Gallery (564 different pictures):

Deterministic Fractal Geometry

[Galerie (564 images différentes) : Géométrie Fractale Déterministe]

Jean-François COLONNA

www.lactamme.polytechnique.fr

jean-francois.colonna@polytechnique.edu
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, 91120 Palaiseau, France
france telecom, France Telecom R&D

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Deterministic Fractal Geometry [Géométrie Fractale Déterministe]:

Fractal Curves [Courbes Fractales]: Bidimensional [Bidimensionnelles]. Tridimensional [Tridimensionnelles].	Fractal Spaces [Espaces Fractals]: Monodimensional [Monodimensionnels]. Bidimensional [Bidimensionnels]. Tridimensional [Tridimensionnels].	Complex Sets [Ensembles dans le Plan Complexe]: Mandelbrot Set [Ensemble de Mandelbrot]. Julia Sets [Ensembles de Julia]. Mandelbrot and Julia Sets [Ensembles de Mandelbrot et de Julia]. Miscellaneous Sets [Ensembles Divers]. Artistic Views [Vues Artistiques].	Quaternionic Sets [Ensembles dans le Corps des Quaternions]: Mandelbrot Set [Ensemble de Mandelbrot]. Julia Sets [Ensembles de Julia]. The Julia Set computed with [L'Ensemble de Julia calculé avec] A=(-0.58151...,0.63588...,0,0): Different Visualization Modes [Différents Modes de Représentation]. Rotations [Rotations]. Stereograms [Stéréogrammes]. Autostereograms [Autostéréogrammes]. Miscellaneous Views [Vues Diverses]. Miscellaneous Sets [Ensembles Divers]. Artistic Views [Vues Artistiques].	Pseudo-Quaternionic Sets [Ensembles dans les Pseudo-Quaternions]: Mandelbrot Sets [Ensembles de Mandelbrot]. Julia Sets [Ensembles de Julia]. Miscellaneous Sets [Ensembles divers].
Octonionic Sets [Ensembles dans les Octonions]: Julia Sets [Ensembles de Julia].	Pseudo-Octonionic Sets [Ensembles dans les Pseudo-Octonions]: Mandelbrot Sets [Ensembles de Mandelbrot]. Julia Sets [Ensembles de Julia]. Miscellaneous Sets [Ensembles divers].	Verhulst Dynamics [Dynamique de Verhulst]: Bidimensional [Bidimensionnelle]. Tridimensional [Tridimensionnelle]. N-dimensional [N-dimensionnelle].	Iterated Function Systems (IFS) [Systèmes de Fonctions Itérées (IFS)].	Trees [Arbres].
Miscellaneous [Divers].

Deterministic Fractal Geometry [Géométrie Fractale Déterministe]:

[More information -en français/in french-]

Fractal Curves [Courbes Fractales]:

Bidimensional Fractal Curves [Courbes Fractales Bidimensionnelles]:

The construction process of the von Koch curve -iteration 3-.

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

The construction of the von Koch curve.

The construction process of the von Koch curve.

About the length of the von Koch curve.

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

About the fractal dimension with the first two iterations -red and green respectively- of the construction of the von Koch curve.

About the fractal dimension with the first two iterations -red and magenta respectively- of the construction of the von Koch curve.

The first four iterations of the construction of the von Koch snowflake.

The first two iterations of the construction of the Minkowski curve.

Bidimensional Hilbert Curve -iteration 1-.

Bidimensional Hilbert Curve -iteration 2-.

Bidimensional Hilbert Curve -iteration 3-.

Bidimensional Hilbert Curve -iteration 4-.

Bidimensional Hilbert Curve -iteration 5-.

Bidimensional Hilbert Curve -iteration 1-.	Bidimensional Hilbert Curve -iteration 2-.	Bidimensional Hilbert Curve -iteration 3-.	Bidimensional Hilbert Curve -iteration 4-.	Bidimensional Hilbert Curve -iteration 5-.
Bidimensional Hilbert Curve -iteration 6-.

The bidimensional [0,1] --> [0,1]x[0,1] Peano Surjection -T defined with 2 digits-.

The bidimensional [0,1] --> [0,1]x[0,1] Peano Surjection -T defined with 4 digits-.

The [0,1] --> [0,1]x[0,1] Peano Surjection -T defined with 6 digits-.

The bidimensional [0,1] --> [0,1]x[0,1] Peano Surjection -T defined with 8 digits-.

A bidimensional Hilbert-like curve defined with {X₁(...),Y₁(...)} -iteration 1-.	A bidimensional Hilbert-like curve defined with {X₂(...),Y₂(...)} -iteration 2-.	A bidimensional Hilbert-like curve defined with {X₃(...),Y₃(...)} -iteration 3-.	A bidimensional Hilbert-like curve defined with {X₄(...),Y₄(...)} -iteration 4-.	A bidimensional Hilbert-like curve defined with {X₅(...),Y₅(...)} -iteration 5-.
A bidimensional Hilbert-like curve defined with {X₆(...),Y₆(...)} -iteration 6-.

A bidimensional Hilbert-like curve defined with {X₁(...),Y₁(...)} -iteration 1-.	A bidimensional Hilbert-like curve defined with {X₂(...),Y₂(...)} -iteration 2-.	A bidimensional Hilbert-like curve defined with {X₃(...),Y₃(...)} -iteration 3-.	A bidimensional Hilbert-like curve defined with {X₄(...),Y₄(...)} -iteration 4-.	A bidimensional Hilbert-like curve defined with {X₅(...),Y₅(...)} -iteration 5-.
A bidimensional Hilbert-like curve defined with {X₆(...),Y₆(...)} -iteration 6-.

A bidimensional Hilbert-like curve defined with {X₁(...),Y₁(...)} related to the Mandelbrot set border -iteration 1-.	A bidimensional Hilbert-like curve defined with {X₁(...),Y₁(...)} related to the Mandelbrot set border -iteration 2-.	A bidimensional Hilbert-like curve defined with {X₁(...),Y₁(...)} related to the Mandelbrot set border -iteration 3-.	A bidimensional Hilbert-like curve defined with {X₁(...),Y₁(...)} related to the Mandelbrot set border -iteration 4-.	A bidimensional Hilbert-like curve defined with {X₁(...),Y₁(...)} related to the Mandelbrot set border -iteration 5-.
A bidimensional Hilbert-like curve defined with {X₁(...),Y₁(...)} related to the Mandelbrot set border -iteration 6-.

A sphere described by means of a bidimensional Hilbert Curve -iteration 5-.

A torus described by means of a bidimensional Hilbert Curve -iteration 5-.

The Bonan-Jeener double bottle described by means of a bidimensional Hilbert Curve -iteration 5-.

A sphere described by means of a bidimensional Hilbert Curve -iteration 7-.	A 'crumpled' sphere described by means of a bidimensional Hilbert Curve -iteration 7-.	A torus described by means of a bidimensional Hilbert Curve -iteration 7-.	The Bonan-Jeener double bottle described by means of a bidimensional Hilbert Curve -iteration 7-.	The Möbius strip described by means of a bidimensional Hilbert Curve -iteration 7-.
The Klein bottle described by means of a bidimensional Hilbert Curve -iteration 7-.	The Klein bottle described by means of a bidimensional Hilbert Curve -iteration 7-.	The Klein bottle described by means of a bidimensional Hilbert-like Curve -iteration 6-.	The Klein bottle described by means of a bidimensional Hilbert-like Curve -iteration 6-.	The Klein bottle described by means of a bidimensional Hilbert-like Curve -iteration 7-.
The Klein bottle described by means of a bidimensional Hilbert-like Curve -iteration 5-.

A sphere described by means of a bidimensional Peano Curve -6 digits-.

A torus described by means of a bidimensional Peano Curve -6 digits-.

The Bonan-Jeener double bottle described by means of a bidimensional Peano Curve -6 digits-.

A sphere described by means of a bidimensional Peano Curve -8 digits-.

A torus described by means of a bidimensional Peano Curve -8 digits-.

The Bonan-Jeener double bottle described by means of a bidimensional Peano Curve -8 digits-.

The Möbius strip described by means of a bidimensional Peano Curve -8 digits-.

The Klein bottle described by means of a bidimensional Peano Curve -8 digits-.

A sphere described by means of a bidimensional Hilbert-like Curve -iteration 5-.

A torus described by means of a bidimensional Hilbert-like Curve -iteration 5-.

The Bonan-Jeener double bottle described by means of a bidimensional Hilbert-like Curve -iteration 5-.

A sphere described by means of a bidimensional Hilbert-like Curve -iteration 6-.	A torus described by means of a bidimensional Hilbert-like Curve -iteration 6-.	The Bonan-Jeener double bottle described by means of a bidimensional Hilbert-like Curve -iteration 6-.	The Möbius strip described by means of a bidimensional Hilbert-like Curve -iteration 6-.	The Klein bottle described by means of a bidimensional Hilbert-like Curve -iteration 6-.
The Klein bottle described by means of a bidimensional Hilbert-like Curve -iteration 6-.

Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 bidimensional Hilbert Curves -iteration 4-.

Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 bidimensional Hilbert Curves -iteration 5-.

Tridimensional Fractal Curves [Courbes Fractales Tridimensionnelles]:

Tridimensional Hilbert Curve -iteration 1-.

Tridimensional Hilbert Curve -iteration 2-.

Tridimensional Hilbert Curve -iteration 3-.

Tridimensional Hilbert Curve -iteration 4-.

Tridimensional Hilbert Curve -iteration 1-.

Tridimensional Hilbert Curve -iteration 2-.

Tridimensional Hilbert Curve -iteration 3-.

Tridimensional Hilbert Curve -iteration 4-.

The tridimensional [0,1] --> [0,1]x[0,1]x[0,1] Peano Surjection -T defined with 3 digits-.

The tridimensional [0,1] --> [0,1]x[0,1]x[0,1] Peano Surjection -T defined with 6 digits-.

The tridimensional [0,1] --> [0,1]x[0,1]x[0,1] Peano Surjection -T defined with 9 digits-.

A tridimensional Hilbert-like curve defined with {X₁(...),Y₁(...),Z₁(...)} -iteration 1-.

A tridimensional Hilbert-like curve defined with {X₂(...),Y₂(...),Z₂(...)} -iteration 2-.

A tridimensional Hilbert-like curve defined with {X₃(...),Y₃(...),Z₃(...)} -iteration 3-.

A tridimensional Hilbert-like curve defined with {X₄(...),Y₄(...),Z₄(...)} -iteration 4-.

A tridimensional Hilbert-like curve defined with {X₅(...),Y₅(...),Z₅(...)} -iteration 5-.

A tridimensional Hilbert-like curve defined with {X₁(...),Y₁(...),Z₁(...)} -iteration 1-.

A tridimensional Hilbert-like curve defined with {X₂(...),Y₂(...),Z₂(...)} -iteration 2-.

A tridimensional Hilbert-like curve defined with {X₃(...),Y₃(...),Z₃(...)} -iteration 3-.

A tridimensional Hilbert-like curve defined with {X₄(...),Y₄(...),Z₄(...)} -iteration 4-.

A tridimensional Hilbert-like curve defined with {X₁(...),Y₁(...),Z₁(...)} and based on an 'open' 3-foil torus knot -iteration 1-.

A tridimensional Hilbert-like curve defined with {X₂(...),Y₂(...),Z₂(...)} and based on an 'open' 3-foil torus knot -iteration 2-.

A tridimensional Hilbert-like curve defined with {X₃(...),Y₃(...),Z₃(...)} and based on an 'open' 3-foil torus knot -iteration 3-.

A tridimensional Hilbert-like curve defined with {X₄(...),Y₄(...),Z₄(...)} and based on an 'open' 3-foil torus knot -iteration 4-.

A tridimensional Hilbert-like curve defined with {X₅(...),Y₅(...),Z₅(...)} and based on an 'open' 3-foil torus knot -iteration 5-.

A tridimensional Hilbert-like curve defined with {X₁(...),Y₁(...),Z₁(...)} and based on an 'open' 3-foil torus knot -iteration 1-.

A tridimensional Hilbert-like curve defined with {X₂(...),Y₂(...),Z₂(...)} and based on an 'open' 3-foil torus knot -iteration 2-.

A tridimensional Hilbert-like curve defined with {X₃(...),Y₃(...),Z₃(...)} and based on an 'open' 3-foil torus knot -iteration 3-.

A tridimensional Hilbert-like curve defined with {X₄(...),Y₄(...),Z₄(...)} and based on an 'open' 3-foil torus knot -iteration 4-.

A tridimensional Hilbert-like curve defined with {X₁(...),Y₁(...),Z₁(...)} and based on an 'open' 3-foil torus knot -iteration 1-.

A tridimensional Hilbert-like curve defined with {X₂(...),Y₂(...),Z₂(...)} and based on an 'open' 3-foil torus knot -iteration 2-.

A tridimensional Hilbert-like curve defined with {X₃(...),Y₃(...),Z₃(...)} and based on an 'open' 3-foil torus knot -iteration 3-.

A tridimensional Hilbert-like curve defined with {X₄(...),Y₄(...),Z₄(...)} and based on an 'open' 3-foil torus knot -iteration 4-.

A tridimensional Hilbert-like curve defined with {X₅(...),Y₅(...),Z₅(...)} and based on an 'open' 3-foil torus knot -iteration 5-.

A tridimensional Hilbert-like curve defined with {X₁(...),Y₁(...),Z₁(...)} and based on an 'open' 5-foil torus knot -iteration 1-.

A tridimensional Hilbert-like curve defined with {X₂(...),Y₂(...),Z₂(...)} and based on an 'open' 5-foil torus knot -iteration 2-.

A tridimensional Hilbert-like curve defined with {X₃(...),Y₃(...),Z₃(...)} and based on an 'open' 5-foil torus knot -iteration 3-.

A tridimensional Hilbert-like curve defined with {X₄(...),Y₄(...),Z₄(...)} and based on an 'open' 5-foil torus knot -iteration 4-.

A tridimensional Hilbert-like curve defined with {X₅(...),Y₅(...),Z₅(...)} and based on an 'open' 5-foil torus knot -iteration 5-.

A tridimensional Hilbert-like curve defined with {X₁(...),Y₁(...),Z₁(...)} and based on an 'open' 7-foil torus knot -iteration 1-.

A tridimensional Hilbert-like curve defined with {X₂(...),Y₂(...),Z₂(...)} and based on an 'open' 7-foil torus knot -iteration 2-.

A tridimensional Hilbert-like curve defined with {X₃(...),Y₃(...),Z₃(...)} and based on an 'open' 7-foil torus knot -iteration 3-.

A tridimensional Hilbert-like curve defined with {X₄(...),Y₄(...),Z₄(...)} and based on an 'open' 7-foil torus knot -iteration 4-.

A tridimensional Hilbert-like curve defined with {X₅(...),Y₅(...),Z₅(...)} and based on an 'open' 7-foil torus knot -iteration 5-.

A parallelepipedic Torus described by means of a tridimensional Hilbert Curve -iteration 4-.

A Jeener-Möbius tridimensional manifold described by means of a tridimensional Hilbert Curve -iteration 4-.

A parallelepipedic Torus described by means of an 'open' 3-foil torus knot -iteration 4-.

A Jeener-Möbius tridimensional manifold described by means of an 'open' 3-foil torus knot -iteration 4-.

Fractal Spaces [Espaces Fractals]:

Monodimensional Fractal Spaces [Espaces Fractals Monodimensionnels]:

The Cantor triadic set -iterations 0 to 5-.

Bidimensional Fractal Spaces [Espaces Fractals Bidimensionnels]:

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 1 to 5-.

Tridimensional Fractal Spaces [Espaces Fractals Tridimensionnels]:

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-.

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-.

An extended Menger sponge -iteration 1-.

An extended Menger sponge -iteration 2-.

An extended Menger sponge -iteration 3-.

An extended Menger sponge -iteration 4-.

An extended Menger sponge -iteration 5-.

An extended Menger sponge -iteration 1-.

An extended Menger sponge -iteration 2-.

An extended Menger sponge -iteration 3-.

An extended Menger sponge -iteration 4-.

An extended Menger sponge -iteration 5-.

An extended Menger sponge -iteration 1-.

An extended Menger sponge -iteration 2-.

An extended Menger sponge -iteration 3-.

An extended Menger sponge -iteration 4-.

An extended Menger sponge -iteration 5-.

An extended Menger sponge -iteration 1-.

An extended Menger sponge -iteration 2-.

An extended Menger sponge -iteration 3-.

An extended Menger sponge -iteration 4-.

An extended Menger sponge -iteration 5-.

An extended Menger sponge -iteration 1-.

An extended Menger sponge -iteration 2-.

An extended Menger sponge -iteration 3-.

An extended Menger sponge -iteration 4-.

An extended Menger sponge -iteration 5-.

An extended Menger sponge -iteration 1-.

An extended Menger sponge -iteration 2-.

An extended Menger sponge -iteration 3-.

An extended Menger sponge -iteration 4-.

An extended Menger sponge -iteration 5-.

An extended Menger sponge -iteration 1-.

An extended Menger sponge -iteration 2-.

An extended Menger sponge -iteration 3-.

An extended Menger sponge -iteration 4-.

An extended Menger sponge -iteration 5-.

An extended Menger sponge -iteration 1-.

An extended Menger sponge -iteration 2-.

An extended Menger sponge -iteration 3-.

An extended Menger sponge -iteration 4-.

An extended Menger sponge -iteration 5-.

An extended Menger sponge -iteration 1-.

An extended Menger sponge -iteration 2-.

An extended Menger sponge -iteration 3-.

An extended Menger sponge -iteration 4-.

An extended Menger sponge -iteration 5-.

An extended Menger sponge -iteration 1-.

An extended Menger sponge -iteration 2-.

An extended Menger sponge -iteration 3-.

An extended Menger sponge -iteration 4-.

An extended Menger sponge -iteration 5-.

An extended Menger sponge -iteration 1-.

An extended Menger sponge -iteration 2-.

An extended Menger sponge -iteration 3-.

An extended Menger sponge -iteration 4-.

An extended Menger sponge -iteration 5-.

A parallelepipedic extended Menger sponge -iteration 1-.

A parallelepipedic extended Menger sponge -iteration 2-.

A parallelepipedic extended Menger sponge -iteration 3-.

A parallelepipedic extended Menger sponge -iteration 4-.

A parallelepipedic extended Menger sponge -iteration 5-.

An amazing generalized cross-section inside the Menger sponge -iteration 5-.	A 'pyramidal' cross-section inside the Menger sponge -iteration 5-, 'O temps tes pyramides' -a Tribute to Jorge Luis Borges-.	A 'double conic' cross-section inside the Menger sponge -iteration 5-, 'O temps tes pyramides' -a Tribute to Jorge Luis Borges-.	A 'conic' cross-section inside the Menger sponge -iteration 5-, 'O temps tes pyramides' -a Tribute to Jorge Luis Borges-.	A spherical cross-section inside the Menger sponge -iteration 5-.
A double spherical cross-section inside the Menger sponge -iteration 5-.	A thin double spherical cross-section inside the Menger sponge -iteration 5-.

A full-random extended Menger sponge -iteration 1-.

A full-random extended Menger sponge -iteration 2-.

A full-random extended Menger sponge -iteration 3-.

A full-random extended Menger sponge -iteration 4-.

A full-random extended Menger sponge -iteration 5-.

A half-random extended Menger sponge -iteration 1-.

A half-random extended Menger sponge -iteration 2-.

A half-random extended Menger sponge -iteration 3-.

A half-random extended Menger sponge -iteration 4-.

A half-random extended Menger sponge -iteration 5-.

An amazing cross-section inside an extended Menger sponge -iteration 1-.

An amazing cross-section inside an extended Menger sponge -iteration 2-.

An amazing cross-section inside an extended Menger sponge -iteration 3-.

An amazing cross-section inside an extended Menger sponge -iteration 4-.

An amazing cross-section inside an extended Menger sponge -iteration 5-.

A half-random extended Menger sponge -iteration 1-.

A half-random extended Menger sponge -iteration 2-.

A half-random extended Menger sponge -iteration 3-.

A half-random extended Menger sponge -iteration 4-.

A half-random extended Menger sponge -iteration 5-.

Untitled 0595.

Untitled 0596.

Distorsion of the Menger sponge -iteration 2-.

Distorsion of the Menger sponge -iteration 3-.

A tridimensional billiard starting with a Menger sponge -iteration 2-.

Complex Sets [Ensembles dans le Plan Complexe]:

More information about Complex Numbers

Complex Mandelbrot Set [Ensemble de Mandelbrot dans le Plan Complexe]:

More information about the Complex Mandelbrot Set

The Mandelbrot set.

Iterations in the complex plane: the computation of the Mandelbrot set.

The connexity of the Mandelbrot set.

The Mandelbrot set computed for 1 to 4 iterations.

The Mandelbrot set computed for 1 to 16 iterations.

Bidimensional zoom in on the Mandelbrot set.

Tridimensional zoom in on the Mandelbrot set.

The Mandelbrot set computed for 1 to 4 iterations with display of the arguments.

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.

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.	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.

The Mandelbrot set with bidimensional display of the arguments and computed with an increasing exponent, from 1 -bottom left- to 16 -top right-.

The Mandelbrot set with tridimensional display of the arguments and computed with an increasing exponent, from 1 -bottom left- to 16 -top right-.

Tridimensional visualization of the Mandelbrot set with mapping of the arguments -the Mont Saint Michel-.

The fiftieth anniversary of CNRS (bird's-eye view).

The fiftieth anniversary of CNRS.

The eightieth anniversary of CNRS (bird's-eye view).

The eightieth anniversary of CNRS.

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

More information about Complex Julia Sets

A Douady rabbit -a complex Julia set computed with A=(-0.13,+0.77)- with display of the arguments.

Iterations in the complex plane: the computation of a Julia set.

16 complex Julia sets.

Journey on the Complex Plane by means of a Bidimensional Hilbert Curve -iteration 1- with display of Julia sets.

Journey on the Complex Plane by means of a Bidimensional Hilbert Curve -iteration 2- with display of Julia sets.

Journey on the Complex Plane by means of a Bidimensional Hilbert Curve -iteration 3- with display of Julia sets.

Journey on the Complex Plane by means of a Bidimensional Hilbert Curve -iteration 4- with display of Julia sets.

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

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.

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

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=Gamma(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].

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

Computation of the roots of Z³=1 using Newton's method.

Computation of the roots of Z⁵=1 using Newton's method.

Computation of the roots of Z³=1 using Newton's method.	Computation of the roots of Z⁴=1 using Newton's method.	Computation of the roots of Z⁵=1 using Newton's method.	Computation of the roots of Z⁶=1 using Newton's method.	Computation of the roots of Z⁷=1 using Newton's method.
Computation of the roots of Z⁸=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]:

More information about Quaternionic Numbers

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

More information about the Quaternionic Mandelbrot Set

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]:

More information about Quaternionic Julia Sets

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):

Autostereograms [Autostéréogrammes]:

Autostereogram of a quaternionic Julia set -tridimensional cross-section-.	Autostereogram of a quaternionic Julia set -tridimensional cross-section-.	True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-.	True colors autostereogram of a quaternionic Julia set -tridimensional cross-section-.	Autostereogram of a quaternionic Julia set and fractal phenomenon -tridimensional cross-section-.
Autostereogram of a quaternionic Julia set -tridimensional cross-section-.

The first autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-.

The first true colors autostereogram movie about quaternionic Julia sets -tridimensional cross-sections-.

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 Q³=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 Q³=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 Q⁸=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]:

More information about Pseudo-Quaternionic Numbers

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-.	A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	Close-up on a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.
Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.	Close-up on a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	Untitled 0279.	Untitled 0280.	Close-up on a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.
Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.	Close-up on a foggy pseudo-quaternionic Mandelbrot set with a (1/O)² conformal transformation in the octonionic space -tridimensional cross-section-.	Close-up on a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.	2.pi rotation about the Y axis of a pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.

The quaternionic Mandelbrot set -tridimensional cross-section-.	The quaternionic Mandelbrot set - using the pseudo-addition and the pseudo-multiplication in C- -tridimensional cross-section-.	The quaternionic Mandelbrot set - using the pseudo-addition and the pseudo-multiplication in C- -tridimensional cross-section-.	The quaternionic Mandelbrot set - using the pseudo-addition and the pseudo-multiplication in C- -tridimensional cross-section-.	The quaternionic Mandelbrot set - using the pseudo-addition and the pseudo-multiplication in C- -tridimensional cross-section-.
The quaternionic Mandelbrot set - using the pseudo-addition and the pseudo-multiplication in C- -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-.

A foggy pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0) and with a rotation about the Y axis -tridimensional cross-section-.

A pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0) and with a rotation about the Y axis and with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -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-.

The quaternionic Julia set -degree=2- computed with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.	The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.	The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.	The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.	The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.
The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.

The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.	The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.	The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.	The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.	The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.
The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- 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=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.58...,+0.63...,0,0) -tridimensional cross-section-.

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 Q³=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 visualizations of the Verhulst dynamics.

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

Tridimensional high resolution visualization of an extended Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-.

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

Tridimensional visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-.	Tridimensional visualization of the Verhulst dynamics -'The Flying Dutchman', a Tribute to Richard Wagner-.	Tridimensional visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-.	Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-.	Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-.
Tridimensional visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-.

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

Tridimensional visualization of the Verhulst dynamics.

N-dimensional Verhulst Dynamics [Dynamique de Verhulst N-dimensionnelle]:

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

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

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]:

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

A foggy pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.
A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -'children's corner' 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') with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -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-.

A pseudo-octonionic Mandelbrot set -tridimensional cross-section-.

Close-up on a foggy pseudo-octonionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.

A pseudo-octonionic Mandelbrot set -tridimensional cross-section-.

Close-up on a foggy pseudo-octonionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.

A pseudo-octonionic Mandelbrot set -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-.

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

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) and with a rotation about the X axis -tridimensional cross-section-.
Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-.	Zoom in on a 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) and 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-.
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.	Zoom in on a 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) and with a 0 to pi 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) and 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) and 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-.

Trees [Arbres]:

A perfect bidimensional fractal tree and the self-similarity.

A binary tree.	A binary tree with 256 leaves.	Artistic view of a binary tree with 256 leaves.	A binary tree with 256 leaves.	A binary tree with 256 leaves.
A binary tree with 4096 leaves.

The three first bifurcation levels (over fifteen) of the human lung tree.

The seven first bifurcation levels (over fifteen) of the human lung tree.

A vibrating ternary tree.

The golden binary tree.

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.

Fractal new Moon.

Recursive pentagon.

Recursive 5-star.

The 64 first lines of the Pascal's Triangle -modulo 2-.

The 64 first lines of the Pascal's Triangle -modulo 3-.

The 64 first lines of the Pascal's Triangle -modulo 5-.

The 64 first lines of the Pascal's Triangle -modulo 7-.

The 64 first lines of the Pascal's Triangle.

Fractal piano keyboard.

Untitled 0194.

Untitled 0264.

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-.

[More information and visual access to more Deterministic Fractal Geometry pictures [Plus d'informations et accès visuel à plus d'images de Géométrie Fractale Déterministe]]
[See the Deterministic Fractal Geometry Slide Show [Visionnez le Diaporama de Géométrie Fractale Déterministe]]

Copyright © Jean-François Colonna, 2000-2023.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2023.

Gallery (564 different pictures): Deterministic Fractal Geometry [Galerie (564 images différentes) : Géométrie Fractale Déterministe]

Jean-François COLONNA

www.lactamme.polytechnique.fr

jean-francois.colonna@polytechnique.edu CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, 91120 Palaiseau, France france telecom, France Telecom R&D

Deterministic Fractal Geometry [Géométrie Fractale Déterministe]:

Deterministic Fractal Geometry [Géométrie Fractale Déterministe]:

Fractal Curves [Courbes Fractales]:

Bidimensional Fractal Curves [Courbes Fractales Bidimensionnelles]:

Tridimensional Fractal Curves [Courbes Fractales Tridimensionnelles]:

Fractal Spaces [Espaces Fractals]:

Monodimensional Fractal Spaces [Espaces Fractals Monodimensionnels]:

Bidimensional Fractal Spaces [Espaces Fractals Bidimensionnels]:

Tridimensional Fractal Spaces [Espaces Fractals Tridimensionnels]:

Complex Sets [Ensembles dans le Plan Complexe]:

Complex Mandelbrot Set [Ensemble de Mandelbrot dans le Plan Complexe]:

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

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

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

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

Quaternionic Sets [Ensembles dans le Corps des Quaternions]:

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

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

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]:

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

Stereograms [Stéréogrammes]:

Autostereograms [Autostéréogrammes]:

Miscellaneous Views [Vues Diverses]:

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

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

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

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

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

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

Verhulst Dynamics [Dynamique de Verhulst]:

Bidimensional Verhulst Dynamics [Dynamique de Verhulst bidimensionnelle]:

Tridimensional Verhulst Dynamics [Dynamique de Verhulst tridimensionnelle]:

N-dimensional Verhulst Dynamics [Dynamique de Verhulst N-dimensionnelle]:

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

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

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

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

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

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

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

Trees [Arbres]:

Miscellaneous [Divers]:

Copyright © Jean-François Colonna, 2000-2023. Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2023.

Copyright © Jean-François Colonna, 2000-2023. Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2023.

Gallery (564 different pictures):

Deterministic Fractal Geometry

[Galerie (564 images différentes) : Géométrie Fractale Déterministe]

jean-francois.colonna@polytechnique.edu
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, 91120 Palaiseau, France
france telecom, France Telecom R&D

Copyright © Jean-François Colonna, 2000-2023.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2023.

Copyright © Jean-François Colonna, 2000-2023.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2023.