-2079	267	44	distribution	distribution	NOUN
concept-2079	267	45	)	)	PUNCT
concept-2079	267	46	.	.	PUNCT
concept-2079	268	1	fractals	fractal	NOUN
concept-2079	268	2	in	in	ADP
concept-2079	268	3	education	education	NOUN
concept-2079	268	4	in	in	ADP
concept-2079	268	5	our	our	PRON
concept-2079	268	6	final	final	ADJ
concept-2079	268	7	analysis	analysis	NOUN
concept-2079	268	8	of	of	ADP
concept-2079	268	9	applications	application	NOUN
concept-2079	268	10	to	to	ADP
concept-2079	268	11	the	the	DET
concept-2079	268	12	real	real	ADJ
concept-2079	268	13	world	world	NOUN
concept-2079	268	14	,	,	PUNCT
concept-2079	268	15	we	we	PRON
concept-2079	268	16	will	will	AUX
concept-2079	268	17	discuss	discuss	VERB
concept-2079	268	18	how	how	SCONJ
concept-2079	268	19	secondary	secondary	ADJ
concept-2079	268	20	mathematics	mathematics	NOUN
concept-2079	268	21	teachers	teacher	NOUN
concept-2079	268	22	might	might	AUX
concept-2079	268	23	instruct	instruct	VERB
concept-2079	268	24	students	student	NOUN
concept-2079	268	25	about	about	ADP
concept-2079	268	26	fractals	fractal	NOUN
concept-2079	268	27	.	.	PUNCT
concept-2079	269	1	although	although	SCONJ
concept-2079	269	2	concept	concept	NOUN
concept-2079	269	3	,	,	PUNCT
concept-2079	269	4	vol	vol	NOUN
concept-2079	269	5	.	.	PUNCT
concept-2079	269	6	xxxix	xxxix	PROPN
concept-2079	269	7	(	(	PUNCT
concept-2079	269	8	2016	2016	NUM
concept-2079	269	9	)	)	PUNCT
concept-2079	269	10	14	14	NUM
concept-2079	269	11	fractals	fractal	NOUN
concept-2079	269	12	are	be	AUX
concept-2079	269	13	not	not	PART
concept-2079	269	14	directly	directly	ADV
concept-2079	269	15	covered	cover	VERB
concept-2079	269	16	as	as	ADP
concept-2079	269	17	a	a	DET
concept-2079	269	18	common	common	ADJ
concept-2079	269	19	core	core	NOUN
concept-2079	269	20	mathematics	mathematic	NOUN
concept-2079	269	21	standard	standard	NOUN
concept-2079	269	22	,	,	PUNCT
concept-2079	269	23	basic	basic	ADJ
concept-2079	269	24	concepts	concept	NOUN
concept-2079	269	25	regarding	regard	VERB
concept-2079	269	26	fractals	fractal	NOUN
concept-2079	269	27	can	can	AUX
concept-2079	269	28	be	be	AUX
concept-2079	269	29	taught	teach	VERB
concept-2079	269	30	indirectly	indirectly	ADV
concept-2079	269	31	.	.	PUNCT
concept-2079	270	1	fractal	fractal	ADJ
concept-2079	270	2	investigations	investigation	NOUN
concept-2079	270	3	such	such	ADJ
concept-2079	270	4	as	as	ADP
concept-2079	270	5	creating	create	VERB
concept-2079	270	6	a	a	DET
concept-2079	270	7	sierpiński	sierpiński	NOUN
concept-2079	270	8	triangle	triangle	NOUN
concept-2079	270	9	and	and	CCONJ
concept-2079	270	10	identifying	identify	VERB
concept-2079	270	11	particular	particular	ADJ
concept-2079	270	12	properties	property	NOUN
concept-2079	270	13	of	of	ADP
concept-2079	270	14	the	the	DET
concept-2079	270	15	model	model	NOUN
concept-2079	270	16	relate	relate	VERB
concept-2079	270	17	to	to	ADP
concept-2079	270	18	students	student	NOUN
concept-2079	270	19	’	'	PUNCT
concept-2079	270	20	abilities	ability	NOUN
concept-2079	270	21	to	to	PART
concept-2079	270	22	create	create	VERB
concept-2079	270	23	mathematical	mathematical	ADJ
concept-2079	270	24	models	model	NOUN
concept-2079	270	25	,	,	PUNCT
concept-2079	270	26	which	which	PRON
concept-2079	270	27	is	be	AUX
concept-2079	270	28	a	a	DET
concept-2079	270	29	common	common	ADJ
concept-2079	270	30	core	core	NOUN
concept-2079	270	31	standard	standard	NOUN
concept-2079	270	32	.	.	PUNCT
concept-2079	271	1	students	student	NOUN
concept-2079	271	2	can	can	AUX
concept-2079	271	3	explore	explore	VERB
concept-2079	271	4	the	the	DET
concept-2079	271	5	idea	idea	NOUN
concept-2079	271	6	of	of	ADP
concept-2079	271	7	fractional	fractional	ADJ
concept-2079	271	8	dimension	dimension	NOUN
concept-2079	271	9	through	through	ADP
concept-2079	271	10	observing	observe	VERB
concept-2079	271	11	and	and	CCONJ
concept-2079	271	12	quantifying	quantify	VERB
concept-2079	271	13	observations	observation	NOUN
concept-2079	271	14	they	they	PRON
concept-2079	271	15	make	make	VERB
concept-2079	271	16	about	about	ADP
concept-2079	271	17	natural	natural	ADJ
concept-2079	271	18	and	and	CCONJ
concept-2079	271	19	man	man	NOUN
concept-2079	271	20	-	-	PUNCT
concept-2079	271	21	made	make	VERB
concept-2079	271	22	phenomenon	phenomenon	NOUN
concept-2079	271	23	.	.	PUNCT
concept-2079	272	1	students	student	NOUN
concept-2079	272	2	in	in	ADP
concept-2079	272	3	algebra	algebra	NOUN
concept-2079	272	4	and	and	CCONJ
concept-2079	272	5	geometry	geometry	NOUN
concept-2079	272	6	must	must	AUX
concept-2079	272	7	understand	understand	VERB
concept-2079	272	8	ideas	idea	NOUN
concept-2079	272	9	involving	involve	VERB
concept-2079	272	10	proportions	proportion	NOUN
concept-2079	272	11	and	and	CCONJ
concept-2079	272	12	scale	scale	NOUN
concept-2079	272	13	that	that	PRON
concept-2079	272	14	directly	directly	ADV
concept-2079	272	15	relate	relate	VERB
concept-2079	272	16	to	to	ADP
concept-2079	272	17	the	the	DET
concept-2079	272	18	concept	concept	NOUN
concept-2079	272	19	of	of	ADP
concept-2079	272	20	self	self	NOUN
concept-2079	272	21	-	-	PUNCT
concept-2079	272	22	similarity	similarity	NOUN
concept-2079	272	23	.	.	PUNCT
concept-2079	273	1	the	the	DET
concept-2079	273	2	wide	wide	ADJ
concept-2079	273	3	range	range	NOUN
concept-2079	273	4	of	of	ADP
concept-2079	273	5	applications	application	NOUN
concept-2079	273	6	involving	involve	VERB
concept-2079	273	7	fractals	fractal	NOUN
concept-2079	273	8	gives	give	VERB
concept-2079	273	9	opportunities	opportunity	NOUN
concept-2079	273	10	for	for	SCONJ
concept-2079	273	11	teachers	teacher	NOUN
concept-2079	273	12	to	to	PART
concept-2079	273	13	enhance	enhance	VERB
concept-2079	273	14	and	and	CCONJ
concept-2079	273	15	widen	widen	VERB
concept-2079	273	16	the	the	DET
concept-2079	273	17	scope	scope	NOUN
concept-2079	273	18	of	of	ADP
concept-2079	273	19	their	their	PRON
concept-2079	273	20	curriculum	curriculum	NOUN
concept-2079	273	21	.	.	PUNCT
concept-2079	274	1	one	one	NUM
concept-2079	274	2	mathematician	mathematician	NOUN
concept-2079	274	3	,	,	PUNCT
concept-2079	274	4	dr	dr	PROPN
concept-2079	274	5	.	.	PROPN
concept-2079	274	6	ron	ron	PROPN
concept-2079	274	7	eglash	eglash	PROPN
concept-2079	274	8	,	,	PUNCT
concept-2079	274	9	designed	design	VERB
concept-2079	274	10	culturally	culturally	ADV
concept-2079	274	11	situated	situated	ADJ
concept-2079	274	12	design	design	NOUN
concept-2079	274	13	tools	tool	NOUN
concept-2079	274	14	(	(	PUNCT
concept-2079	274	15	csdt	csdt	NOUN
concept-2079	274	16	,	,	PUNCT
concept-2079	274	17	csdt.rpi.edu	csdt.rpi.edu	PROPN
concept-2079	274	18	)	)	PUNCT
concept-2079	274	19	,	,	PUNCT
concept-2079	274	20	for	for	SCONJ
concept-2079	274	21	teachers	teacher	NOUN
concept-2079	274	22	and	and	CCONJ
concept-2079	274	23	students	student	NOUN
concept-2079	274	24	to	to	PART
concept-2079	274	25	engage	engage	VERB
concept-2079	274	26	with	with	ADP
concept-2079	274	27	fractals	fractal	NOUN
concept-2079	274	28	.	.	PUNCT
concept-2079	275	1	the	the	DET
concept-2079	275	2	tools	tool	NOUN
concept-2079	275	3	do	do	AUX
concept-2079	275	4	not	not	PART
concept-2079	275	5	overwhelm	overwhelm	VERB
concept-2079	275	6	the	the	DET
concept-2079	275	7	students	student	NOUN
concept-2079	275	8	with	with	ADP
concept-2079	275	9	the	the	DET
concept-2079	275	10	mathematics	mathematic	NOUN
concept-2079	275	11	behind	behind	ADP
concept-2079	275	12	fractals	fractal	NOUN
concept-2079	275	13	but	but	CCONJ
concept-2079	275	14	do	do	AUX
concept-2079	275	15	provide	provide	VERB
concept-2079	275	16	teachers	teacher	NOUN
concept-2079	275	17	with	with	ADP
concept-2079	275	18	tools	tool	NOUN
concept-2079	275	19	needed	need	VERB
concept-2079	275	20	to	to	PART
concept-2079	275	21	better	well	ADV
concept-2079	275	22	explain	explain	VERB
concept-2079	275	23	the	the	DET
concept-2079	275	24	mathematical	mathematical	ADJ
concept-2079	275	25	concepts	concept	NOUN
concept-2079	275	26	to	to	ADP
concept-2079	275	27	students	student	NOUN
concept-2079	275	28	.	.	PUNCT
concept-2079	276	1	the	the	DET
concept-2079	276	2	java	java	PROPN
concept-2079	276	3	applets	applet	NOUN
concept-2079	276	4	allow	allow	VERB
concept-2079	276	5	the	the	DET
concept-2079	276	6	teacher	teacher	NOUN
concept-2079	276	7	to	to	ADP
concept-2079	276	8	better	well	ADV
concept-2079	276	9	differentiate	differentiate	VERB
concept-2079	276	10	(	(	PUNCT
concept-2079	276	11	meet	meet	VERB
concept-2079	276	12	the	the	DET
concept-2079	276	13	needs	need	NOUN
concept-2079	276	14	of	of	ADP
concept-2079	276	15	all	all	DET
concept-2079	276	16	the	the	DET
concept-2079	276	17	students	student	NOUN
concept-2079	276	18	in	in	ADP
concept-2079	276	19	the	the	DET
concept-2079	276	20	classroom	classroom	NOUN
concept-2079	276	21	)	)	PUNCT
concept-2079	276	22	as	as	SCONJ
concept-2079	276	23	they	they	PRON
concept-2079	276	24	can	can	AUX
concept-2079	276	25	explore	explore	VERB
concept-2079	276	26	the	the	DET
concept-2079	276	27	tools	tool	NOUN
concept-2079	276	28	at	at	ADP
concept-2079	276	29	their	their	PRON
concept-2079	276	30	own	own	ADJ
concept-2079	276	31	speed	speed	NOUN
concept-2079	276	32	and	and	CCONJ
concept-2079	276	33	the	the	DET
concept-2079	276	34	teacher	teacher	NOUN
concept-2079	276	35	can	can	AUX
concept-2079	276	36	generate	generate	VERB
concept-2079	276	37	extension	extension	NOUN
concept-2079	276	38	activities	activity	NOUN
concept-2079	276	39	based	base	VERB
concept-2079	276	40	on	on	ADP
concept-2079	276	41	the	the	DET
concept-2079	276	42	needs	need	NOUN
concept-2079	276	43	of	of	ADP
concept-2079	276	44	the	the	DET
concept-2079	276	45	students	student	NOUN
concept-2079	276	46	.	.	PUNCT
concept-2079	277	1	one	one	NUM
concept-2079	277	2	positive	positive	ADJ
concept-2079	277	3	benefit	benefit	NOUN
concept-2079	277	4	of	of	ADP
concept-2079	277	5	using	use	VERB
concept-2079	277	6	the	the	DET
concept-2079	277	7	csdt	csdt	NOUN
concept-2079	277	8	tools	tool	NOUN
concept-2079	277	9	is	be	AUX
concept-2079	277	10	that	that	SCONJ
concept-2079	277	11	students	student	NOUN
concept-2079	277	12	make	make	VERB
concept-2079	277	13	the	the	DET
concept-2079	277	14	connection	connection	NOUN
concept-2079	277	15	between	between	ADP
concept-2079	277	16	mathematics	mathematic	NOUN
concept-2079	277	17	and	and	CCONJ
concept-2079	277	18	the	the	DET
concept-2079	277	19	real	real	ADJ
concept-2079	277	20	world	world	NOUN
concept-2079	277	21	,	,	PUNCT
concept-2079	277	22	often	often	ADV
concept-2079	277	23	times	time	NOUN
concept-2079	277	24	,	,	PUNCT
concept-2079	277	25	exploring	explore	VERB
concept-2079	277	26	their	their	PRON
concept-2079	277	27	own	own	ADJ
concept-2079	277	28	culture	culture	NOUN
concept-2079	277	29	or	or	CCONJ
concept-2079	277	30	the	the	DET
concept-2079	277	31	cultures	culture	NOUN
concept-2079	277	32	of	of	ADP
concept-2079	277	33	their	their	PRON
concept-2079	277	34	peers	peer	NOUN
concept-2079	277	35	(	(	PUNCT
concept-2079	277	36	eglash	eglash	NOUN
concept-2079	277	37	,	,	PUNCT
concept-2079	277	38	222	222	NUM
concept-2079	277	39	-	-	NUM
concept-2079	277	40	223	223	NUM
concept-2079	277	41	)	)	PUNCT
concept-2079	277	42	.	.	PUNCT
concept-2079	278	1	this	this	PRON
concept-2079	278	2	helps	help	VERB
concept-2079	278	3	them	they	PRON
concept-2079	278	4	challenge	challenge	VERB
concept-2079	278	5	negative	negative	ADJ
concept-2079	278	6	stereotypes	stereotype	NOUN
concept-2079	278	7	they	they	PRON
concept-2079	278	8	have	have	AUX
concept-2079	278	9	regarding	regard	VERB
concept-2079	278	10	their	their	PRON
concept-2079	278	11	own	own	ADJ
concept-2079	278	12	mathematics	mathematics	NOUN
concept-2079	278	13	abilities	ability	NOUN
concept-2079	278	14	as	as	ADV
concept-2079	278	15	well	well	ADV
concept-2079	278	16	as	as	ADP
concept-2079	278	17	their	their	PRON
concept-2079	278	18	peers	peer	NOUN
concept-2079	278	19	,	,	PUNCT
concept-2079	278	20	a	a	DET
concept-2079	278	21	powerful	powerful	ADJ
concept-2079	278	22	way	way	NOUN
concept-2079	278	23	to	to	PART
concept-2079	278	24	address	address	VERB
concept-2079	278	25	issues	issue	NOUN
concept-2079	278	26	of	of	ADP
concept-2079	278	27	race	race	NOUN
concept-2079	278	28	and	and	CCONJ
concept-2079	278	29	class	class	NOUN
concept-2079	278	30	in	in	ADP
concept-2079	278	31	the	the	DET
concept-2079	278	32	mathematics	mathematic	NOUN
concept-2079	278	33	classroom	classroom	NOUN
concept-2079	278	34	.	.	PUNCT
concept-2079	279	1	the	the	DET
concept-2079	279	2	african	african	ADJ
concept-2079	279	3	fractals	fractal	NOUN
concept-2079	279	4	java	java	PROPN
concept-2079	279	5	applet	applet	NOUN
concept-2079	279	6	is	be	AUX
concept-2079	279	7	excellent	excellent	ADJ
concept-2079	279	8	example	example	NOUN
concept-2079	279	9	of	of	ADP
concept-2079	279	10	meshing	mesh	VERB
concept-2079	279	11	theoretical	theoretical	ADJ
concept-2079	279	12	mathematics	mathematic	NOUN
concept-2079	279	13	and	and	CCONJ
concept-2079	279	14	making	make	VERB
concept-2079	279	15	it	it	PRON
concept-2079	279	16	accessible	accessible	ADJ
concept-2079	279	17	and	and	CCONJ
concept-2079	279	18	relevant	relevant	ADJ
concept-2079	279	19	for	for	ADP
concept-2079	279	20	high	high	ADJ
concept-2079	279	21	school	school	NOUN
concept-2079	279	22	students	student	NOUN
concept-2079	279	23	.	.	PUNCT
concept-2079	280	1	the	the	DET
concept-2079	280	2	tool	tool	NOUN
concept-2079	280	3	is	be	AUX
concept-2079	280	4	divided	divide	VERB
concept-2079	280	5	into	into	ADP
concept-2079	280	6	three	three	NUM
concept-2079	280	7	sections	section	NOUN
concept-2079	280	8	,	,	PUNCT
concept-2079	280	9	background	background	NOUN
concept-2079	280	10	,	,	PUNCT
concept-2079	280	11	applications	application	NOUN
concept-2079	280	12	,	,	PUNCT
concept-2079	280	13	and	and	CCONJ
concept-2079	280	14	african	african	ADJ
concept-2079	280	15	culture	culture	NOUN
concept-2079	280	16	.	.	PUNCT
concept-2079	281	1	in	in	ADP
concept-2079	281	2	the	the	DET
concept-2079	281	3	background	background	NOUN
concept-2079	281	4	section	section	NOUN
concept-2079	281	5	,	,	PUNCT
concept-2079	281	6	students	student	NOUN
concept-2079	281	7	explore	explore	VERB
concept-2079	281	8	some	some	DET
concept-2079	281	9	fundamental	fundamental	ADJ
concept-2079	281	10	definitions	definition	NOUN
concept-2079	281	11	that	that	PRON
concept-2079	281	12	make	make	VERB
concept-2079	281	13	up	up	ADP
concept-2079	281	14	fractal	fractal	ADJ
concept-2079	281	15	geometry	geometry	NOUN
concept-2079	281	16	such	such	ADJ
concept-2079	281	17	as	as	ADP
concept-2079	281	18	recursion	recursion	NOUN
concept-2079	281	19	,	,	PUNCT
concept-2079	281	20	fractal	fractal	ADJ
concept-2079	281	21	dimension	dimension	NOUN
concept-2079	281	22	,	,	PUNCT
concept-2079	281	23	and	and	CCONJ
concept-2079	281	24	iterate	iterate	VERB
concept-2079	281	25	their	their	PRON
concept-2079	281	26	own	own	ADJ
concept-2079	281	27	fractal	fractal	ADJ
concept-2079	281	28	design	design	NOUN
concept-2079	281	29	based	base	VERB
concept-2079	281	30	on	on	ADP
concept-2079	281	31	the	the	DET
concept-2079	281	32	koch	koch	PROPN
concept-2079	281	33	curve	curve	NOUN
concept-2079	281	34	.	.	PUNCT
concept-2079	282	1	in	in	ADP
concept-2079	282	2	applications	application	NOUN
concept-2079	282	3	,	,	PUNCT
concept-2079	282	4	students	student	NOUN
concept-2079	282	5	investigate	investigate	VERB
concept-2079	282	6	and	and	CCONJ
concept-2079	282	7	design	design	VERB
concept-2079	282	8	fractals	fractal	NOUN
concept-2079	282	9	that	that	PRON
concept-2079	282	10	come	come	VERB
concept-2079	282	11	from	from	ADP
concept-2079	282	12	natural	natural	ADJ
concept-2079	282	13	occurring	occurring	NOUN
concept-2079	282	14	phenomena	phenomenon	NOUN
concept-2079	282	15	such	such	ADJ
concept-2079	282	16	as	as	ADP
concept-2079	282	17	non	non	ADJ
concept-2079	282	18	-	-	ADJ
concept-2079	282	19	linear	linear	ADJ
concept-2079	282	20	spirals	spiral	NOUN
concept-2079	282	21	from	from	ADP
concept-2079	282	22	plants	plant	NOUN
concept-2079	282	23	,	,	PUNCT
concept-2079	282	24	ferns	fern	NOUN
concept-2079	282	25	/	/	SYM
concept-2079	282	26	algae	algae	NOUN
concept-2079	282	27	,	,	PUNCT
concept-2079	282	28	iterations	iteration	NOUN
concept-2079	282	29	with	with	ADP
concept-2079	282	30	da	da	PROPN
concept-2079	282	31	vinci	vinci	PROPN
concept-2079	282	32	’s	’s	PART
concept-2079	282	33	tree	tree	NOUN
concept-2079	282	34	drawing	drawing	NOUN
concept-2079	282	35	,	,	PUNCT
concept-2079	282	36	crystal	crystal	NOUN
concept-2079	282	37	structures	structure	NOUN
concept-2079	282	38	,	,	PUNCT
concept-2079	282	39	engineering	engineer	VERB
concept-2079	282	40	such	such	ADJ
concept-2079	282	41	as	as	ADP
concept-2079	282	42	sierpiński	sierpiński	PROPN
concept-2079	282	43	gasket	gasket	NOUN
concept-2079	282	44	antenna	antenna	NOUN
concept-2079	282	45	models	model	NOUN
concept-2079	282	46	for	for	ADP
concept-2079	282	47	cell	cell	NOUN
concept-2079	282	48	phones	phone	NOUN
concept-2079	282	49	,	,	PUNCT
concept-2079	282	50	and	and	CCONJ
concept-2079	282	51	human	human	ADJ
concept-2079	282	52	structures	structure	NOUN
concept-2079	282	53	such	such	ADJ
concept-2079	282	54	as	as	ADP
concept-2079	282	55	lungs	lung	NOUN
concept-2079	282	56	.	.	PUNCT
concept-2079	283	1	finally	finally	ADV
concept-2079	283	2	,	,	PUNCT
concept-2079	283	3	in	in	ADP
concept-2079	283	4	the	the	DET
concept-2079	283	5	african	african	ADJ
concept-2079	283	6	fractals	fractal	NOUN
concept-2079	283	7	section	section	NOUN
concept-2079	283	8	,	,	PUNCT
concept-2079	283	9	they	they	PRON
concept-2079	283	10	explore	explore	VERB
concept-2079	283	11	background	background	NOUN
concept-2079	283	12	regarding	regard	VERB
concept-2079	283	13	fractals	fractal	NOUN
concept-2079	283	14	in	in	ADP
concept-2079	283	15	african	african	ADJ
concept-2079	283	16	architecture	architecture	NOUN
concept-2079	283	17	,	,	PUNCT
concept-2079	283	18	art	art	NOUN
concept-2079	283	19	,	,	PUNCT
concept-2079	283	20	religion	religion	NOUN
concept-2079	283	21	,	,	PUNCT
concept-2079	283	22	and	and	CCONJ
concept-2079	283	23	how	how	SCONJ
concept-2079	283	24	they	they	PRON
concept-2079	283	25	may	may	AUX
concept-2079	283	26	be	be	AUX
concept-2079	283	27	used	use	VERB
concept-2079	283	28	in	in	ADP
concept-2079	283	29	the	the	DET
concept-2079	283	30	future	future	NOUN
concept-2079	283	31	of	of	ADP
concept-2079	283	32	their	their	PRON
concept-2079	283	33	society	society	NOUN
concept-2079	283	34	.	.	PUNCT
concept-2079	284	1	students	student	NOUN
concept-2079	284	2	are	be	AUX
concept-2079	284	3	able	able	ADJ
concept-2079	284	4	to	to	PART
concept-2079	284	5	design	design	VERB
concept-2079	284	6	the	the	DET
concept-2079	284	7	fractals	fractal	NOUN
concept-2079	284	8	in	in	ADP
concept-2079	284	9	-	-	PUNCT
concept-2079	284	10	between	between	ADP
concept-2079	284	11	the	the	DET
concept-2079	284	12	historical	historical	ADJ
concept-2079	284	13	and	and	CCONJ
concept-2079	284	14	cultural	cultural	ADJ
concept-2079	284	15	discussions	discussion	NOUN
concept-2079	284	16	,	,	PUNCT
concept-2079	284	17	via	via	ADP
concept-2079	284	18	the	the	DET
concept-2079	284	19	java	java	NOUN
concept-2079	284	20	applets	applet	NOUN
concept-2079	284	21	(	(	PUNCT
concept-2079	284	22	eglash	eglash	NOUN
concept-2079	284	23	,	,	PUNCT
concept-2079	284	24	“	"	PUNCT
concept-2079	284	25	csdt	csdt	NOUN
concept-2079	284	26	”	"	PUNCT
concept-2079	284	27	)	)	PUNCT
concept-2079	284	28	.	.	PUNCT
concept-2079	285	1	concept	concept	NOUN
concept-2079	285	2	,	,	PUNCT
concept-2079	285	3	vol	vol	NOUN
concept-2079	285	4	.	.	PUNCT
concept-2079	286	1	xxxix	xxxix	PROPN
concept-2079	286	2	(	(	PUNCT
concept-2079	286	3	2016	2016	NUM
concept-2079	286	4	)	)	PUNCT
concept-2079	286	5	15	15	NUM
concept-2079	286	6	conclusion	conclusion	NOUN
concept-2079	286	7	we	we	PRON
concept-2079	286	8	have	have	AUX
concept-2079	286	9	discussed	discuss	VERB
concept-2079	286	10	the	the	DET
concept-2079	286	11	mathematical	mathematical	ADJ
concept-2079	286	12	roots	root	NOUN
concept-2079	286	13	of	of	ADP
concept-2079	286	14	fractal	fractal	ADJ
concept-2079	286	15	geometry	geometry	NOUN
concept-2079	286	16	,	,	PUNCT
concept-2079	286	17	applications	application	NOUN
concept-2079	286	18	to	to	ADP
concept-2079	286	19	the	the	DET
concept-2079	286	20	real	real	ADJ
concept-2079	286	21	world	world	NOUN
concept-2079	286	22	,	,	PUNCT
concept-2079	286	23	and	and	CCONJ
concept-2079	286	24	finally	finally	ADV
concept-2079	286	25	,	,	PUNCT
concept-2079	286	26	ways	way	NOUN
concept-2079	286	27	of	of	ADP
concept-2079	286	28	introducing	introduce	VERB
concept-2079	286	29	secondary	secondary	ADJ
concept-2079	286	30	students	student	NOUN
concept-2079	286	31	to	to	ADP
concept-2079	286	32	this	this	DET
concept-2079	286	33	topic	topic	NOUN
concept-2079	286	34	.	.	PUNCT
concept-2079	287	1	as	as	SCONJ
concept-2079	287	2	more	more	ADJ
concept-2079	287	3	research	research	NOUN
concept-2079	287	4	is	be	AUX
concept-2079	287	5	done	do	VERB
concept-2079	287	6	utilizing	utilize	VERB
concept-2079	287	7	fractals	fractal	NOUN
concept-2079	287	8	in	in	ADP
concept-2079	287	9	both	both	CCONJ
concept-2079	287	10	pure	pure	ADJ
concept-2079	287	11	and	and	CCONJ
concept-2079	287	12	applied	applied	ADJ
concept-2079	287	13	settings	setting	NOUN
concept-2079	287	14	,	,	PUNCT
concept-2079	287	15	scientists	scientist	NOUN
concept-2079	287	16	,	,	PUNCT
concept-2079	287	17	mathematicians	mathematician	NOUN
concept-2079	287	18	,	,	PUNCT
concept-2079	287	19	econophysicists	econophysicist	NOUN
concept-2079	287	20	,	,	PUNCT
concept-2079	287	21	and	and	CCONJ
concept-2079	287	22	computer	computer	NOUN
concept-2079	287	23	scientists	scientist	NOUN
concept-2079	287	24	will	will	AUX
concept-2079	287	25	find	find	VERB
concept-2079	287	26	ways	way	NOUN
concept-2079	287	27	to	to	PART
concept-2079	287	28	better	well	ADV
concept-2079	287	29	explain	explain	VERB
concept-2079	287	30	phenomena	phenomenon	NOUN
concept-2079	287	31	using	use	VERB
concept-2079	287	32	this	this	DET
concept-2079	287	33	tool	tool	NOUN
concept-2079	287	34	of	of	ADP
concept-2079	287	35	mathematics	mathematic	NOUN
concept-2079	287	36	.	.	PUNCT
concept-2079	288	1	the	the	DET
concept-2079	288	2	future	future	NOUN
concept-2079	288	3	looks	look	VERB
concept-2079	288	4	bright	bright	ADJ
concept-2079	288	5	for	for	ADP
concept-2079	288	6	fractals	fractal	NOUN
concept-2079	288	7	!	!	PUNCT
concept-2079	289	1	bibliography	bibliography	NOUN
concept-2079	289	2	barnsley	barnsley	PROPN
concept-2079	289	3	,	,	PUNCT
concept-2079	289	4	michael	michael	PROPN
concept-2079	289	5	.	.	PUNCT
concept-2079	290	1	fractals	fractal	NOUN
concept-2079	290	2	everywhere	everywhere	ADV
concept-2079	290	3	,	,	PUNCT
concept-2079	290	4	second	second	ADJ
concept-2079	290	5	edition	edition	NOUN
concept-2079	290	6	.	.	PUNCT
concept-2079	291	1	ed	ed	NOUN
concept-2079	291	2	.	.	PUNCT
concept-2079	292	1	cambridge	cambridge	PROPN
concept-2079	292	2	,	,	PUNCT
concept-2079	292	3	ma	ma	PROPN
concept-2079	292	4	:	:	PUNCT
concept-2079	292	5	academic	academic	ADJ
concept-2079	292	6	press	press	PROPN
concept-2079	292	7	,	,	PUNCT
concept-2079	292	8	inc	inc	PROPN
concept-2079	292	9	.	.	PROPN
concept-2079	292	10	,	,	PUNCT
concept-2079	292	11	1993	1993	NUM
concept-2079	292	12	.	.	PUNCT
concept-2079	293	1	print	print	NOUN
concept-2079	293	2	.	.	PUNCT
concept-2079	294	1	barnsley	barnsley	PROPN
concept-2079	294	2	,	,	PUNCT
concept-2079	294	3	michael	michael	PROPN
concept-2079	294	4	,	,	PUNCT
concept-2079	294	5	dietmar	dietmar	PROPN
concept-2079	294	6	saupe	saupe	PROPN
concept-2079	294	7	,	,	PUNCT
concept-2079	294	8	and	and	CCONJ
concept-2079	294	9	edward	edward	PROPN
concept-2079	294	10	vrscay	vrscay	NOUN
concept-2079	294	11	.	.	PUNCT
concept-2079	295	1	fractals	fractal	NOUN
concept-2079	295	2	in	in	ADP
concept-2079	295	3	multimedia	multimedia	NOUN
concept-2079	295	4	.	.	PUNCT
concept-2079	296	1	newyork	newyork	NOUN
concept-2079	296	2	:	:	PUNCT
concept-2079	296	3	springer	springer	NOUN
concept-2079	296	4	-	-	PUNCT
concept-2079	296	5	verlag	verlag	PROPN
concept-2079	296	6	,	,	PUNCT
concept-2079	296	7	2002	2002	NUM
concept-2079	296	8	.	.	PUNCT
concept-2079	297	1	print	print	NOUN
concept-2079	297	2	.	.	PUNCT
concept-2079	298	1	banu	banu	PROPN
concept-2079	298	2	,	,	PUNCT
concept-2079	298	3	s.	s.	PROPN
concept-2079	298	4	,	,	PUNCT
concept-2079	298	5	j.	j.	PROPN
concept-2079	298	6	barba	barba	PROPN
concept-2079	298	7	,	,	PUNCT
concept-2079	298	8	and	and	CCONJ
concept-2079	298	9	k.s	k.s	PROPN
concept-2079	298	10	.	.	PROPN
concept-2079	298	11	chan	chan	PROPN
concept-2079	298	12	.	.	PUNCT
concept-2079	299	1	“	"	PUNCT
concept-2079	299	2	texture	texture	ADJ
concept-2079	299	3	analysis	analysis	NOUN
concept-2079	299	4	in	in	ADP
concept-2079	299	5	cytology	cytology	NOUN
concept-2079	299	6	using	use	VERB
concept-2079	299	7	fractals	fractal	NOUN
concept-2079	299	8	.	.	PUNCT
concept-2079	299	9	”	"	PUNCT
concept-2079	300	1	applications	application	NOUN
concept-2079	300	2	of	of	ADP
concept-2079	300	3	digital	digital	ADJ
concept-2079	300	4	image	image	NOUN
concept-2079	300	5	processing	process	VERB
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concept-2079	300	7	:	:	SYM
concept-2079	300	8	1990	1990	NUM
concept-2079	300	9	.	.	PUNCT
concept-2079	301	1	web	web	NOUN
concept-2079	301	2	.	.	PROPN
concept-2079	301	3	22	22	NUM
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concept-2079	301	6	>	>	X
concept-2079	301	7	brown	brown	PROPN
concept-2079	301	8	,	,	PUNCT
concept-2079	301	9	william	william	PROPN
concept-2079	301	10	.	.	PUNCT
concept-2079	302	1	“	"	PUNCT
concept-2079	302	2	mandelbrot	mandelbrot	PROPN
concept-2079	302	3	set	set	VERB
concept-2079	302	4	is	be	AUX
concept-2079	302	5	as	as	ADV
concept-2079	302	6	complicated	complicated	ADJ
concept-2079	302	7	as	as	SCONJ
concept-2079	302	8	it	it	PRON
concept-2079	302	9	could	could	AUX
concept-2079	302	10	be	be	AUX
concept-2079	302	11	.	.	PUNCT
concept-2079	302	12	”	"	PUNCT
concept-2079	303	1	new	new	ADJ
concept-2079	303	2	scientist	scientist	NOUN
concept-2079	303	3	28	28	NUM
concept-2079	303	4	sept	sept	PROPN
concept-2079	303	5	.	.	PROPN
concept-2079	303	6	1991	1991	NUM
concept-2079	303	7	:	:	PUNCT
concept-2079	303	8	n.d	n.d	PROPN
concept-2079	303	9	.	.	PROPN
concept-2079	303	10	web	web	PROPN
concept-2079	303	11	.	.	PROPN
concept-2079	303	12	17	17	NUM
concept-2079	303	13	july	july	PROPN
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concept-2079	303	15	/	/	SYM
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concept-2079	303	17	>	>	X
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concept-2079	303	19	,	,	PUNCT
concept-2079	303	20	will	will	AUX
concept-2079	303	21	.	.	PUNCT
concept-2079	304	1	“	"	PUNCT
concept-2079	304	2	fractals	fractal	NOUN
concept-2079	304	3	in	in	ADP
concept-2079	304	4	finance	finance	NOUN
concept-2079	304	5	and	and	CCONJ
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concept-2079	304	7	.	.	PUNCT
concept-2079	304	8	”	"	PUNCT
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concept-2079	305	2	dame	dame	PROPN
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concept-2079	305	4	,	,	PUNCT
concept-2079	305	5	n.d	n.d	PROPN
concept-2079	305	6	.	.	PROPN
concept-2079	305	7	web	web	PROPN
concept-2079	305	8	.	.	PROPN
concept-2079	306	1	22	22	NUM
concept-2079	306	2	july	july	PROPN
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concept-2079	306	4	.	.	PUNCT
concept-2079	307	1	<	<	X
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concept-2079	307	3	nce%20and	nce%20and	PROPN
concept-2079	307	4	%	%	NOUN
concept-2079	307	5	20risk.ppt	20risk.ppt	NUM
concept-2079	307	6	>	>	X
concept-2079	307	7	.	.	PUNCT
concept-2079	308	1	budinski	budinski	ADJ
concept-2079	308	2	-	-	PUNCT
concept-2079	308	3	petkovic	petkovic	ADJ
concept-2079	308	4	,	,	PUNCT
concept-2079	308	5	lj	lj	PROPN
concept-2079	308	6	.	.	PROPN
concept-2079	308	7	,	,	PUNCT
concept-2079	308	8	i.	i.	PROPN
concept-2079	308	9	loncarevic	loncarevic	PROPN
concept-2079	308	10	,	,	PUNCT
concept-2079	308	11	z.m	z.m	PROPN
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concept-2079	308	15	and	and	CCONJ
concept-2079	308	16	s.b	s.b	PROPN
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concept-2079	308	19	.	.	PUNCT
concept-2079	309	1	“	"	PUNCT
concept-2079	309	2	fractal	fractal	ADJ
concept-2079	309	3	properties	property	NOUN
concept-2079	309	4	of	of	ADP
concept-2079	309	5	financial	financial	ADJ
concept-2079	309	6	markets	market	NOUN
concept-2079	309	7	.	.	PUNCT
concept-2079	309	8	”	"	PUNCT
concept-2079	309	9	physica	physica	VERB
concept-2079	309	10	a	a	DET
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concept-2079	309	12	:	:	SYM
concept-2079	309	13	43	43	NUM
concept-2079	309	14	-	-	SYM
concept-2079	309	15	53	53	NUM
concept-2079	309	16	.	.	PUNCT
concept-2079	310	1	fractal	fractal	ADJ
concept-2079	310	2	properties	property	NOUN
concept-2079	310	3	of	of	ADP
concept-2079	310	4	financial	financial	ADJ
concept-2079	310	5	markets	market	NOUN
concept-2079	310	6	.	.	PUNCT
concept-2079	311	1	web	web	NOUN
concept-2079	311	2	.	.	PROPN
concept-2079	311	3	22	22	NUM
concept-2079	311	4	july	july	PROPN
concept-2079	311	5	2014	2014	NUM
concept-2079	311	6	.	.	PUNCT
concept-2079	312	1	<	<	X
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concept-2079	312	3	>	>	X
concept-2079	312	4	crilly	crilly	PROPN
concept-2079	312	5	,	,	PUNCT
concept-2079	312	6	a.j	a.j	PROPN
concept-2079	312	7	.	.	PROPN
concept-2079	312	8	,	,	PUNCT
concept-2079	312	9	r.a	r.a	PROPN
concept-2079	312	10	.	.	PROPN
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concept-2079	312	12	,	,	PUNCT
concept-2079	312	13	and	and	CCONJ
concept-2079	312	14	h.	h.	PROPN
concept-2079	312	15	jones	jones	PROPN
concept-2079	312	16	.	.	PUNCT
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concept-2079	313	2	and	and	CCONJ
concept-2079	313	3	chaos	chaos	NOUN
concept-2079	313	4	.	.	PUNCT
concept-2079	314	1	new	new	PROPN
concept-2079	314	2	york	york	PROPN
concept-2079	314	3	:	:	PUNCT
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concept-2079	314	5	-	-	PUNCT
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concept-2079	314	7	,	,	PUNCT
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concept-2079	314	9	.	.	PUNCT
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concept-2079	315	2	.	.	PUNCT
concept-2079	316	1	concept	concept	NOUN
concept-2079	316	2	,	,	PUNCT
concept-2079	316	3	vol	vol	NOUN
concept-2079	316	4	.	.	PUNCT
concept-2079	317	1	xxxix	xxxix	PROPN
concept-2079	317	2	(	(	PUNCT
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concept-2079	317	4	)	)	PUNCT
concept-2079	317	5	16	16	NUM
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concept-2079	317	7	,	,	PUNCT
concept-2079	317	8	robert	robert	PROPN
concept-2079	317	9	.	.	PROPN
concept-2079	318	1	an	an	DET
concept-2079	318	2	introduction	introduction	NOUN
concept-2079	318	3	to	to	ADP
concept-2079	318	4	chaotic	chaotic	ADJ
concept-2079	318	5	dynamical	dynamical	ADJ
concept-2079	318	6	systems	system	NOUN
concept-2079	318	7	.	.	PUNCT
concept-2079	319	1	ed	ed	NOUN
concept-2079	319	2	.	.	PUNCT
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concept-2079	319	4	,	,	PUNCT
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concept-2079	319	9	,	,	PUNCT
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concept-2079	319	11	.	.	PUNCT
concept-2079	320	1	print	print	NOUN
concept-2079	320	2	.	.	PUNCT
concept-2079	321	1	devaney	devaney	PROPN
concept-2079	321	2	,	,	PUNCT
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concept-2079	321	4	.	.	PUNCT
concept-2079	322	1	“	"	PUNCT
concept-2079	322	2	the	the	DET
concept-2079	322	3	sierpirt	sierpirt	NOUN
concept-2079	322	4	.	.	PUNCT
concept-2079	323	1	triangle	triangle	NOUN
concept-2079	323	2	.	.	PUNCT
concept-2079	323	3	”	"	PUNCT
concept-2079	324	1	n.p	n.p	PROPN
concept-2079	324	2	.	.	PROPN
concept-2079	324	3	,	,	PUNCT
concept-2079	324	4	2	2	NUM
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concept-2079	324	6	.	.	NOUN
concept-2079	324	7	1995	1995	NUM
concept-2079	324	8	.	.	PUNCT
concept-2079	325	1	web	web	NOUN
concept-2079	325	2	.	.	PROPN
concept-2079	326	1	10	10	NUM
concept-2079	326	2	july	july	PROPN
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concept-2079	326	4	.	.	PUNCT
concept-2079	327	1	<	<	X
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concept-2079	327	5	,	,	PUNCT
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concept-2079	327	7	.	.	PUNCT
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concept-2079	328	2	fractals	fractal	NOUN
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concept-2079	328	5	computing	computing	NOUN
concept-2079	328	6	and	and	CCONJ
concept-2079	328	7	indigenous	indigenous	ADJ
concept-2079	328	8	design	design	NOUN
concept-2079	328	9	.	.	PUNCT
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concept-2079	329	2	,	,	PUNCT
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concept-2079	330	2	.	.	PUNCT
concept-2079	331	1	eglash	eglash	PROPN
concept-2079	331	2	,	,	PUNCT
concept-2079	331	3	ron	ron	PROPN
concept-2079	331	4	.	.	PUNCT
concept-2079	332	1	“	"	PUNCT
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concept-2079	332	10	computing	compute	VERB
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concept-2079	332	12	culture	culture	NOUN
concept-2079	332	13	.	.	PUNCT
concept-2079	332	14	”	"	PUNCT
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concept-2079	333	9	.	.	PUNCT
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concept-2079	335	4	.	.	PUNCT
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concept-2079	392	48	barnsley	barnsley	PROPN
concept-2079	392	49	,	,	PUNCT
concept-2079	392	50	louisa	louisa	PROPN
concept-2079	392	51	barnsley	barnsley	PROPN
concept-2079	392	52	,	,	PUNCT
concept-2079	392	53	will	will	AUX
concept-2079	392	54	rood	rood	VERB
concept-2079	392	55	,	,	PUNCT
concept-2079	392	56	gary	gary	PROPN
concept-2079	392	57	flake	flake	PROPN
concept-2079	392	58	,	,	PUNCT
concept-2079	392	59	david	david	PROPN
concept-2079	392	60	pennock	pennock	PROPN
concept-2079	392	61	,	,	PUNCT
concept-2079	392	62	and	and	CCONJ
concept-2079	392	63	nigel	nigel	PROPN
concept-2079	392	64	lesmoirgordon	lesmoirgordon	PROPN
concept-2079	392	65	.	.	PUNCT
concept-2079	393	1	the	the	DET
concept-2079	393	2	colours	colour	NOUN
concept-2079	393	3	of	of	ADP
concept-2079	393	4	infinity	infinity	NOUN
concept-2079	393	5	:	:	PUNCT
concept-2079	393	6	the	the	DET
concept-2079	393	7	beauty	beauty	NOUN
concept-2079	393	8	and	and	CCONJ
concept-2079	393	9	power	power	NOUN
concept-2079	393	10	of	of	ADP
concept-2079	393	11	fractals	fractal	NOUN
concept-2079	393	12	.	.	PUNCT
concept-2079	394	1	london	london	PROPN
concept-2079	394	2	:	:	PUNCT
concept-2079	394	3	springer	springer	NOUN
concept-2079	394	4	-	-	PUNCT
concept-2079	394	5	verlag	verlag	PROPN
concept-2079	394	6	,	,	PUNCT
concept-2079	394	7	2010	2010	NUM
concept-2079	394	8	.	.	PUNCT
concept-2079	395	1	print	print	NOUN
concept-2079	395	2	.	.	PUNCT
concept-2079	396	1	smith	smith	PROPN
concept-2079	396	2	,	,	PUNCT
concept-2079	396	3	t.g	t.g	PROPN
concept-2079	396	4	.	.	PROPN
concept-2079	396	5	,	,	PUNCT
concept-2079	396	6	g.d	g.d	PROPN
concept-2079	396	7	.	.	PROPN
concept-2079	396	8	lange	lange	PROPN
concept-2079	396	9	,	,	PUNCT
concept-2079	396	10	and	and	CCONJ
concept-2079	396	11	w.b	w.b	PROPN
concept-2079	396	12	.	.	PROPN
concept-2079	396	13	marks	marks	PROPN
concept-2079	396	14	.	.	PUNCT
concept-2079	397	1	“	"	PUNCT
concept-2079	397	2	fractal	fractal	ADJ
concept-2079	397	3	methods	method	NOUN
concept-2079	397	4	and	and	CCONJ
concept-2079	397	5	results	result	NOUN
concept-2079	397	6	in	in	ADP
concept-2079	397	7	cellular	cellular	ADJ
concept-2079	397	8	morphology	morphology	NOUN
concept-2079	397	9	--	--	PUNCT
concept-2079	397	10	dimensions	dimension	NOUN
concept-2079	397	11	,	,	PUNCT
concept-2079	397	12	lacunarity	lacunarity	NOUN
concept-2079	397	13	and	and	CCONJ
concept-2079	397	14	multifractals	multifractal	NOUN
concept-2079	397	15	..	..	PUNCT
concept-2079	397	16	”	"	PUNCT
concept-2079	397	17	journal	journal	NOUN
concept-2079	397	18	of	of	ADP
concept-2079	397	19	neuroscience	neuroscience	NOUN
concept-2079	397	20	methods	method	NOUN
concept-2079	397	21	69	69	NUM
concept-2079	397	22	:	:	PUNCT
concept-2079	397	23	123	123	NUM
concept-2079	397	24	-	-	SYM
concept-2079	397	25	136	136	NUM
concept-2079	397	26	.	.	PUNCT
concept-2079	398	1	web	web	NOUN
concept-2079	398	2	.	.	PROPN
concept-2079	399	1	22	22	NUM
concept-2079	399	2	july	july	PROPN
concept-2079	399	3	2014	2014	NUM
concept-2079	399	4	.	.	PUNCT
concept-2079	400	1	<	<	X
concept-2079	400	2	http://www.sciencedirect.com/science/article/pii/s0165027096000805	http://www.sciencedirect.com/science/article/pii/s0165027096000805	X
concept-2079	400	3	>	>	X