Gallery:

Deterministic Fractal Geometry

[Galerie: Géométrie Fractale Déterministe]

Deterministic Fractal Geometry [Géométrie Fractale Déterministe]:

Bidimensional Fractal Curves [Courbes Fractales Bidimensionnelles]:

The first two iterations of the construction of the von Koch curve.

The construction process of the von Koch curve.

The construction process of the von Koch curve.

Zoom in on the von Koch curve.

The self-similarity of the von Koch curve.

Bidimensional Hilbert Curve -iteration 4-.




Tridimensional Fractal Curves [Courbes Fractales Tridimensionnelles]:

Tridimensional Hilbert Curve -iteration 3-.




Complex Sets [Ensembles dans le Plan Complexe]:

[more information about Complex Numbers -en français/in french-]
[more information about the Complex Mandelbrot Set -en français/in french-]
[more information about Complex Julia Sets -en français/in french-]

Complex Mandelbrot and Julia Sets [Ensembles de Mandelbrot et de Julia dans le Plan Complexe]:

The Mandelbrot set computed for 1 to 16 iterations with display of the arguments.

Bidimensional zoom in on the Mandelbrot set with display of the arguments.

Bidimensional zoom in on the Mandelbrot set with display of the arguments.

Tridimensional visualization of the Mandelbrot set with mapping of the arguments -the Mont Saint Michel-.	Tridimensional zoom in on the Mandelbrot set.	Tridimensional zoom in on the Mandelbrot set.	Tridimensional zoom in on the Mandelbrot set.	Tridimensional zoom in on the Mandelbrot set with mapping of the arguments.
A tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments.	A tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments.	A tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments.	A tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments.	A tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments.

Along the border of the Mandelbrot set.

Along the border of the Mandelbrot set.

16 complex Julia sets along the border of the Mandelbrot set with display of the iteration numbers.

16 complex Julia sets along the border of the Mandelbrot set with display of the arguments.

16 complex Julia sets.




Miscellaneous Complex Sets [Ensembles Divers dans le Plan Complexe]:

Bidimensional zoom in on the Z=Gamma(Z) iteration with display of the arguments.

Tridimensional display of the Z=Gamma(Z) iteration inside (-20.0,+20.0)x(-20.0,+20.0) (bird's-eye view).

Tridimensional display of the Z=Gamma(Z) iteration inside (-20.0,+20.0)x(-20.0,+20.0).

Bidimensional zoom in on the Z=Zeta(Z) iteration with display of the arguments.

Tridimensional display of the Z=Zeta(Z) iteration inside (-20.0,+20.0)x(-20.0,+20.0) (bird's-eye view).

Tridimensional display of the Z=Zeta(Z) iteration inside (-20.0,+20.0)x(-20.0,+20.0).

Computation of the roots of Z^3=1 using Newton's method.

Computation of the roots of Z^5=1 using Newton's method.




Artistic Views of Complex Sets [Vues Artistiques d'Ensembles Calculés dans le Plan Complexe]:

Tridimensional visualization of the Mandelbrot set.	Cloudy Mandelbrot set.	Morning sun pool.	Mandelbrot rainbow mountain with fog.	Mandelbrot set in the sky.
Convolution of a detail of the Mandelbrot set.




Quaternionic Sets [Ensembles dans le Corps des Quaternions]:

For each of them, a tridimensional cross-section -using the XYZ hyperplane- is displayed.

[more information about Quaternionic Numbers -en français/in french-]
[more information about the Quaternionic Mandelbrot Set -en français/in french-]
[more information about Quaternionic Julia Sets -en français/in french-]

Quaternionic Mandelbrot Set [Ensemble de Mandelbrot dans le Corps des Quaternions]:

The quaternionic Mandelbrot set -tridimensional cross-section-.

Zoom in on the quaternionic Mandelbrot set -tridimensional cross-sections-.




Quaternionic Julia Sets [Ensembles de Julia dans le Corps des Quaternions]:

The quaternionic Julia set computed with A=(0,1,0,0) -tridimensional cross-section-.

The quaternionic Julia set computed with A=(0,1,0,0) -tridimensional cross-section-.

The quaternionic Julia set computed with A=(0,1,0,0) -tridimensional cross-section-.

The quaternionic Julia set computed with A=(0,1,0,0) -tridimensional cross-section-.

The quaternionic Julia set computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.

The quaternionic Julia set -degree=2- computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.

The quaternionic Julia set -degree=8- computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.

Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-.

Quaternionic Julia sets along the border of the Mandelbrot set with motion blur -tridimensional cross-sections-.




The Quaternionic Julia Set computed with [l'Ensemble de Julia dans le Corps des Quaternions Calculé avec] A=(-0.5815147625160462,0.6358885017421603,0,0):

Different Visualization Modes [Différents Modes de Représentation]:

A quaternionic Julia set -tridimensional cross-section-.

The quaternionic Julia set -degree=2- computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.

A quaternionic Julia set -tridimensional cross-section-.

A quaternionic Julia set -tridimensional cross-section-.

A quaternionic Julia set -tridimensional cross-section-.




Rotations in the Quaternionic Space [Rotations dans le Corps des Quaternions]:

2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-.

2.pi rotation about the Y axis of a quaternionic Julia set with motion blur -tridimensional cross-section-.

2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-.

2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-.

2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-.




Stereograms [Stéréogrammes]:

A set of 4x3 stereograms of the quaternionic Julia set computed with A=(0,1,0,0) -tridimensional cross-section-.

A set of 4x3 stereograms of the quaternionic Julia set computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.




Autostereograms [Autostéréogrammes]:

Autostereogram of a quaternionic Julia set -tridimensional cross-section-.	The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-.	True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-.	The first true colors autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-.	Autostereogram of a quaternionic Julia set and fractal phenomenon -tridimensional cross-section-.
Autostereogram of a quaternionic Julia set -tridimensional cross-section-.




Miscellaneous Views [Vues Diverses]:

Zoom in on a quaternionic Julia set -tridimensional cross-sections-.	Zoom in on a quaternionic Julia set -tridimensional cross-sections-.	Zoom in on a quaternionic Julia set -tridimensional cross-sections-.	Pan on a quaternionic Julia set -tridimensional cross-sections-.	Translation along the fourth axis of a quaternionic Julia set -tridimensional cross-sections-.
Integration of 128 tridimensional cross-sections of a quaternionic Julia set computed along its fourth axis.




Miscellaneous Quaternionic Sets [Ensembles Divers dans le Corps des Quaternions]:

Computation of the roots of Q^3=1 using Newton's method with translation along the third axis of the quaternionic space.

The quaternionic fractal set obtained when computing the roots of Q^3=1 using Newton's method with translation along the third axis of the quaternionic space -tridimensional cross-section-.

The quaternionic fractal set obtained when computing the roots of Q^3=1 using Newton's method with translation along the third axis of the quaternionic space -tridimensional cross-section-.




Artistic Views of Quaternionic Sets [Vues Artistiques d'Ensembles Calculés dans le Corps des Quaternions]:

Artistic view of a quaternionic Julia set -tridimensional cross-section-.	Artistic view of a quaternionic Julia set -tridimensional cross-section-.	Artistic view of 128 quaternionic Julia sets -tridimensional cross-sections-.	Artistic view of a 2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-.	Quaternionic UFO.
Animation of a quaternionic Julia island.	Quaternionic Julia island.	Rattle snake.




Pseudo-Quaternionic Sets [Ensembles dans l'Ensemble des Pseudo-Quaternions]:

For each of them, a tridimensional cross-section -using the XYZ hyperplane- is displayed.

[more information about Pseudo-Quaternionic Numbers -en français/in french-]


Pseudo-Quaternionic Mandelbrot Sets ("MandelBulb") [Ensembles de Mandelbrot ("MandelBulb") dans l'Ensemble des Pseudo-Quaternions]:

Zoom in on a pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	Zoom in on a pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.
Close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	A pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -'the children round' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-.	A pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.
2.pi rotation about the Y axis of a pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.




Pseudo-Quaternionic Julia Sets ("MandelBulb" like) [Ensembles de Julia (comme des "MandelBulb"s) dans l'Ensemble des Pseudo-Quaternions]:

A foggy pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.	Artistic view of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0) -a Tribute to José Hernández- -tridimensional cross-section-.	Artistic view of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.	A foggy pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.	2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') -tridimensional cross-section-.
2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') -tridimensional cross-section-.	2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') -tridimensional cross-section-.	2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') -tridimensional cross-section-.	2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') -tridimensional cross-section-.	2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') -tridimensional cross-section-.
2.pi rotation about the Y axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') -tridimensional cross-section-.	Sixteen pseudo-quaternionic Julia sets ('MandelBulb' like: 'JuliaBulb's) -tridimensional cross-sections-.




Miscellaneous Pseudo-Quaternionic Sets ("MandelBulb" like) [Ensembles divers (comme des "MandelBulb"s) dans l'Ensemble des Pseudo-Quaternions]:

A foggy pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(0,1,0,0) and with a locally variable exponent between 2 and 12 -tridimensional cross-section-.

2.pi rotation about the Y axis of a 'mixing' between a pseudo-quaternionic Mandelbrot set and a pseudo-quaternionic Julia set -tridimensional cross-section-.

The pseudo-quaternionic fractal set obtained when computing the roots of Q^3=1 using Newton's method with translation along the third axis of the pseudo-quaternionic space (a 'NewtonBulb') -tridimensional cross-section-.




Verhulst Dynamics [Dynamique de Verhulst]:

Bidimensional Verhulst Dynamics [Dynamique de Verhulst bidimensionnelle]:

Bidimensional visualization of the Verhulst dynamics.

Bidimensional visualization of the Verhulst dynamics -(grey,orange,red) display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-.

Bidimensional zoom in on the Verhulst dynamics.

Tridimensional visualization of the Verhulst dynamics.

Beautiful self-similarity.

Bidimensional display of the rounding-off errors when computing the Verhulst dynamics.

Tridimensional display of the rounding-off errors when computing the Verhulst dynamics.




Tridimensional Verhulst Dynamics [Dynamique de Verhulst tridimensionnelle]:

Tridimensional visualization of the Verhulst dynamics.	Tridimensional visualization of the Verhulst dynamics.	Tridimensional visualization of the Verhulst dynamics.	Tridimensional visualization of the Verhulst dynamics.	Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.
Tridimensional visualization of the Verhulst dynamics.




Octonionic Sets [Ensembles dans l'Ensemble des Octonions]:

For each of them, a tridimensional cross-section -using the XYZ hyperplane- is displayed.



Octonionic Julia Sets [Ensembles de Julia dans l'Ensemble des Octonions]:

The octonionic Julia set computed with A=(0,1,0,0,0,0,0,0) -tridimensional cross-section-.

The octonionic Julia set computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.




Pseudo-Octonionic Sets [Ensembles dans l'Ensemble des Pseudo-Octonions]:

For each of them, a tridimensional cross-section -using the XYZ hyperplane- is displayed.



Pseudo-Octonionic Mandelbrot Sets ("MandelBulb") [Ensembles de Mandelbrot ("MandelBulb") dans l'Ensemble des Pseudo-Octonions]:

A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -'the children round' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Zoom in on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.




Pseudo-Octonionic Julia Sets ("JuliaBulb") [Ensembles de Julia ("JuliaBulb") dans l'Ensemble des Pseudo-Octonions]:

Pi rotation about the Y axis of pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	Close-up on a foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	Close-up on a foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.

A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(0,1,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) with a rotation about the X axis -tridimensional cross-section-.
Pi/2 rotation about the X axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') -tridimensional cross-section-.	Close-up on a foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) with a rotation about the X axis -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) with a rotation about the X axis -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) with a rotation about the X axis -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.




Miscellaneous Pseudo-Octonionic Sets ("MandelBulb" like) [Ensembles divers (comme des "MandelBulb"s) dans l'Ensemble des Pseudo-Octonions]:

Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	Close-up on an hybrid pseudo-octonionic Mandelbrot-Julia set ('MandelBulb' like: a 'MandelJuliaBulb') -tridimensional cross-section-.	Close-up on a foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(0,1,0,0,0,0,0,0) and with a locally variable exponent between 2 and 12 -tridimensional cross-section-.	A pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) with a locally variable exponent that is equal to 4, 5 or 6 and with a rotation about the X axis -tridimensional cross-section-.




Iterated Function Systems (IFS) [Systèmes de Fonctions Itérées (IFS)]:

Bidimensional Hilbert Curve -iteration 4-.

Tridimensional Hilbert Curve -iteration 3-.

Tridimensional Hilbert Curve -iteration 4-.

A bidimensional fern computed by means of an 'Iterated Function System' -IFS-.

A bidimensional Sierpinski 'carpet' computed by means of an 'Iterated Function System' -IFS-.

A pyramidal Menger sponge computed by means of an 'Iterated Function System' -IFS-.

Various bidimensional fractal crosses.

Tridimensional fractal cross -iteration 5-.

Tridimensional fractal cross -iteration 5-.




Miscellaneous [Divers]:

A foggy 'MandelBox' -tridimensional cross-section-.

Close-up on a foggy 'MandelBox' -tridimensional cross-section-.

An extended foggy 'MandelBox' -tridimensional cross-section-.

A tridimensional fractal structure.

A tridimensional fractal structure.

Fractal new Moon.

Recursive pentagon.

Recursive 5-star.

The Sierpinski carpet -iteration 1-.	The Sierpinski carpet -iteration 2-.	The Sierpinski carpet -iteration 3-.	The Sierpinski carpet -iteration 4-.	The Sierpinski carpet -iteration 5-.
The Sierpinski carpet -iteration 5-.

The Menger sponge -iteration 1-.

The Menger sponge -iteration 2-.

The Menger sponge -iteration 3-.

The Menger sponge -iteration 4-.

The Menger sponge -iteration 5-.

An amazing cross-section inside the Menger sponge -iteration 1-.

An amazing cross-section inside the Menger sponge -iteration 2-.

An amazing cross-section inside the Menger sponge -iteration 3-.

An amazing cross-section inside the Menger sponge -iteration 4-.

An amazing cross-section inside the Menger sponge -iteration 5-.

The 64 first lines of the Pascal's Triangle.

A perfect bidimensional fractal tree and the self-similarity.

Fractal piano keyboard.

No Title 0194.

Binomial multiplicative cascade with ponderations equal to 0.4 -left- and 1-0.4=0.6 -right-.

Binomial multiplicative cascade with ponderations equal to 0.3 -left- and 1-0.3=0.7 -right-.

Copyright (c) Jean-François Colonna, 2000-2015.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2015.