Fractal

**fractal**
	mathematical set of non-integral dimension
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Subclass of	set;
Part of	mathematics;
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	Q81392; Library of Congress authority ID: sh85051147; Bibliothèque nationale de France ID: 119730272; NDL Authority ID: 00576561; BNCF Thesaurus ID: 7037; NL CR AUT ID: ph120342; BabelNet ID: 00036150n; J9U ID: 987007548246005171
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<nowiki>fractal; 프락탈; Brotamynd; Fraktal; Фрактал; fractal; Fractal; Tampaha; fraktál; фрактал; Fraktalo; Fraktal; 프랙탈; Фрактал; frakto; fraktál; Fraktal; ফ্রাক্টাল; fractale; Фрактал; Phân dạng; Fraktālis; Fraktaalmeetkunde; фрактал; Impindampindwano; fractal; fraktal; fraktal; Fraktal; ಫ್ರಾಕ್ಟಲ್‌; فراکتاڵ; fractal; كسيرة; 碎形; fraktál; Fraktal; Fractal; fractal; Фрактал; Fraktal; Fraktali; Ֆրակտալ; 分形; fraktal; ფრაქტალი; フラクタル; Fractal; פרקטל; Фрактал; भग्न; 分形; ਫ੍ਰੈਕਟਲ; பகுவல்; frattale; Fraktal; Fraktal; фрактал; Фрактал; fraktal; برخال; แฟร็กทัล; Frattali; fractal; Fraktaali; 分形; fraktal; Fraktalas; fraktal; Fractal; фрактал; Fraktal; Fraktal; fraktal; ഫ്രാക്ടൽ; fractal; фрактал; Фрактал; Ffractal; codach; Fractal; Fractal; Φράκταλ; Фрактал; oggetto geometrico; önismétlő geometriai alakzat; мноства, якое валодае ўласьцівасьцю самападобнасьці; множество, обладающее свойством самоподобия; selbstähnliche Mengen und Geometrien; tipo de conjunto em matemática; الگو‌های تگرار شونده یعنی برابری جز با کل; 组成部分与整体以某种方式相似的几何形状; matematična množica neintegralne razsežnosti; フランスの数学者ブノワ・マンデルブロが導入した幾何学の概念; vondrona matematika; obiekt samopodobny i wzorzysty; צורה גאומטרית; meetkundige figuur die zelfgelijkend is; objecte matemàtic; objet mathématique dont la structure est invariante par changement d'échelle; 일부 작은 조각이 전체와 비슷한 기하학적 형태; mathematical set of non-integral dimension; أشكال هندسية تتدرج زيادة أو نقصاناً; itsesimilaarinen joukko; objeto geométrico; geometría fractal; fractales; geometria fractal; геометрический фрактал; стохастический фрактал; фрактальная структура; фракталы; фрактальная графика; Fraktale; Fraktale Geometrie; frachtal; هندسه برخالی; فراکتال; فراکتال‌ها; هندسه فراکتال‌ها; فرکتال; هندسه برخال‌ها; هندسه برخال ها; فرکتال‌ها; هندسه فراکتال ها; 分形学; 分形几何; 自相似性; 分數維形; 碎形; fraktal funktion; fraktal geometri; fraktalgeometri; fraktalfunktion; monsterkurva; Fractalis; Fractales; Itsesimilaari fraktaali; Fraktaalit; Murtomuoto; Fraktaalifunktio; Fraktaaligeometria; Фракталдар; fraktalo; Curve frattali; Geometria dei frattali; Struttura frattale; Geometria frattale; Frattali; ফ্র্যাক্টাল; fractalité; géométrie fractale; fractal; fractales; fraktali; Studiu dei frattali; Fractal; fraktāļi; Фрактали; fraktali; monofraktal; množica fraktalov; 프랙탈 곡선; 프랙탈 기하학; 차원분열도형; 프랙털; 차원 분열 도형; fractaal; fractals; fractalen; Fraktalai; Geometri fraktal; Fraktale; Fraktaler; Fraktali; fractals; Fraktaalsus; Fraktaal; แฟรกทัล; เรขาคณิตสาทิสรูป; เรขาคณิตเศษส่วน; Фрактална геометрия; Фрактали; fractals; fractal set; fractal sets; هندسة فركتلية; هندسة كسرانية; كسيري; الهندسة الكسيرية; فركتل; هندسه كسيريه; كسيرية; Μορφοκλασματικό σύνολο; Fractal; Fractal</nowiki>

Overview

Parameter plane -1D
Parameter plane - 2D and Mandelbrot set (z²+c)
parameter plane - 3D
Julia set
Koch snowflake
Barnsley fern
Sierpinski triangle- 2D
Sierpinsky pyramid - 3D
Sierpinski carpet -2D
Menger sponge - 3D
$A via OpenCL rendered fractal image$

A via OpenCL rendered fractal image

Mandelbrot set

Julia set

Three-dimensional fractals

Power 9 mandelbulb
Detail of a power 9 mandelbulb
Detail of a power 9 mandelbulb
Power 7 juliabulb
Detail of a power 5 mandelbulb
Detail of a power 20 mandelbulb
$LAI4D 3D fractal flower (live sample online)$

LAI4D 3D fractal flower (live sample online)

Various

Koch surface
Koch surface evolution
Koch surface, third iteration
galaxy of galaxies from M-Set
$Fibonacci word fractal$

Fibonacci word fractal
$Boundary of the Fibonacci word fractal$

Boundary of the Fibonacci word fractal
Fibonacci word gasket
$The Fibonacci word fractal$

The Fibonacci word fractal
$The Fibonacci word fractal (compact variant)$

The Fibonacci word fractal (compact variant)
$The Fibonacci word fractal (zvastika variant)$

The Fibonacci word fractal (zvastika variant)
$The Fibonacci word fractal (diagonal variant)$

The Fibonacci word fractal (diagonal variant)
$The 3 types of Fibonacci word fractals$

The 3 types of Fibonacci word fractals
$Pinwheel fractal$

Pinwheel fractal
$5 circles inversion fractal$

5 circles inversion fractal
One iteration of the Inverse Julia transformation $\scriptstyle {\sqrt {z+0.75}}$
7 iterations of the Inverse Julia transformation $\scriptstyle {\sqrt {z+0.75}}$
real numbers with even digits
Von Koch curve with random orientation
Von Koch curve with random interval
Fractal percolation p=75%
Brownian surface
Weierstrass function
IFS 3 ratios
Takagi or blancmange curve
$Self-affine fractal set$

Self-affine fractal set
A random Cantor set
$The Collatz fractal$

The Collatz fractal
"Exponential parameter space"
$Rauzy fractal$

Rauzy fractal
Uniform Triangle Mass Center grade 5
Fractal H-I de Rivera
world of portals

Fractal flame

Fractal Flame
Fractal Flame
Fractal Flame
Fractal Flame
Fractal Flame
Fractal Flame
Fractal Flame
Fractal Flame
Fractal Flame
Fractal Flame
Fractal Flame

Fractal dimension

Nature

Fractals in nature; see also Category:Fractals in nature:

boundary of brownian motion
Percolation front (at the percolation threshold)
Self-avoiding random walk
2D Diffusion-limited aggregation
Percolation cluster(just below threshold)
Brownian motion
Coastline of Norway
Ball of crumpled paper
Aveoli of the lungs
Neuron (Purkinje Cell)
Cerebellum of the Human Brain

Sceneries

Fractal sceneries and landscapes generated from various iterated formulas:

$Mandelbrot set rendered by a fractal-based scenery generator:Terragen$

Mandelbrot set rendered by a fractal-based scenery generator:Terragen
$Mandelbrot set rendered by a fractal-based scenery generator:Terragen$

Mandelbrot set rendered by a fractal-based scenery generator:Terragen
$Julia set rendered by a fractal-based scenery generator:Terragen$

Julia set rendered by a fractal-based scenery generator:Terragen
Flames on a Mandelbrot set rendered by Terragen
Detail of the Magnet julia set rendered by Terragen
Detail of the Mandelbrot set rendered by Terragen

Art

Fractal Art:

Jerusalem Cross
Bos
Bril
Bubbles
Elektriciteit
Goud
Kompas
Kroon
Maan
Copper life-form
Masterplan
Modern
Nederland
Olie
Plant
Rosette
Snow
Fractal rocket science
Alien generator
Spheres
Swirl
Vlinders
Vuur
Wolk
Super-volcano
Spiralförmiges Fraktal
Blackhole Sun
BorgArt
Mutant daisies - keep out!
Knife in the dark
"Who is this doing this alpha-beta type psychedelic funkin'"
Scorpion fog
$Julia set fractal animation$

Julia set fractal animation
Thailand-1
"Worldegg"
"Way into my microchip"
"Flames on a Mandelbrot set"
"Thinking of Art"
"Art and Jazz"
Fractal XaoS UFO
Fractal Xaos psychedelic.png
Barnsly fern to Sierpinsky triangle animation
$Vicsek fractal evolving into fractal tree.$

Vicsek fractal evolving into fractal tree.
Mandelbrot Image by own software 1
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Mandelbrot Image by own software 27
Mandelbrot Image by own software 28
Mandelbrot Image by own software 29
Mandelbrot Image by own software 30
Mandelbrot Set in blue 01 by own software
Mandelbrot Animated Image by own software 1
Mandelbrot Animated Image by own software 2
Mandelbrot Animated Image by own software 3
Mandelbrot set color cycling video