Fractal

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Please look also at Category Fractals page

Contents

1 Overview
2 Mandelbrot set
3 Julia set
4 Three-dimensional fractals
5 Various
6 Fractal flame
7 Fractal dimension
8 Nature
9 Sceneries
10 Art
11 Music
12 Basin Boundaries

Overview[edit]

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

Mandelbrot set[edit]

See also Mandelbrot set

Mandelbrot set (z²+c)
z³+c
z⁴+c
z⁵+c
z⁶+c
z⁷+c
Mandelbrot set

Julia set[edit]

See also Julia set

Julia set z²+1/4
Julia set z²-1
Julia set for z³+c
Douady rabbit
Dendrite Julia set
Spiral in a julia set

Three-dimensional fractals[edit]

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)

Various[edit]

Burning Ship fractal
Apfelmann im Gras
Buddhabrot
Buddhabrot
Koch snowflake
Sierpinski triangle
Rectangular leaf fern
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 $z^{3}-1$
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
Uniform Triangle Mass Center grade 5

Fractal flame[edit]

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

Fractal dimension[edit]

$Britain-fractal-coastline-combined.jpg$

Nature[edit]

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[edit]

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
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[edit]

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"
Fractal XaoS UFO
Fractal Xaos psychedelic.png
Barnsly fern to Sierpinsky triangle animation
Vicsek fractal evolving into fractal tree.
Mandelbrot Image by own software 1
Mandelbrot Image by own software 2
Mandelbrot Image by own software 3
Mandelbrot Image by own software 4
Mandelbrot Image by own software 5
Mandelbrot Image by own software 6
Mandelbrot Image by own software 7
Mandelbrot Image by own software 8
Mandelbrot Image by own software 9
Mandelbrot Image by own software 10
Mandelbrot Image by own software 11
Mandelbrot Image by own software 12
Mandelbrot Image by own software 13
Mandelbrot Image by own software 14
Mandelbrot Image by own software 15
Mandelbrot Image by own software 16
Mandelbrot Image by own software 19
Mandelbrot Image by own software 20
Mandelbrot Image by own software 21
Mandelbrot Image by own software 23
Mandelbrot Image by own software 18
Mandelbrot Image by own software 24
Mandelbrot Image by own software 25
Mandelbrot Image by own software 17
Mandelbrot Image by own software 26
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
Play media

Mandelbrot set color cycling video

Music[edit]

Fractals and music:

Basin Boundaries[edit]

The basin boundaries form a Cantor set...

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Fractals