Gallery (551 different pictures):

Generalities about Visualization

[Galerie (551 images différentes) : Généralités sur la Visualisation]

Generalities about Visualization [Généralités sur la Visualisation]:

Generalities about Visualization [Généralités sur la Visualisation]:

Curve Visualization [Visualisation de Courbes]:

An helix on a sphere.	An helix on a 'crumpled' sphere.	An helix on a torus.	An helix on a 'tridimensional epicycloïdal' pseudo-torus.	An helix on a 'tridimensional epicycloïdal' pseudo-torus.
An helix on the Klein bottle.	Two helices on the Bonan-Jeener-Klein triple bottle.





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 '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-.	The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 5-.	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-.





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





A Part of the DNA double helix -a Tribute to Francis Crick, Rosalind Franklin and James Watson-.





A twisting rope.

3-foil knot.

3-foil torus knot on its torus.

5-foil torus knot on its torus.

7-foil torus knot on its torus.

Random intertwining.	Intertwining based on a bidimensional square lattice.	Intertwining based on a conformal mapping of a bidimensional square lattice.	Intertwining based on the geometry of a disk.	Intertwining based on the geometry of the sphere.
Intertwining based on the geometry of the Boy surface.	Intertwining based on the geometry of a Möbius strip.	Intertwining based on the geometry of a Klein bottle.	Intertwining based on the geometry of the Bonan-Jeener-Klein triple bottle.	Intertwining based on the geometry of a shell (Jeener surface 1).
Intertwining based on the geometry of the Lorenz attractor.




Intersection Visualization [Visualisation d'Intersections]:

A straigth line -a monodimensional manifold- or a cylinder -a bidimensional manifold- in the distance?.

A cylinder -a bidimensional manifold-.

A cylinder -a bidimensional manifold-.





Bidimensional cross-sections of a cylinder.

Bidimensional cross-sections of a cylinder.

Bidimensional cross-sections of the Klein bottle.

Bidimensional cross-sections of the Klein bottle.

Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle.

Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle.

Bidimensional cross-sections of the Jeener unilateral node.

Bidimensional cross-sections of the Jeener unilateral node.

Bidimensional cross-sections of the Jeener unilateral node.




Surface Visualization [Visualisation de Surfaces]:

A one sheet hyperboloid of revolution -negative curvature-.

A plane -zero curvature-.

A sphere -positive curvature-.





A sphere.	A sphere defined by means of three bidimensional fields.	A sphere -positive curvature-.	A sphere described by means of a Bidimensional Hilbert Curve -iteration 7-.	A sphere described by means of a Bidimensional Peano Curve -8 digits-.
A sphere described by means of a Bidimensional Hilbert-like Curve -iteration 6-.	Bidimensional brownian motion on a sphere.	Bidimensional closed self-avoiding brownian motion on a sphere.	Bidimensional closed self-avoiding brownian motion on a sphere.

A set of spheres with holes.

A set of twisted spheres.

Distorsion of a sphere.

Distorsion of a sphere.

Distorsion of a sphere.

Distorsion of a sphere.

The 'exponential' of a sphere.	The 'cosine' of a sphere.	The 'sine' of a sphere.	The 'tangent' of a sphere.	The 'hyperbolic cosine' of a sphere.
The 'hyperbolic sine' of a sphere.	The 'hyperbolic tangent' of a sphere.

The 'exponential' of a sphere.	The 'cosine' of a sphere.	The 'sine' of a sphere.	The 'tangent' of a sphere.	The 'hyperbolic cosine' of a sphere.
The 'hyperbolic sine' of a sphere.	The 'hyperbolic tangent' of a sphere.





The pseudo-sphere.





A 'linear' Horner surface of the fourth degree.

A 'circular' Horner surface of the second degree.

A 'hyperbolic' Horner surface 1 of the second degree.

A 'hyperbolic' Horner surface 2 of the second degree.





A cylinder.

A cone.

A two sheet hyperboloid of revolution.





A torus.	A torus by means of three bidimensional fields.	A torus.	A torus described by means of a Bidimensional Hilbert Curve -iteration 7-.	A torus described by means of a Bidimensional Peano Curve -8 digits-.
A torus described by means of a Bidimensional Hilbert-like Curve -iteration 6-.	Bidimensional brownian motion on a torus.	Bidimensional closed self-avoiding brownian motion on a torus.	Bidimensional closed self-avoiding brownian motion on a torus.

Four overlaped torus.

Sixteen overlaped torus.

Sixty-four overlaped torus.





A two-hole pseudo-torus.	A 'bidimensional epicycloïdal' pseudo-torus.	A 'bidimensional epicycloïdal' pseudo-torus.	A 'tridimensional epicycloïdal' pseudo-torus.	Artistic view of a 'tridimensional epicycloïdal' pseudo-torus.
A 'tridimensional epicycloïdal' pseudo-torus.	A 'thick' helix.





1-foil torus knot -obvious knot- on its torus and its asociated Möbius strip.	3-foil torus knot on its torus.	3-foil torus knot on its torus.	5-foil torus knot on its torus.	5-foil torus knot on its torus.
7-foil torus knot on its torus.	7-foil torus knot on its torus.





Tridimensional representation of a quadridimensional Calabi-Yau manifold.	Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-.	Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-.	5x5 identical bidimensional closed self-avoiding brownian motions on a tridimensional representation of a quadridimensional Calabi-Yau manifold.	5x5 identical bidimensional closed self-avoiding brownian motions on a tridimensional representation of a quadridimensional Calabi-Yau manifold.
5x5 various bidimensional closed self-avoiding brownian motions on a tridimensional representation of a quadridimensional Calabi-Yau manifold.

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 4-.

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

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





The Möbius strip.	The Möbius strip.	The Möbius strip.	The Möbius strip.	Artistic view of the Möbius strip.
The Möbius strip.	The Möbius strip described by means of a Bidimensional Hilbert Curve -iteration 7-.	The Möbius strip described by means of a Bidimensional Peano Curve -8 digits-.	The Möbius strip described by means of a Bidimensional Hilbert-like Curve -iteration 6-.	Bidimensional brownian motion on the Möbius strip.
Bidimensional closed self-avoiding brownian motion on the Möbius strip.	Bidimensional closed self-avoiding brownian motion on the Möbius strip.

Distorsion of the Möbius strip.

Distorsion of the Möbius strip.

Distorsion of the Möbius strip.

Distorsion of the Möbius strip.

A gaussian mixing of a sphere and of the Möbius strip defined by means of three bidimensional fields.

An interpolation between the Möbius strip and a 'double sphere' defined by means of three sets of bidimensional fields.





The Jeener unilateral node.

The Jeener toric node.





The Klein bottle.	Artistic view of the Klein bottle.	The Klein bottle.	The Klein bottle described by means of a Bidimensional Hilbert Curve -iteration 7-.	The Klein bottle described by means of a Bidimensional Peano Curve -8 digits-.
The Klein bottle described by means of a Bidimensional Hilbert-like Curve -iteration 6-.	Bidimensional brownian motion on the Klein bottle.	Bidimensional closed pseudo-self-avoiding brownian motion on the Klein bottle.	Bidimensional closed pseudo-self-avoiding brownian motion on the Klein bottle.

The Klein bottle in motion.

The Klein bottle in motion.

The Klein bottle in motion.

A 'crumpled' Klein bottle defined by means of three bidimensional fields.

A dynamic 'crumpled' Klein bottle defined by means of three sets of bidimensional fields.





The double Jeener bottle.

The Bonan-Jeener double bottle.

The Bonan-Jeener double bottle described by means of a Bidimensional Hilbert Curve -iteration 7-.

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

The Bonan-Jeener double bottle described by means of a Bidimensional Hilbert-like Curve -iteration 6-.

The Jeener twin bottles.

Distorsion of the Bonan-Jeener-Klein double bottle.

Distorsion of the Bonan-Jeener-Klein double bottle.

Distorsion of the Bonan-Jeener-Klein double bottle.

Distorsion of the Bonan-Jeener-Klein double bottle.

Distorsion of the Bonan-Jeener-Klein double bottle.





The Jeener-Klein triple bottle.	The Jeener-Klein triple bottle.	The Bonan-Jeener-Klein triple bottle.	Bidimensional brownian motion on the Bonan-Jeener-Klein triple bottle.	Bidimensional closed pseudo-self-avoiding brownian motion on the Bonan-Jeener-Klein triple bottle.
Bidimensional closed pseudo-self-avoiding brownian motion on the Bonan-Jeener-Klein triple bottle.	A 'square' spiral on the Bonan-Jeener-Klein triple bottle.

The u=v line on the Bonan-Jeener-Klein triple bottle.

The u=v line on the Bonan-Jeener-Klein triple bottle and a strip.

Distorsion of the Bonan-Jeener-Klein triple bottle.





The Jeener's quadruple bilateral bottle.

The Jeener's quadruple bilateral bottle.

The quadruple Jeener bottle.





The Jeener-Klein quintuple bottle.

The Jeener-Klein quintuple bottle.

The Jeener-Klein quintuple bottle.

Artistic view of the Jeener-Klein quintuple bottle.





The interlaced epicycloidal Jeener bottle.

The interlaced epicycloidal Jeener bottle.

The interlaced epicycloidal Jeener bottle.





The interlaced hypocycloidal Jeener bottle.





The Jeener intertwining.	The Jeener-Klein bottle spiral.	The Jeener-Klein bottle 'epicycloidal' spiral.	The Jeener-Klein bottle frieze.	The Jeener-Klein bottle loop 1.
The Jeener-Klein bottle loop 2.	The Jeener-Klein bottle loop 2.





An interpolation between the Klein bottle and a 'double sphere' defined by means of three sets of bidimensional fields.

An interpolation between the Klein bottle and the double Jeener bottle defined by means of three sets of bidimensional fields.

Interpolation between the Jeener-Klein quintuple bottle and the Bonan-Jeener-Klein triple bottle.

An interpolation between the Bonan-Jeener-Klein triple bottle and a 'double sphere' defined by means of three sets of bidimensional fields.





The Boy surface.	Rotation about X and Y axes of the Boy surface.	The Boy surface.	Bidimensional brownian motion on the Boy surface.	Bidimensional closed pseudo-self-avoiding brownian motion on the Boy surface.
Bidimensional closed pseudo-self-avoiding brownian motion on the Boy surface.	A 'square' spiral on the Boy surface.

The Boy surface in motion.

Rotation about the Y axis of the Boy surface with motion blur.

From à rectangle to the Boy surface.

From a sphere to the Boy surface.





A shell (Jeener surface 1).	A shell (Jeener surface 1).	A shell (Jeener surface 1) in motion.	The Jeener shell -1-.	The Jeener shell -2-.
The Jeener waves -1-.	The Jeener hypocycloidal snail.	The Jeener nautilus.	The Jeener triton.	The Jeener 'bulot' -a shell-.
The Jeener giant clam.	An interpolation between a shell (Jeener surface 1) and a 'double sphere' defined by means of three sets of bidimensional fields.	An arbitrary surface (Jeener surface 2) in motion.	An arbitrary surface (Jeener surface 2).	An arbitrary surface (Jeener surface 2) in motion.
The Jeener bud.	The Jeener flower.	Untitled 0292.	The Jeener opera -10-Sydney-.





A Lissajous surface.

A Lissajous surface.

A Lissajous surface.

A Lissajous surface in motion.

A twisting Lissajous surface.





A 'crumpled' sphere defined by means of three bidimensional fields.	A 'crumpled' sphere defined by means of three bidimensional fields.	Fractal 'celestial body' based on a sphere.	Fractal 'celestial body' based on a sphere.	Fractal 'celestial body' based on a sphere.
Fractal 'celestial body' based on a sphere.





A 'crumpled' torus defined by means of three bidimensional fields.

A 'crumpled' torus defined by means of three bidimensional fields.

A 'crumpled' torus defined by means of three bidimensional fields.

Fractal 'celestial body' based on a torus.

Fractal 'celestial body' based on a torus.

Fractal 'celestial body' based on the Bonan-Jeener-Klein triple bottle.





A Peano 'fractal plane' defined by means of three bidimensional fields.





A 'crumpled' 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 'fractal plane' with overhangings described by means of a Bidimensional Hilbert Curve -iteration 7-.

A 'fractal plane' with overhangings described by means of a Bidimensional Hilbert Curve -iteration 7-.

A 'fractal plane' with overhangings described by means of a Bidimensional Hilbert-like Curve -iteration 6-.





A fractal surface defined by means of three bidimensional fields.	A fractal surface (one iteration) defined by means of three bidimensional fields.	A fractal surface (two iterations) defined by means of three bidimensional fields.	A fractal surface (three iterations) defined by means of three bidimensional fields.	A fractal surface (four iterations) defined by means of three bidimensional fields.
A fractal surface (five iterations) defined by means of three bidimensional fields.	A fractal surface (six iterations) defined by means of three bidimensional fields.	A fractal surface (seven iterations) defined by means of three bidimensional fields.	A fractal surface (eight iterations) defined by means of three bidimensional fields.	A fractal surface (four iterations) defined by means of three bidimensional fields.
A fractal surface (four iterations) defined by means of three bidimensional fields.	A dynamic fractal surface (four iterations) defined by means of three sets of bidimensional fields.





Archimedian gaussian surface (bird's-eye view).





Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation).





A 'square' spiral.	A 'square' spiral on a sphere.	A 'square' spiral on a torus.	A 'square' spiral on the Möbius strip.	A 'square' spiral on the Klein bottle.
A 'square' spiral on the Bonan-Jeener-Klein triple bottle.	A 'square' spiral on the Boy surface.





Bidimensional Hilbert Curve -iteration 7-.	A sphere described by means of a Bidimensional Hilbert Curve -iteration 7-.	A torus 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 Bonan-Jeener double bottle described by means of a Bidimensional Hilbert Curve -iteration 7-.	A 'fractal plane' with overhangings described by means of a Bidimensional Hilbert Curve -iteration 7-.





A Bidimensional Hilbert-like Curve defined with {X6(...),Y6(...)} -iteration 6-.	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 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 Bonan-Jeener double bottle described by means of a Bidimensional Hilbert-like Curve -iteration 6-.




Tridimensional Manifold Visualization [Visualisation de Variétés Tridimensionnelles]:

Tridimensional fractal structure.

Bidimensional cross-sections inside a fractal structure.

Tridimensional fractal structure.

Bidimensional cross-sections inside a fractal structure.





A parallelepipedic Hyper-Torus.

A Ball.

A 'linear' Horner manifold of the third degree.

A 'circular' Horner manifold of the first degree.

A 'hyperbolic' Horner manifold 1 of the first degree.

A 'hyperbolic' Horner manifold 2 of the first degree.

Rotation about the Y (vertical) axis of a Jeener-Möbius tridimensional manifold that can also be viewed as a set of 4x3 stereograms.

A Jeener-Möbius tridimensional manifold.

Rotation about the Y (vertical) axis of a Jeener-Möbius tridimensional manifold that can also be viewed as a set of 4x3 stereograms.

A Jeener-Möbius tridimensional manifold.

A Jeener-Möbius tridimensional manifold.





A tridimensional structure based on a 1/O conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.

A tridimensional structure based on a 1/O conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.

A tridimensional structure based on a 1/O conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.




Tridimensional Visualization of Bidimensional Scalar Fields [Visualisation de Champs Scalaires Bidimensionnels]:

A fractal landscape.

Wavelet transform of a bidimensional fractal field.




Visualization of Tridimensional Scalar Fields [Visualisation de Champs Scalaires Tridimensionnels]:

A tridimensional twisted torus-like manifold defined by means of three tridimensional fields.

A tridimensional Möbius-like manifold defined by means of three tridimensional fields.

A tridimensional fractal manifold defined by means of three tridimensional fields.





Black and white display of a tridimensional function.

Black and white display of a tridimensional function.

Color display of a tridimensional function.

Color display of a tridimensional function.




Visualization of Tridimensional Vector Fields [Visualisation de Champs de Vecteurs Tridimensionnels]:

The normal field of a shell (Jeener surface 1).	The normal field of a shell (Jeener surface 1).	The normal field of a shell (Jeener surface 1).	The normal field of the Klein bottle.	The normal field of the Bonan-Jeener-Klein triple bottle.
The normal field of a 'crumpled' sphere defined by means of three bidimensional fields.	The normal field of a tridimensional representation of a quadridimensional Calabi-Yau manifold.	The normal field of a fractal surface defined by means of three bidimensional fields.	The normal field of a fractal surface defined by means of three bidimensional fields.




Visualization of Bidimensional Time-Dependent Scalar Fields [Visualisation de Champs Scalaires Bidimensionnels Dépendant du Temps]:

Dynamics of a bidimensional fractal structure.

Tridimensional fractal structure.




Visualization of Tridimensional Time-Dependent Scalar Fields [Visualisation de Champs Scalaires Tridimensionnels Dépendant du Temps]:

Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation).




Picture Sharpening [Amélioration de la netteté d'une image]:

A tridimensional fractal manifold defined by means of three tridimensional fields.

A tridimensional fractal manifold defined by means of three tridimensional fields -picture sharpening-.

A tridimensional fractal manifold defined by means of three tridimensional fields -picture sharpening-.

Tridimensional representation of a quadridimensional Calabi-Yau manifold.

Tridimensional representation of a quadridimensional Calabi-Yau manifold -picture sharpening-.

Tridimensional representation of a quadridimensional Calabi-Yau manifold -picture sharpening-.

A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.

A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section, picture sharpening-.

A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section, picture sharpening-.




Stereograms [Stéréogrammes]:

A set of 4x3 stereograms displaying a tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps.

A set of 4x3 stereograms displaying a tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps.

Rotation about the Y (vertical) axis of a tridimensional representation of quadridimensional Calabi-Yau manifolds that can also be viewed as a set of 4x3 stereograms -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-.	Rotation about the Y (vertical) axis of a tridimensional representation of quadridimensional Calabi-Yau manifolds that can also be viewed as a set of 4x3 stereograms -Calabi-Yau manifolds attached to every point of our familiar tridimensional space?-.	Rotation about the Y (vertical) axis of a tridimensional representation of quadridimensional Calabi-Yau manifolds that can also be viewed as a set of 4x3 stereograms -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-.	Rotation about the Y (vertical) axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms.	Rotation about the Y (vertical) axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms.
Rotation about the Y (vertical) axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms.	Rotation about the Y (vertical) axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms.

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=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-.	Rotation about the Y (vertical) axis of a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') that can also be viewed as a set of 4x3 stereograms -tridimensional cross-section-.	A set of 4x3 stereograms of a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	A set of 4x3 stereograms of a close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.
A set of 4x3 stereograms of a close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	A set of 4x3 stereograms of a close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	A set of 4x3 stereograms of a tridimensional visualization of the Verhulst dynamics.	A set of 4x3 stereograms of a tridimensional visualization of the Verhulst dynamics.	A set of 4x3 stereograms of a tridimensional visualization of the Verhulst dynamics.
A set of 4x3 stereograms of a tridimensional visualization of the Verhulst dynamics.	A set of 4x3 stereograms of a tridimensional visualization of the Verhulst dynamics.	A set of 4x3 stereograms of an interpolation between a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') and a tridimensional Verhulst dynamics -tridimensional cross-section-.

Rotation about the Y (vertical) axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms.	Rotation about the Y (vertical) axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms.	A set of 4x3 stereograms of the Solar System with a green virtual planet -virtual planet point of view-.	A set of 4x3 stereograms of the Solar System with a green virtual planet -virtual planet point of view-.	A set of 4x3 stereograms of the Solar System with a green virtual planet -virtual planet point of view-.
A set of 4x3 stereograms of the Solar System with a green virtual planet -virtual planet point of view-.	A set of 4x3 stereograms of the Solar System with a green virtual planet -virtual planet point of view-.

A set of 4x3 stereograms of a fractal sphere.	A set of 4x3 stereograms of a fractal torus.	Rotation about the Y (vertical) axis of the 1-foil torus knot on its torus and its asociated Möbius strip, that can also be viewed as a set of 4x3 stereograms.	A set of 4x3 stereograms of a fractal Möbius strip.	Rotation about the Y (vertical) axis of the 3-foil torus knot on its torus, that can also be viewed as a set of 4x3 stereograms.
A set of 4x3 stereograms of a fractal 3-foil torus knot.	Rotation about the Y (vertical) axis of the 5-foil torus knot on its torus, that can also be viewed as a set of 4x3 stereograms.	A set of 4x3 stereograms of a fractal 5-foil torus knot.	Rotation about the Y (vertical) axis of the 7-foil torus knot on its torus, that can also be viewed as a set of 4x3 stereograms.	A set of 4x3 stereograms of a fractal 7-foil torus knot.
A set of 4x3 stereograms of a fractal polyhedron.	Rotation about the Y (vertical) axis of the u=v line on the Bonan-Jeener-Klein triple bottle and a strip, that can also be viewed as a set of 4x3 stereograms.	Rotation about the Y (vertical) axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms.	A set of 4x3 stereograms of a fractal Klein bottle.	Rotation about the Y (vertical) axis of the Jeener-Klein triple bottle that can also be viewed as a set of 4x3 stereograms.
Rotation about the Y (vertical) axis of sixteen interlaced torus that can also be viewed as a set of 4x3 stereograms.	Rotation about the Y (vertical) axis of a Jeener-Möbius tridimensional manifold that can also be viewed as a set of 4x3 stereograms.	Rotation about the Y (vertical) axis of a Jeener-Möbius tridimensional manifold that can also be viewed as a set of 4x3 stereograms.	A set of 4x3 stereograms of a fractal hypercube.

A set of 4x3 stereograms of a fractal-fractal tree.

A set of 4x3 stereograms of a fractal Notre-Dame de la Garde, Marseilles.

Rotation about the Y (vertical) axis of a tridimensional fractal aggregate that can also be viewed as a set of 4x3 pseudo-stereograms.

Rotation about the Y (vertical) axis of a tridimensional brownian motion that can also be viewed as a set of 4x3 stereograms.

Visualization by means of a set of 4x3 stereograms of the density iso-surfaces (density=0.42) during a tridimensional diffusion process of 128312 particles.

A set of 4x3 stereograms of a tridimensional integration of an anisotropic gaussian Fourier filtering of a random field with a 2.pi rotation of the kernel.

Rotation about the Y (vertical) axis of the CMAP logo that can also be viewed as a set of 4x3 stereograms.

Rotation about the Y (vertical) axis of a tridimensional fractal structure that can also be viewed as a set of 4x3 stereograms.

A set of 4x3 stereograms of a fractal mountain.	A set of 4x3 stereograms of a few Babel Towers.	A set of 4x3 stereograms of a few Monument Valleys at sunset.	A set of 4x3 stereograms of a few Monument Valleys at sunset.	A set of 4x3 stereograms of a tridimensional fractal structure.
A set of 4x3 stereograms of a tridimensional fractal structure.	A set of 4x3 stereograms of a tridimensional fractal structure -the space-time foam?-.	A set of 4x3 stereograms of a tridimensional fractal structure.	A set of 4x3 stereograms of a tridimensional interpolation between a fractal structure and a cubic mesh.	A set of 4x3 stereograms of a tridimensional interpolation between a fractal structure and a cubic mesh.
A set of 4x3 stereograms of a tridimensional filamentous fractal structure.	A set of 4x3 stereograms of a tridimensional filamentous fractal structure.




Autostereograms [Autostéréogrammes]:

[More information]
[do you want to know how to generate an autostereogram with a C test program?]

Autostereograms of a Volcano [Autostéréogrammes d'un Volcan]:

Autostereogram with an hidden volcano and 64 self-portraits.	Autostereogram with an hidden volcano.	Autostereogram with an hidden volcano.	Autostereogram -using periodical light clouds as desguise texture- with a hidden gaussian mountain.	Autostereogram with an hidden volcano.
Autostereogram with an hidden volcano.	Autostereogram with an hidden volcano and fractal phenomenon.	Autostereogram with an hidden volcano.	Autostereogram with an hidden volcano.	Autostereogram with an hidden volcano.
Autostereogram with an hidden volcano by means of only 231 random points.




Autostereograms of Quaternionic Julia Sets [Autostéréogrammes d'Ensembles de Julia Calculés dans le Corps des Quaternions]:

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-.




More Autostereograms [Autres Exemples d'Autostéréogrammes]:

Autostereogram -using a periodical paradoxal structure as a desguise texture- with an hidden gaussian mountain.	Double autostereogram -using a periodical paradoxal structure and periodical light clouds as desguise textures- with two hidden gaussian mountains.	Autostereogram with an hidden ring and ghost bows.	Autostereogram of 8 color-multiplexed quaternionic Julia sets -tridimensional cross-sections-.	Two multiplexed autostereograms by means of a pi/2 rotation.
Autostereogram with an hidden volcano and an animated disguise texture.	True colors autostereogram of a fractal landscape.	Autostereogram of Monument Valley.

Autostereogram of the CMAP.

Autostereogram of the 20-th anniversary of the CMAP (10/1994).




Anaglyphs [Anaglyphes]:

Anaglyphic glasses.

Anaglyph -blue=right, red=left- of an hypercube.	Anaglyph -blue=right, red=left- of a fractal hypercube.	Anaglyph -blue=right, red=left- of the Tridimensional Hilbert Curve -iteration 3-.	Anaglyph -blue=right, red=left- of the Tridimensional Hilbert Curve -iteration 4-.	Anaglyph -blue=right, red=left- of a tridimensional fractal cross -iteration 4-.
Anaglyph -blue=right, red=left- of a tridimensional fractal cross -iteration 5-.

Anaglyph -blue=right, red=left- of the Lorenz attractor.	Anaglyph -blue=right, red=left- of a tridimensional representation of a quadridimensional Calabi-Yau manifold.	Anaglyph -blue=right, red=left- of an artistic view of a pyramidal Menger Sponge computed by means of an 'Iterated Function System' -IFS-.	Anaglyph -blue=right, red=left- of a tridimensional interpolation between a fractal structure and a cubic mesh.	Anaglyph -blue=right, red=left- of a tridimensional interpolation between a fractal structure and a cubic mesh.
Anaglyph -blue=right, red=left- of a tridimensional fractal structure.	Anaglyph -blue=right, red=left- of a tridimensional fractal structure -the space-time foam?-.	Anaglyph -blue=right, red=left- of a tridimensional fractal structure.	Anaglyph -blue=right, red=left- of a fractal-fractal tree.

Anaglyph -blue=right, red=left- of a tridimensional filamentous fractal structure.	Anaglyph -blue=right, red=left- of a tridimensional filamentous fractal structure.	Anaglyph -blue=right, red=left- of a fractal sphere.	Anaglyph -blue=right, red=left- of a fractal torus.	Anaglyph -blue=right, red=left- of a fractal 3-foil torus knot.
Anaglyph -blue=right, red=left- of a fractal 5-foil torus knot.	Anaglyph -blue=right, red=left- of a fractal 7-foil torus knot.	Anaglyph -blue=right, red=left- of a fractal polyhedron.	Anaglyph -blue=right, red=left- of a fractal Möbius strip.	Anaglyph -blue=right, red=left- of a fractal Klein bottle.

Anaglyph -blue=right, red=left- of a fractal Notre-Dame de la Garde, Marseilles.

Anaglyph -blue=right, red=left- of a pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -'the children round' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-.

Anaglyph -blue=right, red=left- of a close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.

Anaglyph -blue=right, red=left- of a close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.





Anaglyph -green=right, red=left- of a tridimensional display of the Mandebrot set.




Cross-Sections with Translations and/or Rotations [Sections avec Translations et/ou Rotations]:

A cylinder -a bidimensional manifold-.

A cylinder -a bidimensional manifold-.

Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -sixteen bidimensional cross-sections-.

Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.

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.

Bidimensional cross-sections of a cylinder.

Bidimensional cross-sections of a cylinder.

Bidimensional cross-sections of the Klein bottle.

Bidimensional cross-sections of the Klein bottle.

Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle.

Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle.

Bidimensional cross-sections of the Jeener unilateral node.

Bidimensional cross-sections of the Jeener unilateral node.

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-.




Enhancement of the Third Dimension -Fog, Depth of Field, Lighting,...- [Améliorations de la Perception de la Troisième Dimension -Brouillard, Profondeur de Champ, Eclairage,...-]:

Cauliflowers, seaweeds, shells,... with fog.

Depth of field effect.

Depth of field effect with motion blur.

A 'spiraling plane' defined by means of three bidimensional fields with depth of field effect.

Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') for sixteen different lightings -tridimensional cross-section-.




Third and Fourth Dimensions Visualization and beyond [Visualisation de la troisième et de la Quatrième Dimensions et au-delà]:

A straigth line -a monodimensional manifold- or a cylinder -a bidimensional manifold- in the distance?.

A cylinder -a bidimensional manifold-.

A cylinder -a bidimensional manifold-.

Hypercube.

A 4-cube -an hypercube-.

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.

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-.

Bidimensional cross-sections of a cylinder.

Bidimensional cross-sections of a cylinder.

Bidimensional cross-sections of the Klein bottle.

Bidimensional cross-sections of the Klein bottle.

Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle.

Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle.

Bidimensional cross-sections of the Jeener unilateral node.

Bidimensional cross-sections of the Jeener unilateral node.

Bidimensional cross-sections of the Jeener unilateral node.




N-Dimensional Space Full Visualization [Visualisation complète d'Espaces à N Dimensions]:

32 points on a trigonometric circle.	The 2 vertices of a 1-cube.	The 4 vertices of a 2-cube.	The 8 vertices of a 3-cube.	The 16 vertices of a 4-cube.
The 32 vertices of a 5-cube.	Rotation about the X axis of the 32 vertices of a 5-cube.	Rotation about the Y axis of the 32 vertices of a 5-cube with fog.

N-dimensional random structure.

N-dimensional random structure.

Tridimensional representation of an octodimensional Calabi-Yau manifold with pseudo-random projection.

Tridimensional representation of an octodimensional Calabi-Yau manifold with pseudo-random projection.

Tridimensional representation of an octodimensional Calabi-Yau manifold with pseudo-random projection.




Time Visualization [Visualisation du Temps]:

Tridimensional display of the dynamics of the bidimensional John Conway's life game.

Tridimensional display of the dynamics of the bidimensional John Conway's life game.

Tridimensional display of the particle trajectories of bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.

N-body problem integration (N=10) displaying the actual Solar System with its simultaneous 2.pi rotation.

The Solar System with a dark blue virtual planet -virtual planet point of view-.

Tridimensional visualization of a bidimensional turbulent flow.

A shell (Jeener surface 1) in motion.

The Klein bottle in motion.

An arbitrary surface (Jeener surface 2) in motion.

A Lissajous surface in motion.

The Lorenz attractor in motion.

Synthesis of tridimensional textures.

Dynamics of a bidimensional fractal structure.




Animation [Animation]:

[See all animations [Voir toutes les animations]]



The Möbius strip.

Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing.

Dynamics of the even distribution of 6 points on a sphere -an Octahedron- by means of simulated annealing.

Bidimensional texture animation by means of the Generalized Product.

Tridimensional texture animation by means of the Generalized Product.

Bidimensional geometrical texture animation.

From Mars to the Sun.

The journey of an Earth-like virtuel planet (green) from Pluto (grey) to the Sun (yellow) -point of view of the virtual planet-.

The bidimensional John Conway's life game.

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

Tridimensional zoom in on the Mandelbrot set.

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

Monument Valley at sunrise with light cloud dynamics -this sequence being periodical-.

Bidimensional rectangular billiard with a central obstacle and an initial flow of rotating particles.

A bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle.

Bidimensional quasi-symmetrical fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.

Tridimensional display of the particle density of a bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle.

The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with cluster(s), with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-.	The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-.	The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- with partial confinement -201 particles-, with a zero death rate and a 100% infection, starting with just one infected person -red particle on bottom left picture-.	The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with a zero death rate and with a 50% infection, starting with just one infected person -red particle on bottom left picture-.	The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- with partial confinement -201 particles-, with a zero death rate and a 50% infection, starting with just one infected person -red particle on bottom left picture-.
The 'exponential' spreading of a tridimensional epidemic -the COVID-19 coronavirus?- without confinement -1430 particles-, with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-.

The random walk of photons escaping the Sun.




Relative Motions, Points of View and Virtual (or Subjective) Chaos [Mouvements Relatifs, Points de Vue et Chaos Virtuel (ou Subjectif)]:

From Pluto to the Sun (linear scales).

The journey of a sphere (dark blue) in a system of pure uniform concentric circular motions -moving point of view (dark blue)-.

The journey of a sphere (dark blue) in a system of pure uniform non concentric circular motions -moving point of view (dark blue)-.

From Pluto to the Sun -extrapolation 2- (non linear scales).

Simulation of 'from Pluto to the Sun -extrapolation 2-' with pure uniform circular motions (non linear scales).




Optical Illusions and Various Problems [Illusions d'optique et Problèmes Divers]:

Untitled 0367 -with an illusion of depth (the red seems to be in the foreground and the blue in the background)-.

Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 304.116 galaxies) obtained by means of a non deterministic fractal process -with an illusion of depth (the red seems to be in the foreground and the blue in the background)-.

Multifractal mountains (bird's-eye view) -with an illusion of depth (the red seems to be in the foreground and the blue in the background)-.

Untitled 0307 -with an illusion of depth (the red seems to be in the foreground and the blue in the background)-.

The Goldbach rainbow -with an illusion of depth (the blue/red seem to be in the foreground and the green/yellow in the background)-.

2 identical grey squares moving over a grey scale.

Two identical grey rectangles in front of a grey scale.

A uniform grey stripe on a grey scale.

The Sierpinski Carpet -iteration 5-.

Black dots (inside random white squares) on a square lattice.

Zollner optical illusion.

Geometrical distorsion.

Geometrical distorsion.

Geometrical distorsion.

Three ghost squares.

Two orthogonal 'hourglasses' moving relative to each other.

Some elementary symbols used to built labyrinths -with a big black ghost structure at pi/4-.

Vibrations 0001.

Vibrations 0002.

Vibrations 0003.

Heap or hole?

An aperiodic Penrose tiling of the Golden Decagon with five hidden cubes.

Cube "in" or cube "out"?

Perspective anomaly with the RGB cube.

Artistic view of a bidimensional texture obtained by means of the self-transformation of a fractal process.

A color palette with an increasing luminance.

A strange and noisy picture with a very simple luminance.

A strange and noisy picture with a very simple luminance.

From cold to warm colors.

From cold to warm colors.

The same bidimensional scalar field displayed with 4 different color palettes.

The same bidimensional scalar field displayed with 4 different color palettes.

The 1.000 first digits -base 10- of 'pi' displayed on an helix -bad point of view-.

The 1.000 first digits -base 10- of 'pi' displayed on an helix -good point of view-.

display of 'pi' with 1.000 digits -base 10- on an helix -good point of view-.

The connexity of the Mandelbrot set.

The connexity of the Mandelbrot set.

Bidimensional clouds or height field.

Different modes of representation of a tridimensional cross-section of a Quaternionic Julia set.

The defaults of the JPEG encoding.

Copyright © Jean-François COLONNA, 2000-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.