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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Art and Science [Art et Science]:

Artistic Creation [Création Artistique].	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].	Astrophysics [Astrophysique].	Signal Processing [Traitement du Signal].
Miscellaneous [Divers].

Art and Science [Art et Science]:

Tributes [Hommages]:

Archimède[s].	Boy, Werner.	Brown, Robert.	Cantor, Georg.	Conway, John Horton.
Copernic, Nicolas.	Crick, Francis.	Dirac, Paul.	Douady, Adrien.	Einstein, Albert.
Eratosthène.	Fatou, Pierre.	Fourier, Joseph.	Franklin, Rosalind.	Galilée.
Gauss, Carl Friedrich.	Goldbach, Christian.	Heisenberg, Werner.	Hilbert, David.	Julia, Gaston.
Kepler, Johannes.	Klein, Felix.	Lévy, Paul.	Lorenz, Edward.	Mandelbrot, Benoît.
Menger, Karl.	$Wavelet transform of a bidimensional fractal field$ Meyer, Yves.	Möbius, August.	$Phase rotation of the wavelet transform of a bidimensional fractal field$ Morlet, Jean.	Newton, Isaac.
Penrose, Roger.	Petit, Jean-Pierre.	Poincaré, Henri.	Ptolémée.	Pythagore.
Riemann, Bernhard.	Schwartz, Laurent.	Sierpinski, Waclaw.	Ulam, Stanislaw.	Verhulst, Pierre François.
von Koch, Helge.	von Neumann, John.	Voronoï, Georgy Fedosievych.	Watson, James.	Werner, Wendelin.
Wiles, Andrew.

Baudelaire, Charles.	Baxter, Stephen.	Böcklin, Arnold.	Borges, Jorge Luis.	Botticelli, Sandro.
Brueghel the Elder, Pieter [Bruegel l'Ancien, Pieter].	Brunelleschi, Filippo.	Clarke, Arthur C..	Cohen, Leonard.	$Tridimensional fractal Self-Portrait$ Dali, Salvador.
Debussy, Claude.	Druillet, Philippe.	Escher, Maurits Cornelis.	$Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold -a Tribute to José Hernández-$ Hernández, José.	Hockney, David.
Jeener, Patrice.	Kandinsky, Vassily.	Klein, Yves.	Lang, Fritz.	Lucas, George.
Magritte, René.	Matisse, Henri.	Mondrian, Piet.	Monet, Claude.	Munch, Edvard.
Serusier, Paul.	Soulages, Pierre.	Tanguy, Yves.	Tatline, Vladimir.	Vasarely, Victor.
Villeneuve, Denis.	Wagner, Richard.

Basdevant, Jean-Louis.	Borg, Jean-Pierre.	Bozon, Sabine.	Delahaye, Jean-Paul.	Martin, Jean-Claude.
$A tridimensional fractal structure -a Tribute to Thierry Mauger-$ Mauger, Thierry.	Révillon, Yves.	Sapoval, Bernard.	Tomasso, Dominique.	Vasseur, Pierre.

Notre-Dame de Paris -a tribute-.

Fractal Notre-Dame de Paris -a tribute-.

Notre-Dame de Paris on fire -the hell fire-.

A new Rose for Notre-Dame de Paris.

Hell on Earth -a Tribute to the seventeen victims of the attacks in January 2015, Paris-

Attacks, 01/2015, Paris.

The tree of life -a Tribute to the victims of the attacks in November 2015, Paris-

Attacks, 11/2015, Paris.

[See the Tributes Slide Show [Visionnez le Diaporama des Hommages]]

Quantum Mechanics [Mécanique Quantique]:

Tridimensional representation of a quadridimensional Calabi-Yau manifold.	Artistic view of a quadridimensional Calabi-Yau manifold.	Artistic view of a quadridimensional Calabi-Yau manifold.	Artistic view of a quadridimensional Calabi-Yau manifold.	Tridimensional representation of a quadridimensional Calabi-Yau manifold.
A truncated quadrimensional Calabi-Yau manifold with a 1/O conformal transformation in the Octonionic space -tridimensional cross-section-.

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]:

Tridimensional accumulation of 512 correlated bidimensional brownian motions -50000 time steps-.

No Title 0254.

No Title 0253.

No Title 0259.

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-.
Tridimensional visualization of the Verhulst dynamics -'The Flying Dutchman', a tribute to Richard Wagner-.	Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.	Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.	Tridimensional visualization of the Verhulst dynamics with a tridimensional non linear transformation of the coordinates.	Tridimensional visualization of the Verhulst dynamics with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.
Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.	Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.	Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.	Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.	Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.
Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.	No Title 0249.	No Title 0250.	No Title 0251.	Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.
Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.	Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.	Tridimensional visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.	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.

No Title 0283.

No Title 0284.

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-.

No Title 0286.

No Title 0291.

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 Q³=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-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	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-.

A pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a 1/O conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a O² conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a (4xO+1)/(1xO-1) conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a 1/O conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a O² conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.
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 O² 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 O² 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/O conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a O² 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/O conformal transformation in the pseudo-octonionic space -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') with a O² 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.

The end of the World.

Arrival -a tribute to the 2016 Denis Villeneuve's movie thanks to a pseudo-quaternionic Julia set-.

A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.	No Title 0232.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.
Close-up on a foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.	No Title 0222.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) -tridimensional cross-section-.

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

Close-up on a foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.58...,+0.63...,0,0,0,0,0,0) and with a rotation about the X axis and with a tridimensional non linear transformation in the pseudo-octonionic space -tridimensional cross-section-.

Artistic view of a pyramidal Menger sponge computed by means of an 'Iterated Function System' -IFS-.	$A fractal pyramidal Menger sponge computed by means of an 'Iterated Function System' -IFS-$ A fractal pyramidal Menger sponge computed by means of an 'Iterated Function System' -IFS-.	$A fractal pyramidal Menger sponge computed by means of an 'Iterated Function System' -IFS-$ A fractal pyramidal Menger sponge computed by means of an 'Iterated Function System' -IFS-.	The Menger sponge -iteration 5-.	An amazing cross-section inside the Menger sponge -iteration 5-.
No Title 0278.	An amazing cross-section inside the Menger sponge -iteration 5- with a 1/O conformal transformation in the Octonionic space -tridimensional cross-section-.	An amazing cross-section inside the Menger sponge -iteration 5- with a O² conformal transformation in the Octonionic space -tridimensional cross-section-.	An amazing cross-section inside the Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	No Title 0233.
No Title 0234.	An extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	An extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	An extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	An extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.
An extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	An extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	An extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	An extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	An extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.
An extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	A parallelepipedic extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	An extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	A full-random extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	No Title 0272.
A half-random extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	An amazing cross-section inside an extended Menger sponge -iteration 5-.	A half-random extended Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	An amazing cross-section inside the Menger sponge -iteration 5- with a tridimensional non linear transformation.	No Title 0231 -a tribute to Philippe Druillet-.
An amazing cross-section inside the Menger sponge -iteration 5- with a tridimensional non linear transformation.	The Menger sponge -iteration 5- with a tridimensional non linear transformation.	No Title 0230.	The Menger sponge -iteration 5- with a tridimensional non linear transformation.	An amazing generalized cross-section inside the Menger sponge -iteration 5-.
A 'pyramidal' cross-section inside the Menger sponge -iteration 5-, 'O temps tes pyramides' -a tribute to Jorge Luis Borges-.	A 'pyramidal' cross-section inside the Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-, 'O temps tes pyramides' -a tribute to Jorge Luis Borges-.	A 'double conic' cross-section inside the Menger sponge -iteration 5-, 'O temps tes pyramides' -a tribute to Jorge Luis Borges-.	A 'double conic' cross-section inside the Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	A 'conic' cross-section inside the Menger sponge -iteration 5-, 'O temps tes pyramides' -a tribute to Jorge Luis Borges-.
A 'conic' cross-section inside the Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	An amazing generalized cross-section inside the Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	A spherical cross-section inside the Menger sponge -iteration 5-.	A spherical cross-section inside the Menger sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	A double spherical cross-section inside the Menger sponge -iteration 5-.
A thin double spherical cross-section inside the Menger sponge -iteration 5-.	The intersection of the Menger sponge -iteration 5- and of a quadridimensional Calabi-Yau manifold -tridimensional representation-.	The intersection of the Menger sponge -iteration 5- and of a quadridimensional Calabi-Yau manifold -tridimensional representation-.	The intersection of the Menger sponge -iteration 5- and of a quadridimensional Calabi-Yau manifold -tridimensional representation- with a (4xO+1)/(1xO-1) conformal transformation in the Octonionic space -tridimensional cross-section-.	The intersection of the Menger sponge -iteration 5- and of a quadridimensional Calabi-Yau manifold -tridimensional representation-.

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

Pegasus.

Mountains at sunrise.	Mountains and fog.	Magical forest.	Fractal synthesis of mountains with vegetation and stormy clouds.	Mountains and fog.
The foggy Babel Tower -a tribute to Brueghel the Elder-.

Monument Valley at sunrise.	Foggy Monument Valley.	Snowy Monument Valley.	Monument Valley à la David Hockney.	Beyond the Gate.
Beyond the Gate.	No Title 0188.	No Title 0189.	No Title 0190.	Artistic view of Monument Valley at sunrise with the Great Bear.
Monument Valley at sunrise.

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.

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 0252.

No Title 0137 -'Jour de Lenteur', a tribute to Yves Tanguy-.

Recursive subdivision of the Golden Rectangle by means of the Golden Ratio -phi-.

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.	Artistic view of a 3-foil torus 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-Klein triple 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-Klein triple bottle.	Chessboard based on the geometry of the Bonan-Jeener-Klein triple bottle.	Intertwining based on the geometry of the Bonan-Jeener-Klein triple bottle.	Intertwining based on the geometry of the Bonan-Jeener-Klein triple bottle.	Intertwining based on the geometry of the Bonan-Jeener-Klein triple bottle.
Intertwining based on the geometry of the Bonan-Jeener-Klein triple 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.
The Mathematics are the key of the Multiverse.	Recursive intertwining.	Intertwining.	Recursive intertwining.	Intertwining.
Intertwining.	Intertwining.	Intertwining.	Intertwining.	Intertwining.
Intertwining.	Chessboard.	Recursive chessboard.	No Title 0115.	Intertwining.
Intertwining.

La diagonale du Flou.

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-Klein triple 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-Klein triple 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-Klein triple bottle.	Artistic variation on a geometrical inversion of the Bonan-Jeener-Klein triple bottle.	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.	No Title 0207.	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.

Astrophysics [Astrophysique]:

Artistic view of the Big Bang.

Where is the Universe?.

The Universe at the heart of a Calabi-Yau manifold.

$Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 1.047.312 galaxies)obtained by means of a non deterministic fractal process and with a gigantic hidden Calabi-Yau structure$
Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 1.047.312 galaxies) obtained by means of a non deterministic fractal process and with a gigantic hidden Calabi-Yau structure.

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]:

No Title 0237.

No Title 0274.

A pseudo-periodical Penrose tiling of the plane.	A pseudo-periodical Penrose tiling of the plane.	A pseudo-periodical Penrose tiling of the plane.	The Penrose city.	$Tridimensional display of a pseudo-periodical Penrose tiling of the plane with a fractal noise$ Tridimensional display of a pseudo-periodical Penrose tiling of the plane with a fractal noise.
A tridimensionally distorded pseudo-periodical Penrose tiling of the plane.

A 'triple stack' of two pseudo-periodical Penrose tilings of the plane.

Tridimensional visualization of a pseudo-periodical Penrose tiling of the Golden Decagon.

Artistic view of a pseudo-periodical Penrose tiling of the Golden Decagon.

A pseudo-periodical Penrose tiling of the Golden Decagon with five hidden cubes.

A tridimensional structure made of six Golden Decagons with pseudo-periodical Penrose tilings.

No Title 0299.

Cormorant.

No Title 0362.	No Title 0363.	No Title 0364.	No Title 0365.	No Title 0366.
No Title 0367 -with an illusion of depth (the red seems to be in the foreground and the blue in the background)-.	No Title 0368.

No Title 0351.

No Title 0352.

No Title 0353.	No Title 0354.	No Title 0355.	No Title 0356.	No Title 0357.
No Title 0358.	No Title 0359.	No Title 0360.

Artistic view of the Bonan-Jeener-Klein triple bottle.	Artistic view of the Bonan-Jeener-Klein triple bottle.	Artistic view of the Bonan-Jeener-Klein triple bottle.	Artistic view of the Bonan-Jeener-Klein triple bottle.	Artistic view of the Bonan-Jeener-Klein triple bottle.
Artistic view of the Bonan-Jeener-Klein triple bottle.	No Title 0300.

No Title 0260.

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.

No Title 0202 -a tribute to Henri Matisse-.

The golden tree.	Artistic view of a binary tree with 256 leaves.	No Title 0239.	No Title 0244.	No Title 0245.
No Title 0246.	No Title 0247.	No Title 0369.

[See the Art and Science Slide Show [Visionnez le Diaporama d'Art et de Science]]

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

Art and Science [Art et Science]:

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]:

Astrophysics [Astrophysique]:

Signal Processing [Traitement du Signal]:

Miscellaneous [Divers]:

Copyright © Jean-François Colonna, 2000-2021.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2021.

Copyright © Jean-François Colonna, 2000-2021.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2021.

A tridimensional intertwining.	A tridimensional intertwining.	A tridimensional intertwining inside a sphere.	A tridimensional intertwining inside a sphere.	A tridimensional intertwining inside a sphere.
A tridimensional intertwining inside a sphere.	A 'recursive' -one iteration-' tridimensional intertwining inside a sphere.	A 'recursive' -two iterations-' tridimensional intertwining inside a sphere.	A tridimensional intertwining inside a torus.	A tridimensional intertwining inside a torus.
A tridimensional intertwining inside a torus.	A tridimensional intertwining inside a torus.	No Title 0306.	No Title 0307 -with an illusion of depth (the red seems to be in the foreground and the blue in the background)-.	A tridimensional intertwining inside the Bonan-Jeener-Klein triple bottle.
A tridimensional intertwining inside the Bonan-Jeener-Klein triple bottle.	A tridimensional intertwining inside the Bonan-Jeener-Klein triple bottle.	A tridimensional intertwining inside the Bonan-Jeener-Klein triple bottle.	No Title 0304.	No Title 0305.
A tridimensional intertwining inside a 'tridimensional epicycloïdal' pseudo-torus.	A tridimensional intertwining inside a 'tridimensional epicycloïdal' pseudo-torus.	A tridimensional intertwining inside a 'tridimensional epicycloïdal' pseudo-torus.	A tridimensional intertwining inside a 'tridimensional epicycloïdal' pseudo-torus.	No Title 0308.
No Title 0309.	A tridimensional intertwining inside a Jeener intertwining.	A tridimensional intertwining inside a Jeener intertwining.	A tridimensional intertwining inside a Jeener intertwining.	A tridimensional intertwining inside a Jeener intertwining.
No Title 0310.	No Title 0311.	A tridimensional intertwining inside the Jeener triton.	A tridimensional intertwining inside the Jeener triton.	A tridimensional intertwining inside the Jeener triton.
A tridimensional intertwining inside the Jeener triton.	No Title 0312.	No Title 0313.	A tridimensional intertwining based on a sphere inside a sphere.	A tridimensional intertwining based on the Bonan-Jeener-Klein triple bottle inside a sphere.
A tridimensional intertwining made of an amazing cross-section inside the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of an amazing cross-section inside the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of an amazing cross-section inside the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of an amazing cross-section inside the Menger sponge -iteration 5- inside a sphere.	No Title 0314.
No Title 0315.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.
No Title 0318.	No Title 0319.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.
A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	No Title 0332.	No Title 0333.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.
A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	No Title 0334.	No Title 0335.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a torus.
A tridimensional intertwining made of the Menger sponge -iteration 5- inside a torus.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a torus.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a torus.	No Title 0339.	No Title 0342.
A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	No Title 0338.
No Title 0341.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of the Menger sponge -iteration 5- inside a sphere.
No Title 0336.	No Title 0337.	A tridimensional intertwining made of the Menger sponge -iteration 5- the Bonan-Jeener-Klein triple bottle.	A tridimensional intertwining made of the Menger sponge -iteration 5- the Bonan-Jeener-Klein triple bottle.	A tridimensional intertwining made of the Menger sponge -iteration 5- the Bonan-Jeener-Klein triple bottle.
A tridimensional intertwining made of the Menger sponge -iteration 5- the Bonan-Jeener-Klein triple bottle.	No Title 0330.	No Title 0331.	A tridimensional intertwining made of an extended Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of an extended Menger sponge -iteration 5- inside a sphere.
A tridimensional intertwining made of an extended Menger sponge -iteration 5- inside a sphere.	A tridimensional intertwining made of an extended Menger sponge -iteration 5- inside a sphere.	No Title 0320.	No Title 0328.	A tridimensional intertwining made of a tridimensional cubic mesh inside a sphere.
A tridimensional intertwining made of a tridimensional cubic mesh inside a sphere.	A tridimensional intertwining made of a tridimensional cubic mesh inside a sphere.	A tridimensional intertwining made of a tridimensional cubic mesh inside a sphere.	No Title 0316.	No Title 0317.
A tridimensional intertwining made of a random tridimensional binary tree inside a sphere.	A tridimensional intertwining made of a random tridimensional binary tree inside a sphere.	A tridimensional intertwining made of a random tridimensional binary tree inside a sphere.	A tridimensional intertwining made of a random tridimensional binary tree inside a sphere.	No Title 0329.
No Title 0323.	A tridimensional intertwining made of a random tridimensional binary tree inside a sphere.	A tridimensional intertwining made of a random tridimensional binary tree inside a sphere.	A tridimensional intertwining made of a random tridimensional binary tree inside a sphere.	A tridimensional intertwining made of a random tridimensional binary tree inside a sphere.
No Title 0324.	No Title 0325.	A tridimensional intertwining made of a tridimensional cross-section inside a pseudo-octonionic Julia set inside a sphere.	A tridimensional intertwining made of a tridimensional cross-section inside a pseudo-octonionic Julia set inside a sphere.	Fractal 'celestial body' based on a torus and a tridimensional intertwining inside a sphere.
Fractal 'celestial body' based on a torus and a tridimensional intertwining inside a sphere.	Fractal 'celestial body' based on a torus and a tridimensional intertwining inside a sphere.	Fractal 'celestial body' based on a torus and a tridimensional intertwining inside a sphere.	Fractal 'celestial body' based on a torus and a 'recursive' -one iteration-' tridimensional intertwining inside a sphere.	Fractal 'celestial body' based on a torus and a 'recursive' -two iterations-' tridimensional intertwining inside a sphere.
Fractal 'celestial body' based on a torus and a tridimensional intertwining inside a torus.	Fractal 'celestial body' based on a torus and a tridimensional intertwining inside the Bonan-Jeener-Klein triple bottle.	Fractal 'celestial body' based on a torus and a tridimensional intertwining based on a sphere inside a sphere.	Fractal 'celestial body' based on a torus and a tridimensional intertwining based on the Bonan-Jeener-Klein triple bottle inside a sphere.	No Title 0321.

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

Art and Science [Art et Science]:

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]:

Astrophysics [Astrophysique]:

Signal Processing [Traitement du Signal]:

Miscellaneous [Divers]:

Copyright © Jean-François Colonna, 2000-2021. Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2021.

Copyright © Jean-François Colonna, 2000-2021. Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2021.

Gallery:

Art and Science

[Galerie: Art et Science]

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

Copyright © Jean-François Colonna, 2000-2021.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2021.

Copyright © Jean-François Colonna, 2000-2021.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2021.