Prokofiev

Userboxes

frCet utilisateur a pour langue maternelle le français.

en-3This user can contribute with an advanced level of English.

Alexis Monnerot-Dumaine

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

My publications, on HAL

Working on articles about fractal geometry.

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

Image Contributions

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

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
• 
  Brownian motion
• 
  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.
• 
  3D diffusion-limited aggregation]]

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.

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

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

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