GALLERY -Visual Version- :

GENERALITIES ABOUT VISUALIZATION

[Généralités sur la Visualisation]

The same bidimensional scalar field displayed with 4 different color palettes

Jean-François COLONNA

CMAP (Centre de Mathématiques APpliquées), Ecole Polytechnique, CNRS
91128 Palaiseau Cedex
France

tel = +33.(0)1.69.33.46.45
jean-francois.colonna@polytechnique.edu

http://www.lactamme.polytechnique.fr

http://www.cmap.polytechnique.fr/~colonna

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(this page was created on 03/15/2000)
(this page -belonging to the CMAP28 site- was last updated on 03/15/2010 09:42:58 -CET-)

Generalities about Visualization [Généralités sur la Visualisation] :

Curve Visualization [Visualisation de Courbes] :
Surface Visualization [Visualisation de Surfaces] :
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,...- [Améliorations de la Perception de la Troisième Dimension -Brouillard, Profondeur de Champ,...] :
Stereograms and Autostereograms [Stéréogrammes et Autostéréogrammes] :

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 Mobius 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 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

A set of spheres with holes

A set of twisted spheres

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

The Mobius strip

The Mobius strip

The Mobius strip

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

An interpolation between the Mobius strip and a sphere defined by means of three sets of bidimensional fields

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

The Klein bottle in motion

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 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

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 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 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 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 Mobius-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,...- [Améliorations de la Perception de la Troisième Dimension -Brouillard, Profondeur de Champ,...] :

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

Stereograms and Autostereograms [Stèrèogrammes et Autostèrèogrammes] :

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 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 [Autostereogrammes d'Ensembles de Julia Calculés dans le Corps des Quaternions] :

Autostereogram of a quaternionic Julia set

The first autostereogram movie about quaternionic Julia sets

True colors autostereogram of a quaternionic Julia set

The first true colors autostereogram movie about quaternionic Julia sets

$Autostereogram of a quaternionic Julia set and fractal phenomenon$

Autostereogram of a quaternionic Julia set

More Autostereograms [Autres Exemples d'Autostéréogrammes] :

Autostereogram with an hidden ring and ghost bows

Autostereogram of 8 color-multiplexed quaternionic Julia sets

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

Stereograms [Stéréogrammes] :

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)

A set of 4x3 stereograms of the quaternionic Julia set computed with A=(-0.5815147625160462,0.6358885017421603,0,0)

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

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-

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

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

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

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

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

$A set of 4x3 stereograms of a fractal mountain$

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

$A set of 4x3 stereograms of a tridimensional fractal structure$

Fourth Dimension Visualization [Visualisation de la Quatrième Dimension] :

Hypercube

Translation along the fourth axis of a quaternionic Julia set

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

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

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] :

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

Vibrations 0001

Vibrations 0002

Vibrations 0003

Heap or hole (bird's-eye view)

Bidimensional clouds or height field

The same bidimensional scalar field displayed with 4 different color palettes

Copyright (c) Jean-François Colonna, 2000-2010.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) / Ecole Polytechnique, 2000-2010.