User:Prokofiev

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Alexis Monnerot-Dumaine [edit]

From Paris (France). Engineer in computer engineering and mathematician.

Working on articles about fractal geometry.

Several contributions in the english and french wikipedias, mainly [List of fractals by Hausdorff dimension].

And a category in Commons: Fibonacci word fractal

See also my mineral contributions.

Image Contributions [edit]

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

1. Fractal patterns [edit]

  • 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

  • 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.

  • A paradoxal Koch curve.

  • Fractal heptahedron.

  • Fractal pyramid.

  • Jerusalem cube.

2. 3-dimensional fractals [edit]

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.

3. The Fibonacci word fractal [edit]

  • 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

4. Heighway's dragon curve [edit]

  • 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

5. Other stuff [edit]

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

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