Prokofiev2

Mandelbrot is no more, but his legacy will iterate for ever

***

This user enjoys studying fractals.

This user comes from France.

This user has a keen interest in mathematics.

This user is fascinated by chaos theory.

This user enjoys thinking in Four Dimensions.

This user knows that math is $\int e^{xy}\,$.

10This user realizes that there are 10 types of people in this world: those who understand binary and those who do not.

Alexis Monnerot-Dumaine from Paris (France). Mathematician working on fractal geometry.

My publications, on HAL

Main Contributions

• list of fractals by Hausdorff dimension
• Fibonacci word
• Rauzy fractal
• Sturmian word
• Dragon curve

And their equivalent in the French Wikipedia.

Cheatsheets: Help:Displaying a formula and Latex on Wikibooks SandBox: User:Prokofiev2/Sandbox

Image Contributions

Most of these images were designed to illustrate the english and french Wikipedia articles dealing about fractal geometry.

1. Fractal patterns

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  2D Cantor set
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  Apollonian gaskett
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  5 circles inversion fractal
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  Box fractal
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  Quadratic Koch curve (type1)
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  Quadratic Koch curve (type2)
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  Pascal triangle modulo 3
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  Pascal triangle modulo 5
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  Hexaflake
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  Koch curve 85 degrees. Cesaro fractal
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  3D Cantor dust
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  Sierpinski hexagon
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  Sierpinski tetraedron
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  H-fractal
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  Quadratic Koch curve 3D (type1)
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  Quadratic Koch curve 3D (type2)
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  Dodecaedron fractal
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  Icosaedron fractal
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  Octaedron fractal
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  Apollonian spheres packing
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  3-dimensional Hilbert curve
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  Logistic map bifurcation diagram
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  3-branches tree (90°)
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  3-branches tree (60°)
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  3-dimensional Greek cross
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  Koch surface
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  Pinwheel fractal
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  Percolation front (at the percolation threshold)
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  Self-avoiding random walk
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  2D Diffusion-limited aggregation
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  Percolation cluster(just below threshold)
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  Brownian motion
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  Julia set z²+1/4
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  Julia set z²-1
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  Douady rabbit
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  Dendrite Julia set
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  real numbers with even digits
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  Von Koch curve with random orientation
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  Von Koch curve with random interval
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  Fractal percolation p=75%
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  Brownian surface
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  Weierstrass function
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  IFS 3 ratios
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  Takagi or blancmange curve
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  Self-affine fractal set
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  A random Cantor set
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  Newton fractal
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  Secant fractal
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  Secant method applied to $z^{3}-1$
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  Halley method applied to $z^{3}-1$
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  Householder method applied to $z^{3}-1$
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  Newton method applied to $z^{3}-1$
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  The Rauzy fractal
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  A golden dragon.
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  A Fractal tree created by B. Mandelbrot.
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  A Fractal tree created by B. Mandelbrot.
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  A Fractal tree created by B. Mandelbrot.
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  Cartesian product of two fractals.
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  Twindragon fractal.
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  Tame twindragon fractal.
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  Ikeda attractor.
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  Mandebrot set embedded in cos(z)+c.
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  Mandebrot set embedded in gaussian exp(-z^2)+c.
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  Construction of the Rauzy fractal
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  Variant of the Rauzy fractal.
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  Variant of the Rauzy fractal.
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  Variant of the Rauzy fractal.
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  Variant of the Rauzy fractal.
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  Boundary of the T-Square fractal.
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  Hausdorff dimension of the coast of Great Britain.
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  Box-counting dimension of the coast of Great Britain.
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  3 different coverings of the coast of Great Britain.
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  Crown fractal
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  Wave fractal
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  Pell fractal

2. 3-dimensional fractals

3 dimensional fractal patterns : Mandelbrot, Mandelbulb, 3D IFS... Mainly generated with Mandelbulber

• 
  Mandelbulb power 8
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  Mandelbulb power 8 (cross section)
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  Mandelbulb power 2
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  Fractal Tetraedron.
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  Fractal Tetraedron with spherical folding.
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  Fractal Dodecaedron.
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  Fractal Icosaedron.
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  Hypercomplex 3D mandelbrot set (section).
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  Quaternion Julia set "Douady rabbit".
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  Quaternion Julia set c=-1 "San Marco".
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  Quaternion Julia set c=i "Dendrite".
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  Quaternion Julia set c=-0,75-0,14i.
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  Quaternion Julia set c=-0,75-0,14i (cross-section XZ).
• 
  Standard Mandelbox.

3. The Fibonacci word fractal

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  Fibonacci word fractal
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  First iterations
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  Inverted Fibonacci word fractal
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  Fibonacci fractal self-similarities
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  60° fibonacci word fractal
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  Construction of the Fibonacci word fractal
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  Construction of the Fibonacci word fractal
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  Construction based on octogons.
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  Fibonacci word cutting sequence - sturmian word
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  The Fibonacci word gasket
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  The Fibonacci word fractal
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  The Fibonacci word fractal (compact variant)
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  The Fibonacci word fractal (zvastika variant)
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  The Fibonacci word fractal (diagonal variant)
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  The Fibonacci word fractal (pi/8 variant)
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  The 3 types of Fibonacci word fractals
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  IFS for the Fibonacci word fractal
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  Fibonacci numbers in the Fibonacci word Fractal
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  Variants of the FWF
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  Dimensions of the FWF
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  Alternative construction of the FWF
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  Alternative construction of the FWF
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  Tiling of the plane by Fibonacci tiles
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  Tiling built from the Fibonacci word fractal
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  Area of the Fibonacci tile
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  Tiling built from a variant of the Fibonacci word fractal
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  Tiling built from the svastika variant of the Fibonacci word fractal

4. Heighway's dragon curve

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  Boundary of the Dragon curve
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  Dragon curve
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  Dragon curve tiling
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  Dragon curve tiling
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  Dragon curve tiling
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  Dragon curve tiling
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  Dragon curve tiling
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  Dragon curve tiling
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  Dragon curve tiling
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  Dragon curve tiling
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  Dragon curve tiling
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  Dragon curve tiling
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  Dragon curve tiling
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  Dragon curve iterations
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  Dragon curve dimensions

5. Other stuff

Artistic views, lanscapes generated from main fractals, and other unsorted stuff

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  Mandelbrot set island
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  Julia set island
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  Magnet Julia set landscape
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  Flames on a Mandelbrot set
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  Mandelbrot river
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  Mandelbrot set island
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  One iteration of the Inverse Julia transform
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  7 iterations of the Inverse Julia transform
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  Samuel Monnier's artistic view of the Fibonacci word fractal
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  Samuel Monnier's artistic view of the Fibonacci word fractal (detail)
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  Samuel Monnier's artistic view of the Fibonacci word fractal
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  Samuel Monnier's artistic view. Detail on a snowflake.
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  Flames on a Mandelbrot set
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  Labradorite
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  Phénomène d'adularescence