Fractal

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Please look also at Category Fractals page

Contents

Overview [edit]

Mandelbrot set [edit]

See also Mandelbrot set

Julia set [edit]

See also Julia set

  • Julia set z²+1/4

  • Julia set z²-1

  • Julia set (highres 01).jpg

  • Julia set for z³+c

  • Julia set (Rev formula 03).jpg
  • Julia set (Rev formula 02).jpg

  • 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

Various [edit]

  • Apfelmann im Gras

  • Rectangular leaf fern

  • 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

  • Fractal flame set

  • 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

  • Sierpinski square.jpg
  • Square koch 0.png
  • Square koch 1.png
  • Square koch 2.png
  • Flower3.jpg
  • Fract000.jpg
  • 3D Cantor set.jpg
  • Dragon trees.jpg
  • Fractal tree (Plate b - 1).jpg
  • Fractal tree (Plate b - 2).jpg
  • Fractal tree (Plate b - 3).jpg
  • Fractal weeds.jpg

  • "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]

  • Fractal dimension.jpg
  • Britain-fractal-coastline-combined.jpg

Nature [edit]

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

  • Fractal Broccoli.jpg
  • Fraktale-Pflanzenstruktur SL275684.JPG
  • Tromsopalme-topdown.jpg
  • Glue1 800x600.jpg
  • Microwaved-DVD.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

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"

  • Mandelbrot 1-lambda.png
  • Fk-148.JPG

  • "Flames on a Mandelbrot set"

  • Fractal XaoS UFO

  • Fractal Xaos psychedelic.png

  • Barnsly fern to Sierpinsky triangle animation

  • Vicsek fractal evolving into fractal tree.

Music [edit]

Fractals and music:

Basin Boundaries [edit]

The basin boundaries form a Cantor set...

  • Gr system experimental2.png
  • GR Basins1.png
  • GR Basins2.png
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