Fractal

From Wikimedia Commons, the free media repository

Please look also at Category Fractals page

[edit] Overview

Mandelbrot set (z²+c)	Julia set	Koch snowflake	Sierpinski triangle
Sierpinsky carpet	Fractal fern	Sierpinski pyramid	Menger sponge

[edit] Mandelbrot set

[edit] Julia set

[edit] Various

Burning Ship fractal	Apfelmann im Gras	Buddhabrot	Buddhabrot
Koch snowflake	Sierpinski triangle	T-Square	Menger sponge
Sierpinski carpet	Sierpiński curve	Hilbert curve	Peano curve
Moore curve stages 1-4	Moore curve stages 0-5	Moore curve in 3D, stage 3	Lebesgue curve or z-order curve
Lebesgue 3D curve, iter. 1	Lebesgue 3D curve, iter. 2	Lebesgue 3D curve, iter. 3	Dragon curve
Banach curve	Gosper curve	Gosper island	Penta plexity
Fraktal als Schneeflocke	Fraktal aus Sechsecken	Fraktal aus Achtecken	Fraktal aus Zehnecken
Fraktal aus Zwölfecken	Fractal flame set	Pythagoras tree	Lévy C curve
Newton fractal	Newton fractal	Secant fractal	Secant method applied to $z 3 - 1$
Halley method applied to $z 3 - 1$	Householder method applied to $z 3 - 1$	Newton method applied to $z 3 - 1$	Bransley's fern
Fractal vortices	Feigenbaum Planet	Smith-Volterra Cantor set	Henon attractor
Koch curve	2D Cantor set	Apollonian gaskett	Box fractal
Quadratic Koch curve (type1)	Quadratic Koch curve (type2)	Monkeys' Tree curve	Boundary of the Dragon curve
Arrowhead Sierpinski curve	Sierpinski arrowhead curve	Evolution of Sierpinski arrowhead curve	Sierpinski arrowhead curve in 3D
Pascal triangle modulo 3	Pascal triangle modulo 5	Hexaflake	Empty Hexaflake
Koch curve 85 degrees. Cesaro fractal	3D Cantor dust	3D Cantor dust stages	Penrose tiling
Dragon curve	Terdragon curve	Terdragon curve boundary	Sierpinski tetraedron
H-fractal	Lorenz attractor	Quadratic Koch curve 3D (type1)	Quadratic Koch curve 3D (type2)
Quadratic Koch surface (type 1, stage 1)	Quadratic Koch surface (type 1, stage 2)	Quadratic Koch surface (type 1, stage 3)	Quadratic Koch surface (type 2, stage 1)
Quadratic Koch surface (type 2, stage 2)	Quadratic Koch surface (type 2, stage 3)	Dodecaedron fractal	Icosaedron fractal
Octaedron fractal	Apollonian spheres packing	3-dimensional Hilbert curve	Hilbert 3D curve, iter. 1
Hilbert 3D curve, iter. 2	Hilbert 3D curve, iter. 3	Hilbert 3D curve, iter. 4	Logistic map bifurcation diagram
3-branches tree (90°)	3-branches tree (60°)	2D Greek cross fractal	Evolution of 2D Greek cross fractal
3-dimensional Greek cross	Evolution of 3D Greek cross fractal	Cantor dust	'
'	Koch surface	Koch surface evolution	Koch surface, third iteration
galaxy of galaxies from M-Set	Fibonacci word fractal	Boundary of the Fibonacci word fractal	Fibonacci word gasket
The Fibonacci word fractal	The Fibonacci word fractal (compact variant)	The Fibonacci word fractal (zvastika variant)	The Fibonacci word fractal (diagonal variant)
The 3 types of Fibonacci word fractals	Pinwheel 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	A random Cantor set	The Collatz fractal



	"Exponential parameter space"	Rauzy fractal

[edit] Fractal flame

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

[edit] Fractal dimension

$Britain-fractal-coastline-combined.jpg$

[edit] Nature

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


Le Havre St Jospeh int1 fractal.jpg	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
3D Diffusion-limited aggregation	Ball of crumpled paper	Aveoli of the lungs

[edit] Sceneries

Fractal sceneries:

Mandelbrot 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

[edit] 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	Thailand-1	"Worldegg"	"Way into my microchip"
		"Flames on a Mandelbrot set"	"Thinking of Art"
"Art and Jazz"