Gallery :

Art and Science

[Galerie : Art et Science]

Jean-François COLONNA
www.lactamme.polytechnique.fr
jean-francois.colonna@polytechnique.edu
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France

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(CMAP28 WWW site : this page was created on 03/15/2000 and last updated on 03/16/2014 08:11:08 -CET-)

Art and Science [Art et Science] :

Tributes [Hommages] :
Quantum Mechanics [Mécanique Quantique] :
Deterministic Chaos [Chaos Déterministe] :
Fractal Geometry [Géométrie Fractale] :
Number Theory [Théorie des Nombres] :
Knots and Intertwinings [Nœuds et Entrelacs] :
Celestial Mechanics [Mécanique Céleste] :
Signal Processing [Traitement du Signal] :
Miscellaneous [Divers] :

Art and Science [Art et Science] :

Tributes [Hommages] :

Archimède[s].	Baudelaire, Charles.	Baxter, Stephen.	Böcklin, Arnold.	Borges, Jorge Luis.
Botticelli, Sandro.	Boy, Werner.	Brown, Robert.	Brueghel the Elder, Pieter [Brueghel l'Ancien, Pieter].	Cartier, Jacques.
Clarke, Arthur C..	Cohen, Leonard.	Conway, John Horton.	Copernic, Nicolas.	$Tridimensional fractal Self-Portrait$ Dali, Salvador.
Einstein, Albert.	Eratosthéne.	Escher, Maurits C..	Fatou, Pierre.	Goldbach, Christian.
Hernandez, José.	Hilbert, David.	Hockney, David.	Julia, Gaston.	Kepler, Johannes.
Klein, Felix.	Mandelbrot, Benoît.	Matisse, Henri.	Möbius, August.	Mondrian, Piet.
Monet, Claude.	Munch, Edvard.	Newton, Isaac.	Penrose, Roger.	Poincaré, Henri.
Pythagore.	Révillon, Yves.	Riemann, Bernhard.	Schwartz, Laurent.	Sierpinski, Waclaw.
Tanguy, Yves.	Vasarely, Victor.	Verhulst, Pierre François.	Tatline, Vladimir.	von Koch, Helge.

Quantum Mechanics [Mécanique Quantique] :

Tridimensional representation of a quadridimensional Calabi-Yau manifold.

Quark and gluon structure of a nucleon.

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

Deterministic Chaos [Chaos Déterministe] :

Bidimensional visualization of the Verhulst dynamics -(grey,orange,red) display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-.	Tridimensional visualization of the Verhulst dynamics.	Tridimensional visualization of the Verhulst dynamics.	Tridimensional visualization of the Verhulst dynamics.	Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.
No Title 0139.	Tridimensional visualization of the Verhulst dynamics.

The Lorenz attractor.

No Title 0087.

$Artistic view of the trajectories of bidimensional fractal aggregates obtained by means of pasting during collisions of particles submitted to an attractive central field of gravity$ Artistic view of the trajectories of bidimensional fractal aggregates obtained by means of pasting during collisions of particles submitted to an attractive central field of gravity.	$Artistic view of the trajectories of tridimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity$ Artistic view of the trajectories of tridimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity.	$Tridimensional artistic view of the trajectories of tridimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity$ Tridimensional artistic view of the trajectories of tridimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity.	$Exploding tridimensional fractal aggregate$ Exploding tridimensional fractal aggregate.	Artistic view of the trajectories of 12 -initially- still particles submitted to an attractive central field of gravity in a tridimensional billiard.
Artistic view of the bidimensional Ising Model with 2-state spins, temperature=0.2 and regular initial conditions (a chessboard).	Artistic view of the bidimensional Ising Model with 2-state spins, temperature=0.2 and random initial conditions.

Fractal Geometry [Géométrie Fractale] :

Morning sun pool.

Mandelbrot set in the sky.

Convolution of a detail of the Mandelbrot set.

The quaternionic Julia set computed with A=(0,1,0,0) -tridimensional cross-section-.	The quaternionic Julia set computed with A=(0,1,0,0) -tridimensional cross-section-.	2.pi rotation about Y and Z axes of a quaternionic Julia set -tridimensional cross-sections-.	A quaternionic Julia set -tridimensional cross-section-.	A quaternionic Julia set -tridimensional cross-section-.
Artistic view of 128 quaternionic Julia sets -tridimensional cross-sections-.

A foggy 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') -'the children round' or 'the consciousness emerging from Mathematics'- -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-.	A foggy 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=(0,1,0,0) and with a locally variable exponent between 2 and 12 -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-.	$The pseudo-quaternionic fractal set obtained when computing the roots of Q^3=1 using Newton's method with translation along the third axis of the pseudo-quaternionic space (a 'NewtonBulb')-tridimensional cross-section-$ The pseudo-quaternionic fractal set obtained when computing the roots of Q^3=1 using Newton's method with translation along the third axis of the pseudo-quaternionic space (a 'NewtonBulb') -tridimensional cross-section-.	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-.	Consciousness exploring Mathematics.
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-.	No Title 0158.	No Title 0159.	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 pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a 1/Z conformal transformation in the complex plane -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a 1/O conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a OxO conformal transformation in the pseudo-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 pseudo-octonionic space -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a 1/Z conformal transformation in the complex plane -tridimensional cross-section-.
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a 1/O conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a OxO conformal transformation in the pseudo-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 pseudo-octonionic space -tridimensional cross-section-.

Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a 'complex' module transformation in the pseudo-octonionic space -tridimensional cross-section-.

Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a 'complex' transformation in the pseudo-octonionic space -tridimensional cross-section-.

No Title 0142.

No Title 0143.

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-.

Artistic view of a tridimensional Sierpinski 'carpet' computed by means of an 'Iterated Function System' -IFS-.

$Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold$

Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold.

$Sixteen interlaced fractal torus$

Sixteen interlaced fractal torus.

Fractal quaternionic shell.

Vibrating Tridimensional Hilbert Curve -iteration 3-.

Mountains at sunrise.

Fractal synthesis of mountains with vegetation and stormy clouds.

Foggy Babel Tower -a tribute to Brueghel the Elder-.

Monument Valley at sunrise.	Foggy Monument Valley.	Monument Valley à la David Hockney.	Beyond the Gate.	Beyond the Gate.
No Title 0188.	No Title 0189.	No Title 0190.

Alien spacecrafts on the Moon.

Alien.

$Artistic view of a tridimensional fractal structure$

Artistic view of a tridimensional fractal structure.

$Tridimensional fractal structure in a tridimensional torus$

Tridimensional fractal structure in a tridimensional torus.

$Synthesis of tridimensional textures by means of a fractal process$

Synthesis of tridimensional textures by means of a fractal process.

No Title 0160.

No Title 0161.

Artistic view of a binomial multiplicative cascade with ponderations equal to 0.3 -left- and 1-0.3=0.7 -right-.

Number Theory [Théorie des Nombres] :

Artistic view of Ph(Zeta).

Artistic view of the prime numbers.

Artistic variation on the generalized Ulam spiral displaying 81 numbers.

No Title 0137 -a tribute to Yves Tanguy-.

Knots and Intertwinings [Nœuds et Entrelacs] :

3-foil torus knots.	5-foil torus knots.	7-foil torus knots.	3-foil torus knots.	5-foil torus knots.
7-foil torus knots.	3-foil torus knots.	5-foil torus knots.	7-foil torus knots.	Artistic variation on 3-foil and 5-foil torus knots.
Artistic variation on 3-foil and 7-foil torus knots.

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.	Geometrical structure.	Paradoxal structure.	Intertwining.	Intertwining.
Intertwining.	Intertwining.	Intertwining.	No Title 0131.	Intertwining.
Intertwining.	Intertwining.	Intertwining.	Intertwining.	Network.
Intertwining.	Intertwining.	Intertwining.	Intertwining.	Intertwining.
Intertwining.	Intertwining.	Intertwining.	Intertwining.	Intertwining.
Intertwining.	Intertwining.	Intertwining.	Intertwining.	Intertwining based on the geometry of the sphere.
Chessboard based on the geometry of the sphere.	Intertwining based on the geometry of the sphere.	Intertwining based on the geometry of the sphere.	Intertwining based on the geometry of the sphere.	Intertwining based on the geometry of the sphere.
Intertwining based on the geometry of the Bonan-Jeener's triple Klein bottle.	Chessboard based on the geometry of the Bonan-Jeener's triple Klein bottle.	Intertwining based on the geometry of the Bonan-Jeener's triple Klein bottle.	Intertwining based on the geometry of the Bonan-Jeener's triple Klein bottle.	Intertwining based on the geometry of the Bonan-Jeener's triple Klein bottle.
Intertwining based on the geometry of the Bonan-Jeener's triple Klein bottle.	Intertwining based on the geometry of the Boy surface.	Chessboard based on the geometry of the Boy surface.	Intertwining based on the geometry of the Boy surface.	Intertwining based on the geometry of the Boy surface.
Intertwining based on the geometry of the Boy surface.	Intertwining based on the geometry of the Boy surface.	No Title 0112.	No Title 0113.	Intertwining.
Intertwining.	Intertwining.	Interpolated intertwining.	Fractal intertwining.	Fractal intertwining.
Fractal network.	Fractal intertwining.	Recursive intertwining.	No Title 0131.	No Title 0114.
Recursive intertwining.	Intertwining.	Recursive intertwining.	Intertwining.	Intertwining.
Intertwining.	Intertwining.	Intertwining.	Intertwining.	Intertwining.
Chessboard.	Recursive chessboard.	No Title 0115.	Intertwining.	Intertwining.

No Title 0116.

No Title 0120.

No Title 0144.

An intertwining animation.	An intertwining animation.	An interpolation between two intertwinings.	An interpolation between two intertwinings.	An animation of the intertwining based on the geometry of the sphere.
An interpolation between an intertwining based on the geometry of the Bonan-Jeener's triple Klein bottle and an intertwining based on the geometry of the sphere.	An interpolation between two intertwinings.	An interpolation between an intertwining based on the geometry of the Bonan-Jeener's triple Klein bottle and an intertwining based on the geometry of the sphere.	$An interpolation between two fractal intertwinings$ An interpolation between two fractal intertwinings.	$An interpolation between two fractal intertwinings$ An interpolation between two fractal intertwinings.
$An interpolation between two fractal networks$ An interpolation between two fractal networks.	An interpolation between two intertwinings.	An interpolation between two intertwinings.	An interpolation between two intertwinings.	An interpolation between two intertwinings.

Intertwining based on the geometry of the Lorenz attractor.

A special Klein bottle.	A special Bonan-Jeener's triple Klein bottle.	Artistic variation on a geometrical inversion of the Bonan-Jeener's triple Klein bottle.	The Bonan-Jeener's 12-bottle before a paradoxal field.	A special shell (Jeener surface 1).
Artistic variation on a geometrical inversion of a shell (Jeener surface 1).	No Title 0123.	The Bonan-Jeener's 12-bottle before a paradoxal field.	The Bonan-Jeener's 12-bottle before a paradoxal field.

Celestial Mechanics [Mécanique Céleste] :

The actual Solar System viewed during 243 years from a dark blue virtual planet -this last one approximately belongs to the plane of Pluto and its distance from the Sun equals the one of Uranus-.

Artistic view of the Solar System viewed from a virtual planet.

Artistic view of the Solar System viewed from a virtual planet -a Tribute to Isaac Newton-.

Artistic view of the Solar System viewed from the Earth.

Artistic view of the Big Bang.

Signal Processing [Traitement du Signal] :

$Artistic view of the tridimensional integration of the phase rotation of the wavelet transform of a bidimensional fractal field$

Artistic view of the tridimensional integration of the phase rotation of the wavelet transform of a bidimensional fractal field.

Miscellaneous [Divers] :

Artistic view of the Bonan-Jeener's triple Klein bottle.	Artistic view of the Bonan-Jeener's triple Klein bottle.	Artistic view of the Bonan-Jeener's triple Klein bottle.	Artistic view of the Bonan-Jeener's triple Klein bottle.	Artistic view of the Bonan-Jeener's triple Klein bottle.
Artistic view of the Bonan-Jeener's triple Klein bottle.

A shell (Jeener surface 1) in motion.

Synthesis of tridimensional textures.

Voronoi diagrams.

$The bidimensional field defining the three coordinates of a fractal surface$

The bidimensional field defining the three coordinates of a fractal surface.

Copyright (c) Jean-François Colonna, 2000-2014.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2014.

Gallery : Art and Science [Galerie : Art et Science]

Jean-François COLONNA www.lactamme.polytechnique.fr jean-francois.colonna@polytechnique.edu CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France

Copyright (c) Jean-François Colonna, 2000-2014. Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2014.

Gallery :

Art and Science

[Galerie : Art et Science]

Jean-François COLONNA
www.lactamme.polytechnique.fr
jean-francois.colonna@polytechnique.edu
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France

Copyright (c) Jean-François Colonna, 2000-2014.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2014.