하미드 나데리 예가네

하미드 나데리 예가네
하미드 나데리 예가네
	Naderi Yeganeh와 그의 작품 A Bird in Flight의 디지털 인쇄물
태어난	( 1990년 7월 26일 (32세); 콤, 이란
국적.	이란어
모교	샤리프 공과대학(M.Sc.); 쿰 대학교 (B.Sc.)
로 알려져 있다	수리 예술
어워드	제38회 IMS 대회 금메달; 제38회 IMS 대회 은메달;

하미드 나데리 예가네(Persian: می ye ye ye ye ye ye ye born born born born born born born born born born born born born born born born born born born born born born born born born born born born, 1990년 7월 26일^[1] ~ )는 이란의 수학 예술가이자 디지털 아티스트이다.^[2]^[3]^[4]그는 실제 사물, 복잡하고 대칭적인 일러스트, 애니메이션, 프랙탈 및 테셀레이션의 ^[5]^[6]^[7]^[8]^[9]그림을 그리기 위해 수학 공식을 사용하는 것으로 알려져 있다.나데리 예가네는 수학을 미술품을 만드는 주요 도구로 사용한다.^[10]그러므로, 그의 작품들은 완전히 수학적 ^[11]^[2]개념으로 묘사될 수 있다.그가 그의 작업에서 사용하는 수학적 개념은 삼각함수, 지수함수, 피보나치 수열, 톱니파 ^[12]^[13]^[14]^[15]등을 포함한다.

그의 아트워크 9,000 Ellipses는 The American Mathemical Monthly – 2017년 ^[16]^[17]^[18]^[19]11월의 배경 표지 이미지로 사용되었습니다.그의 작품 하트는 미국 수학 ^[20]^[21]협회가 발행하는 2016년 Calendar of Mathematical Images의 2월 페이지에 이미지로 사용되었습니다.2018년 미국 시애틀 센터 온 ^[22]^[23]^[24]컨템포러리 아트(Center on Contemporary Art)에서 열린 아트★매스 전시의 엽서 이미지로 그의 아트버드가 활용됐다.나데리 예가네의 작품 중 하나가 2015년 ^[25]가을 이란 수학회 뉴스레터 표지 이미지로 사용되었습니다.A Bird in Flight and Boat를 포함한 그의 작품은 국제수학지식신탁(IMKT)^[26]^[27]^[28] 웹사이트의 여러 페이지에 사용되고 있다.그의 작품인 A Bird in Flight는 맥마스터 ^[5]대학의 생명과학 프로그램의 출판물인 STATure의 1권 전 페이지에 사용되었습니다.

교육

나데리 예가네는 쿰^[29] 대학에서 수학 학사 학위를 받았고 M 학위를 받았습니다.샤리프 ^[30]^[31]^[29]공과대학 순수 수학 박사그의 MSC 논문은 동적 시스템에서 ^[32]불변 다양체의 근사 및 시각화를 위한 수치 방법에 초점을 맞췄다.2014년 5월 고등기술대학원에서 열린 제38회 이란수학회 전국수학대회에서 금메달을, 2015년 ^[33]^[34]^[35]^[36]5월 야즈드대에서 열린 제39회 IMS 전국수학대회에서 은메달을 획득했다.2013년부터 2020년까지 대학 예산 관리에 의해 발행되고 이란 MSRT에 의해 발행된 Qom 대학의 성과와 통계에 대한 특별 보고서에는 2013년 대학 학생들의 5대 뛰어난 업적 중 하나로 Naderi Yeganeh가 제38회 IMS 수학 대회에서 금메달을 획득했다고 나와 있다.-^[37] 시간 간격입니다.제38회 IMS 경기위원 중 한 명에 따르면 쿰 대학 학생이 금메달을 딴 것이 이 ^[38]대회의 하이라이트였다.

작동하다

실물의 도면

나데리 예가네는 수학 ^[4]공식으로 실물을 그리는 두 가지 방법을 도입했다.첫 번째 방법으로, 그는 우연히 몇 개의 흥미로운 도형을 찾기 위해 수만 개의 컴퓨터로 만들어진 수학 도형을 만듭니다.그리고 그는 우연히 발견된 모양과 실제 ^[39]^[40]물체의 유사성을 높이기 위해 방정식을 조금 바꿨다.예를 들어, 그는 이 방법을 사용하여 새, 물고기, ^[41]^[42]^[43]^[44]범선과 비슷한 모양을 발견했다.두 번째 방법에서는 단계별로 실제 물체를 그린다.각 단계에서 그는 어떤 수학 공식이 그림을 ^[45]^[4]만들어 낼지 알아내려고 한다.예를 들어, 그는 삼각함수를 ^[46]^[47]^[48]^[45]^[49]^[50]이용하여 나는 새, 나비, 사람의 얼굴, 식물을 그렸다.Naderi Yeganeh는 "그런 모양을 만들기 위해서는 삼각함수의 특성을 아는 것이 매우 유용합니다."^[51]^[46]라고 말합니다.2018년 샤리프 공과대학 홍보담당과의 인터뷰에서 Naderi Yeganeh는 다음과 같이 말했다.저는 수학적 개념을 한 단락에서 충분히 설명할 수 있는 방식으로 예술작품에 사용합니다.그것은 예술작품의 과학적 토대를 더 쉽게 이해할 ^[52]수 있게 해준다.

날아다니는 새

Naderi Yeganeh가 그의 첫 번째 방법으로 만든 500개의 선분들로 구성된 A Bird in Flight의 버전입니다.

비행 중인 새의 또 다른 버전은 20,001개의 원으로 이루어졌는데, 나데리 예가네는 그의 두 번째 ^[47]방법으로 그것을 만들었다.

예가네의 방법을 사용하여 실물을 그리는 예로는 나데리 예가네에 의해 소개된 많은 새와 같은 기하학적 형상의 이름인 "날고 있는 새"가 있다.예가네는 위의 두 가지 방법으로 그림을 그렸습니다.그의 첫 번째 방법으로 만든 비행 중인 새의 예는 데카르트 평면에 정의된 500개의 세그먼트로 구성되어 있다. 여기서 k $k=1,2,3,\ldots ,500$ , $k=1,2,3,\ldots ,500$ , $3$ $500$ {\ $displaystyle$ k $= 1, 2,$ $3,\ldots,$ 500 $k=1,2,3,\ldots ,500$ }에 $대해$ k{\ $displaystyle$ k $}$ - 라인 $k$ 세그먼트의 끝점은 다음과 같다.

\leftfac {3}{2}}\sin ^{7}\leftfac {2\pi k}{500}}+{\right}, {\frac {1}{4}}\cos ^2}\frac {6\pi}{500}\right}\right

그리고.

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

sin

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

（

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

k

500

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

）

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

、

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

2

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

( （

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

k

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

-

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

3

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

）

\left({\frac {1}{5}}\sin \left({\frac {6\pi k}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\sin ^{2}\left({\frac {2\pi k}{500}}-{\frac {\pi }{3}}\right)\right)

（ 2 π k 500 - ） {

displaystyle \ left

\

frac { 6

\

pi k

} {

500

} + { \

frac

{

5

} 、 { \ frac { \ frac } } 、 { \

frac

} }

、

{ \ fright 、 { \ fright } { \

frac

{ \ frac { \

frac

} } } }

위에서 정의한 500개의 선분은 날아다니는 새와 비슷한 모양을 데카르트 평면에서 형성합니다.새의 날개에 있는 선분들을 보면 착시현상을 일으켜 보는 이로 하여금 선분들이 곡선이라고 생각하게 만들 수 있다.따라서, 그 모양은 또한 광학 ^[47]^[8]^[13]^[53]^[50]^[54]예술작품으로 여겨질 수 있다.Naderi Yeganeh의 두 번째 방법에 의해 설계된 비행 중인 새의 $R(k)$ 또 다른 버전은 모든 원의 $\left(A(k),B(k)\right)$ 중심 ( $\left(A(k),B(k)\right)$ $\left(A(k),B(k)\right)$ k $\left(A(k),B(k)\right)$ ) , $\left(A(k),B(k)\right)$ ( $\left(A(k),B(k)\right)$ ) $\left(A(k),B(k)\right)$ \ $display style$ $\left$ ( $A$ ( $k$ ) , $B$ ( $k$ ) \ right ) $\left(A(k),B(k)\right)$ } 및 $\left(A(k),B(k)\right)$ $R(k)$ R ( $R(k)$ )의 결합입니다 $k=-10000,-9999,\ldots ,9999,10000$ 서 k $k=-10000,-9999,\ldots ,9999,10000$ $k=-10000,-9999,\ldots ,9999,10000$ $k=-10000,-9999,\ldots ,9999,10000$ $k=-10000,-9999,\ldots ,9999,10000$ $k=-10000,-9999,\ldots ,9999,10000$ $k=-10000,-9999,\ldots ,9999,10000$ , , , $999,128$ 및

({displaystyle A(k)=frac {3k}{20000}+\sin \leftfrac {{pi}{2}\leftfrac {k}{right})\cos ^{6}\frac {41\pi k}{right})\cos ^{6}\cos ^{6}\fright} +\fright}

{begin{aligned}B(k)=-\cos \left cos \frac {k} {2}\right cos {1+{\frac {3} {2}}\cos ^6}\left cos \ frac {200}\fcos ^6}\right cos ^6} \ left }\&+{\frac {1}{2}}\cos ^{10}\leftfac {3\pi k}{100000}}\right)\cos ^{10}\frac {9\pi k}{100000}\right}\cos ^{10}\frac {18\pi k}{100000}\right}\cos } arnectedededdlight

R(k)=frac {1}{50}+{\frac {1}{10}}\sin ^{2}\left frac {41\pi k}{pi k}\right}\sin ^2}\frac {9\pi k}{100000}}\frcos ^{\fright}

위에서 정의한 20,001개의 원의 집합은 날아다니는 새를 닮은 데카르트 평면의 부분 집합을 형성합니다.비록 이 버전의 방정식은 500개의 세그먼트로 만들어진 버전보다 훨씬 더 복잡하지만, 그것은 실제 나는 ^[47]새와 훨씬 더 닮았다.2016년 나데리 예가네에 의해 발매된 이 버전의 비행 중인 새와 유사한 다른 작품들은 나는 앵무새, 까치,^[46] 황새의 형태이다.

프랙탈과 테셀레이션

Naderi Yeganeh는 ^[55]^[56]대륙에서 영감을 얻은 프랙탈과 테셀레이션을 디자인했습니다.예를 들어, 2015년에 그는 아프리카와 유사한 팔각형과 그 측면의 ^[41]^[14]^[57]^[25]반전을 가진 프랙탈 아프리카를 묘사했다.그리고 그는 북미와 남미 같은 ^[58]다각형으로 테셀레이션을 만들었습니다.

프랙탈 아프리카

프랙탈 아프리카는 나데리 예가네에 ^[41]^[59]의해 소개된 무한한 수의 아프리카와 유사한 팔각형으로 이루어진 프랙탈이다.프랙탈의 팔각형은 서로 비슷하고 아프리카 ^[8]^[60]지도와 어느 정도 유사합니다.프랙탈 내의 다양한 크기의 옥타곤의 수는 피보나치 시퀀스에 관련되어 있습니다.1, 2, 3, 5, 8, 13, 21, 34, ….프랙탈의 가장 큰 팔각형의 높이는 두 번째 팔각형의 높이보다 θ배 크며, 여기서 θ는 잘 알려진 ^[14]^[13]^[61]황금비이다.

전시회 및 회의

미술 ① 수학, 현대미술센터(워싱턴, 시틀),^[62] 2018년 3월 1일~4월 14일.
2018년 ^[63]4월 26일 - 6월 2일, 섀크 아트 센터 예술 + 수학 교차로.
LASER Talks in the International Society for the Arts, Sciences and Technology,^[64] 2018년 8월 10일 테헤란(이란 테란)

접수처

2015년 CNN은 나데리 예가네의 작품에 대한 동영상 제목으로 "이것이 다음 다빈치인가?"라는 질문을, CNN 아랍어는 그에 ^[65]^[66]^[67]대한 기사로 "이것이 이란 학생 다빈치의 후계자인가?"라는 제목을 사용했다.2015년 아시아 소사이어티 필리핀은 페이스북에 올린 글에서 "하미드 나데리 예가네는 예술을 통해 수학의 아름다움을 드러낸다"^[68]^[69]고 밝혔다.2015년, 국립수학박물관은 페이스북에 올린 글에서 "하미드 나데리 예가네는 그래프 예술을 한 단계 끌어올렸다!"^[70]고 말했다.2016년 수학과 응용연구소는 수학 방정식으로 사람의 얼굴을 그리는 방법을 보여주는 나데리 예가네의 블로그 투고에 대해 "수학이 ^[71]이기는 또 다른 이유"라고 논평했다.2016년 코스모스는 하미드 나데리 예가네와의 인터뷰에서 "왜 고등학교 수학은 이렇게 될 수 없었을까?"라는 질문을 던졌다.독자들이 나데리 예가네의 작품을 수학 ^[72]^[4]교육에 사용하는 가능성에 대해 생각하게 하기 위해서였다.2016년 Mathematic in Education and Industry는 트윗에서 "Hamid Naderi Yeganhe는 삼각함수로 ^[73]식물 이미지를 만든 수학 예술가입니다."라고 말했다.2016년, Barbour Design Inc.는 자체 블로그에서 "이러한 종종 섬세하게 복잡한 작품들은 꽤 놀랍고, 더 놀라운 것은 예가네가 그것들을 ^[74]생산하기 위해 수학 방정식을 기반으로 컴퓨터 프로그램을 쓴다는 것이다."라고 말했다.2017년 미국수학협회는 트윗에서 나데리 예가네의 애니메이션 중 하나에 대해 "삼각함수의 아름다움을 보라"^[75]고 평했다.2017년 필즈 인스티튜트는 트윗을 통해 ^[76]나데리 예가네의 작품을 "아름다운 수학"이라고 표현했다.2017년 버클리랩은 Naderi Yeganeh의 블로그 투고 중 하나에 대해 "몇 개의 방정식과 컴퓨터로 무장한 놀라운 대칭 이미지를 생성하라"^[77]고 논평했다.

보기

나데리 예가네는 ^[78]예술에서 수학적 도구를 사용하는 방법이 무한히 많다고 믿는다.2015년 CNN Style과의 인터뷰에서 그는 "수학의 힘은 무한하다.우리가 ^[8]^[79]만들 수 있는 훌륭한 예술작품은 무한히 많다.그는 "컴퓨터로 만든 예술이 인간의 창의성과 충돌한다고 생각하지 않지만,^[2] 예술가의 역할을 바꿀 수 있다"고 말한다.그는 2016년 동아사이언스와의 인터뷰에서 나에게 수학은 예술 ^[80]작품을 만드는 최고의 도구라고 말했다.Hamid Naderi Yeganeh는 실제로 인식할 수 있는 것과 유사한 수학적 대상을 도입하는 것이 젊은이들로 하여금 수학을 ^[81]추구하도록 장려할 수 있다고 믿는다.그는 수학이 국제 문화이고 수학은 국가 ^[82]간의 평화와 사랑을 증진시키는 데 도움을 줄 수 있다고 믿는다.나데리 예가네는 파이가 국제적인 숫자이며 국가 ^[58]간 평화의 상징이 될 수 있다고 믿는다.

갤러리

다음은 예가네의 수학적 ^[47]수치 몇 가지 예입니다.

하트, 2014년

물고기, 2015년

보트, 2015년

15,000개의 움직이는 서클

플라워스, 2020년

휴먼 페이스, 2016년

레퍼런스

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외부 링크

미국 수학회 하미드 나데리 예가네의 수학적 개념 그림
Humpington Post에 Hamid Naderi Yeganeh 블로그 투고
http://alum.sharif.edu/~http://http://htp

[1] "دانشگاه قم/مصاحبه با آقای..." (in Persian). University of Qom. Retrieved April 20, 2015.

[:0-2] Zhao, Han (2018-05-07). "Can an algorithm be art?". Christian Science Monitor. ISSN 0882-7729. Archived from the original on 2018-05-08. Retrieved 2018-05-09.

[3] Crum, Maddie (August 18, 2015). "These Delicate Drawings Are The Handiwork Of A Very Smart Computer". The Huffington Post. Archived from the original on August 21, 2015. Retrieved August 23, 2015.

[articlecosmos-4] Smith, Belinda (February 29, 2016). "The art and beauty of mathematics". Cosmos. Archived from the original on May 14, 2016. Retrieved July 8, 2016.

[:6-5] "Inside Art" (PDF). STATure (STATistical applications for undergraduate research exploration). McMaster University. 1. April 2021. Archived (PDF) from the original on 2021-08-02. Retrieved 2021-08-14 – via MacSphere (McMaster University’s Institutional Repository).

[6] MacDonald, Fiona (February 19, 2016). "7 times mathematics became art and blew our minds". Science Alert. Archived from the original on January 29, 2017. Retrieved January 23, 2017.

[7] Grandi, C. (May 2020). "Using Art to Teach Mathematics". Mathematics in School. Mathematical Association. 49 (3): 2–7.

[:1-8] Chung, Stephy (September 18, 2015). "Next da Vinci? Math genius using formulas to create fantastical works of art". CNN. Archived from the original on February 2, 2017. Retrieved January 23, 2017.

[9] Haavisto, Aino (2022-08-04). "Ohjelmointi ja taide, osa 3: Taidetta laskukaavoilla" [Programming and art, part 3: Art with formulas]. Dimensiolehti (in Finnish). Matemaattisten Aineiden Opettajien Liitto MAOL ry. Retrieved 2022-08-07.

[10] 林桂光 (24 October 2020). "編程的技術應用與學習表現" [Application of Programming Technology and Learning Performance]. MASTER-INSIGHT.COM (in Chinese). Archived from the original on 28 October 2020. Retrieved 27 October 2020.

[11] "STEAM Series: Math and Art". West Windsor Arts Council. Archived from the original on 2019-07-29. Retrieved 2019-07-29.

[12] "Teaching Coding Languages in Noncoding Courses". New York University, Faculty of Arts & Science. September 6, 2019. Archived from the original on 19 October 2020. Retrieved 20 October 2020.

[:3-13] Naderi Yeganeh, Hamid. "Importing Things From the Real World Into the Territory of Mathematics!". Huffington Post (blog). Archived from the original on 2015-12-18. Retrieved 2020-10-20.

[London-Mathematical-Society-ref-14] "Hamid Naderi Yeganeh: Fractal Africa". The De Morgan Forum – London Mathematical Society. September 21, 2016. Archived from the original on October 11, 2016. Retrieved October 10, 2016.

[15] Naderi Yeganeh, Hamid. "Using the Sawtooth Wave to Create Some Beautiful Images". HuffPost. Archived from the original on 24 October 2020. Retrieved 20 October 2020.

[16] "About the Cover". The American Mathematical Monthly. 124: 772. November 2017. JSTOR 10.4169/amer.math.monthly.124.9.772.

[17] "AMM_Nov_2017.PNG" (PNG). Mathematical Association of America. Archived from the original on 1 November 2017. Retrieved 26 February 2020.

[18] "Iranian Math Whiz Da Vinci Design on Cover of U.S. Mathematics Monthly". Kayhan. November 6, 2017. Archived from the original on January 26, 2018. Retrieved January 25, 2018.

[19] Naderi Yeganeh, Hamid (November 10, 2016). "These Beautiful Images Are Created By Drawing Ellipses". Huffington Post (blog). Archived from the original on December 11, 2015. Retrieved December 1, 2017.

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v t 프랙탈
특성.	프랙탈 치수 아수아드 박스 카운트 히구치 상관 관계 하우스도르프 포장. 토폴로지 재귀 자기유사성
반복 함수 시스템.	반슬리 양치류 칸토어 집합 코흐 눈꽃 멩거 스펀지 시에르핀스키 카펫 시에르핀스키 삼각형 아폴로 개스킷 피보나치어 공간 채우기 곡선 블랑망주 곡선 드람 곡선 민코프스키 용곡선 힐베르트 곡선 코흐 곡선 레비 C 곡선 무어 곡선 페아노 곡선 시에르핀스키 곡선 Z차 곡선 스트링 T-제곱 n플레이크 빅섹 프랙탈 헥사플레이크 고스퍼 곡선 피타고라스나무 바이어스트라스 함수
이상한 매력자	다분할계
L계	프랙탈 캐노피 공간 채우기 곡선 H 트리
이스케이프 타임 프랙탈	불타는 배 프랙탈 줄리아 세트 가득 찬 뉴턴 프랙탈 두아디토끼 랴푸노프 프랙탈 만델브로트 집합 미시우레비치 점 멀티봇 세트 뉴턴 프랙탈 트리콘 만델박스 만델구
렌더링 기술	버드하브 궤도 트랩 피커버 줄기
랜덤 프랙탈	브라운 운동 갈색나무 브라운 모터 프랙탈 풍경 레비 비행 침투 이론 자기 회피 보행
사람	마이클 반즐리 게오르크 칸토르 빌 고스퍼 펠릭스 하우스도르프 데스몬드 폴 헨리 개스톤 줄리아 헬게 폰 코흐 폴 레비 알렉산드르 랴푸노프 브누아 만델브로 하미드 나데리 예가네 루이스 프라이 리처드슨 바츠와프 시에르핀스키
다른.	"영국 해안은 얼마나 깁니다?" 해안선의 역설 프랙탈 아트 하우스도르프 차원에 따른 프랙탈 목록 자연의 프랙탈 기하학 (1982년 책) 프랙탈의 아름다움 (1986년 책) 혼돈: 새로운 과학 만들기 (1987년 책) 만화경 카오스 이론

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