User:Prokofiev2

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

***

	This user enjoys studying about 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

$\int e^{xy}\,$

10	This 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.

[edit] Image Contributions

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

[edit] 1. Fractal patterns

2D Cantor set
Apollonian gaskett
5 circles inversion fractal
Box fractal
Quadratic Koch curve (type1)
Quadratic Koch curve (type2)
Pascal triangle modulo 3
Pascal triangle modulo 5
Hexaflake
Koch curve 85 degrees. Cesaro fractal
3D Cantor dust
Sierpinski hexagon
Sierpinski tetraedron
H-fractal
Quadratic Koch curve 3D (type1)
Quadratic Koch curve 3D (type2)
Dodecaedron fractal
Icosaedron fractal
Octaedron fractal
Apollonian spheres packing
3-dimensional Hilbert curve
Logistic map bifurcation diagram
3-branches tree (90°)
3-branches tree (60°)
3-dimensional Greek cross
Koch surface
Pinwheel fractal
Percolation front (at the percolation threshold)
Self-avoiding random walk
2D Diffusion-limited aggregation
Percolation cluster(just below threshold)
Brownian motion
3D Diffusion-limited aggregation
Julia set z²+1/4
Julia set z²-1
Douady rabbit
Dendrite Julia set
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
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 $z 3 - 1$
The Rauzy fractal
A golden dragon.
A Fractal tree created by B. Mandelbrot.
A Fractal tree created by B. Mandelbrot.
A Fractal tree created by B. Mandelbrot.
Cartesian product of two fractals.
Twindragon fractal.
Tame twindragon fractal.
Ikeda attractor.
Mandebrot set embedded in cos(z)+c.
Mandebrot set embedded in gaussian exp(-z^2)+c.
Construction of the Rauzy fractal
Variant of the Rauzy fractal.
Variant of the Rauzy fractal.
Variant of the Rauzy fractal.
Variant of the Rauzy fractal.
Boundary of the T-Square fractal.
Hausdorff dimension of the coast of Great Britain.
Box-counting dimension of the coast of Great Britain.
3 different coverings of the coast of Great Britain.

[edit] 2. 3-dimensional fractals

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

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

[edit] 3. The Fibonacci word fractal

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

[edit] 4. Heighway's dragon curve

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

[edit] 5. Other stuff

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

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

User:Prokofiev2

Contents

[edit] Main Contributions

[edit] Image Contributions

[edit] 1. Fractal patterns

[edit] 2. 3-dimensional fractals

[edit] 3. The Fibonacci word fractal

[edit] 4. Heighway's dragon curve

[edit] 5. Other stuff

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