Gallery :

Generalities about Visualization

[Galerie : Généralités sur la Visualisation]

• Curve Visualization [Visualisation de Courbes] :
• Surface Visualization [Visualisation de Surfaces] :
• Tridimensional Manifold Visualization [Visualisation de Variétés Tridimensionnelles] :
• Tridimensional Visualization of Bidimensional Scalar Fields [Visualisation de Champs Scalaires Bidimensionnels] :
• Visualization of Tridimensional Scalar Fields [Visualisation de Champs Scalaires Tridimensionnels] :
• Visualization of Tridimensional Vector Fields [Visualisation de Champs de Vecteurs Tridimensionnels] :
• Visualization of Bidimensional Time-Dependent Scalar Fields [Visualisation de Champs Scalaires Bidimensionnels Dépendant du Temps] :
• Visualization of Tridimensional Time-Dependent Scalar Fields [Visualisation de Champs Scalaires Tridimensionnels Dépendant du Temps] :
• Enhancement of the Third Dimension -Fog, Depth of Field, Lighting,...- [Améliorations de la Perception de la Troisième Dimension -Brouillard, Profondeur de Champ, Eclairage,...-] :
• Stereograms [Stéréogrammes] :
• Autostereograms [Autostéréogrammes] :
• Autostereograms of a Volcano [Autostéréogrammes d'un Volcan] :
• Autostereograms of Quaternionic Julia Sets [Autostéréogrammes d'Ensembles de Julia Calcules dans le Corps des Quaternions] :
• More Autostereograms [Autres Exemples d'Autostéréogrammes] :
• Anaglyphs [Anaglyphes] :
• Fourth Dimension Visualization [Visualisation de la Quatrième Dimension] :
• N-Dimensional Space Visualization [Visualisation d'Espaces à N Dimensions] :
• Time Visualization [Visualisation du Temps] :
• Relative Motions, Points of View and Virtual (or Subjective) Chaos [Mouvements Relatifs, Points de Vue et Chaos Virtuel (ou Subjectif)] :
• Optical Illusions and Various Problems [Illusions d'optique et Problèmes Divers] :

Generalities about Visualization [Généralités sur la Visualisation] :

Curve Visualization [Visualisation de Courbes] :

A twisting rope.	3-foil knot.	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's triple Klein bottle.	Intertwining based on the geometry of a shell (Jeener surface 1).	Intertwining based on the geometry of the Lorenz attractor.




Surface Visualization [Visualisation de Surfaces] :

A Peano 'fractal plane' defined by means of three bidimensional fields.	A sphere.	A set of spheres with holes.	A set of twisted spheres.	A sphere defined by means of three bidimensional fields.
A crumpled sphere defined by means of three bidimensional fields.	A crumpled sphere defined by means of three bidimensional fields.	The pseudo-sphere -a Tribute to Jacques Cartier-.	A torus.	A torus.
A crumpled torus defined by means of three bidimensional fields.	3-foil torus knot on its torus.	5-foil torus knot on its torus.	7-foil torus knot on its torus.	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.

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 ?-.

The Möbius strip.	The Möbius strip.	The Möbius strip.	The Möbius strip.	1-foil torus knot on its torus and its asociated Möbius strip.
3-foil torus knot on its torus.	5-foil torus knot on its torus.	7-foil torus knot on its torus.	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 Klein bottle in motion.	The Klein bottle.	The Klein bottle.	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 quadruple Jeener bottle.	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.	The Jeener's triple Klein bottle.	The Jeener's triple Klein bottle.	The Jeener's quadruple bilateral bottle.	The Jeener's quadruple bilateral bottle.
The Jeener's quintuple Klein bottle.	The Jeener's quintuple Klein bottle.	The Bonan-Jeener's triple Klein bottle.	The u=v line on the Bonan-Jeener's triple Klein bottle.	The u=v line on the Bonan-Jeener's triple Klein bottle and a strip.
Interpolation between the Jeener's quintuple Klein bottle and the Bonan-Jeener's triple Klein bottle.	An interpolation between the Bonan-Jeener's triple Klein bottle and a 'double sphere' defined by means of three sets of bidimensional fields.

A shell (Jeener surface 1).	A shell (Jeener surface 1).	A shell (Jeener surface 1) in motion.	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.

Rotation about the Y axis of the Boy surface with motion blur.	The Boy surface.	The Boy surface in motion.	Rotation about X and Y axes of the Boy surface.	The Boy surface.
From à rectangle to the Boy surface.	From a sphere to the Boy surface.

A Lissajous surface.

A Lissajous surface.

A Lissajous surface.

A Lissajous surface in motion.

A twisting Lissajous surface.

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).




Tridimensional Manifold Visualization [Visualisation de Variétés Tridimensionnelles] :

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

A Jeener-Mobuis tridimensional manifold.

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

A Jeener-Mobuis tridimensional manifold.




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's triple Klein 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).




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-.




Stereograms [Stéréogrammes] :

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=(-0.58...,+0.63...,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's triple Klein 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's triple Klein 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-Mobuis tridimensional manifold that can also be viewed as a set of 4x3 stereograms.	Rotation about the Y (vertical) axis of a Jeener-Mobuis 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.




Anaglyphs [Anaglyphes] :

Anaglyph of an hypercube.

Anaglyph of a fractal hypercube.

Anaglyph of the tridimensional Hilbert Curve -iteration 3-.

Anaglyph of the tridimensional Hilbert Curve -iteration 4-.

Anaglyph of the Lorenz attractor.	Anaglyph of a tridimensional representation of a quadridimensional Calabi-Yau manifold.	Anaglyph of an artistic view of a tridimensional Sierpinski 'carpet' computed by means of an 'Iterated Function System' -IFS-.	Anaglyph of a tridimensional interpolation between a fractal structure and a cubic mesh.	Anaglyph of a tridimensional interpolation between a fractal structure and a cubic mesh.
Anaglyph of a tridimensional fractal structure.	Anaglyph of a tridimensional fractal structure -the space-time foam ?-.	Anaglyph of a tridimensional fractal structure.	Anaglyph of a fractal-fractal tree.

Anaglyph of a tridimensional filamentous fractal structure.	Anaglyph of a tridimensional filamentous fractal structure.	Anaglyph of a fractal sphere.	Anaglyph of a fractal torus.	Anaglyph of a fractal 3-foil torus knot.
Anaglyph of a fractal 5-foil torus knot.	Anaglyph of a fractal 7-foil torus knot.	Anaglyph of a fractal polyhedron.	Anaglyph of a fractal Möbius strip.	Anaglyph of a fractal Klein bottle.

Anaglyph of a fractal Notre-Dame de la Garde, Marseilles.

Anaglyph of a tridimensional display of the Mandebrot set.

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

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

Anaglyph of a close-up on a pseudo-quaternionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.




Fourth Dimension Visualization [Visualisation de la Quatrième Dimension] :

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-.




N-Dimensional Space Visualization [Visualisation 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.




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.

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.




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

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

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




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

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.

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

Zollner optical illusion.

Geometrical distorsion.

Geometrical distorsion.

Geometrical distorsion.

Vibrations 0001.

Vibrations 0002.

Vibrations 0003.

Heap or hole ?

Cube "in" or cube "out" ?

Bidimensional clouds or height field.

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

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

Copyright (c) Jean-François Colonna, 2000-2013.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2013.