Gallery (679 different pictures):

Art and Science

[Galerie (679 images différentes) : Art et Science]

Jean-François COLONNA
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www.lactamme.polytechnique.fr

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, 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.	Collatz, Lothar.
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.	Meyer, Yves.	Möbius, August.	Morlet, Jean.
Newton, Isaac.	Peano, Giuseppe.	Penrose, Roger.	Petit, Jean-Pierre.	Poincaré, Henri.
Ptolémée.	Pythagore.	Riemann, Bernhard.	Rubik, Ernö.	Schwartz, Laurent.
Sierpinski, Waclaw.	Ulam, Stanislaw.	Verhulst, Pierre François.	von Koch, Helge.	von Neumann, John.
Voronoï, Georgy Fedosievych.	Watson, James.	Werner, Wendelin.	Wiles, Andrew.	Yoccoz, Jean-Cristophe.

Arp, Jean.	Atlan, Jean-Michel.	Baudelaire, Charles.	Baxter, Stephen.	Böcklin, Arnold.
Borges, Jorge Luis.	Botticelli, Sandro.	Brueghel the Elder, Pieter [Bruegel l'Ancien, Pieter].	Brunelleschi, Filippo.	Callas, Maria.
Clarke, Arthur C..	Cohen, Leonard.	Dali, Salvador.	Delaunay, Robert & Sonia.	Debussy, Claude.
Druillet, Philippe.	Escher, Maurits Cornelis.	Farmer, Philip José.	Hernández, José.	Hockney, David.
Jeener, Patrice.	Kandinsky, Vassily.	Klein, Yves.	Lang, Fritz.	Lee, Gentry.
Lucas, George.	Magritte, René.	Matisse, Henri.	Mondrian, Piet.	Monet, Claude.
Munch, Edvard.	Rodtchenko, Alexander.	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.
Mauger, Thierry.	Révillon, Yves.	Sapoval, Bernard.	Tomasso, Dominique.	Vasseur, Pierre.

Notre-Dame de Paris -a tribute-.	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.
A new Rose for Notre-Dame de Paris.

Attacks, 01/2015, Paris.

La liberté individuelle.

Attacks, 11/2015, Paris.

David versus Goliath: there is a war between Ukraine and Russia.

The Road to Chaos -06/19/2022-.

On the Road to Chaos again -07/07/2024-.

[More information and visual access to more Tributes pictures [Plus d'informations et accès visuel à plus d'images d'Hommages]]

[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-.	Untitled 0609.	Untitled 0611.	Untitled 0610.

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-.

Untitled 0254.

Untitled 0253.

Untitled 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-.	Untitled 0249.	Untitled 0250.	Untitled 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-.	Untitled 0139.
Tridimensional visualization of the Verhulst dynamics.

The Lorenz attractor.

Untitled 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 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.

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.

Untitled 0612.

Fractal Geometry [Géométrie Fractale]:

Mandelbrot set in the sky.

Convolution of a detail of the Mandelbrot set.

Untitled 0283.

Untitled 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-.

Untitled 0286.

Untitled 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=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-.	A foggy pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,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 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=(-0.581514...,+0.635888...,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-.	Untitled 0158.
Untitled 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-.

Untitled 0597.

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-.

Untitled 0142.

Untitled 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=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-.	Untitled 0232.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,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=(-0.581514...,+0.635888...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.	Untitled 0222.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,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=(-0.581514...,+0.635888...,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=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-.
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-.

A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,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=(-0.581514...,+0.635888...,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-.	The Menger Sponge -iteration 5-.	An amazing cross-section inside the Menger Sponge -iteration 5-.
A twisted Menger Sponge -iteration 5-.	Untitled 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-.
Untitled 0233.	Untitled 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-.
Untitled 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.
Untitled 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.	Untitled 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-, 'Ô 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-, 'Ô temps tes pyramides' -a Tribute to Jorge Luis Borges-.	A 'double conic' cross-section inside the Menger Sponge -iteration 5-, 'Ô 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-, 'Ô 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-.

Untitled 0595.

Untitled 0596.

Distorsion of the Menger Sponge -iteration 2-.

Distorsion of the Menger Sponge -iteration 3-.

Vibrating Tridimensional Hilbert Curve -iteration 3-.

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.	Untitled 0188.	Untitled 0189.	Untitled 0190.	Artistic view of Monument Valley at sunrise with the Great Bear.
Monument Valley at sunrise.

Alien spacecrafts on the Moon.

Untitled 0613.

Alien.

Artistic view of a tridimensional fractal structure.

Tridimensional fractal structure in a tridimensional torus.

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.

Artistic view of the 100.000 first digits -base 10- of 'pi'.

Artistic views of the 100.000 first digits -base 10- of 'pi'.

Tridimensional display of an Archimedes spiral displaying 'pi' with 50 digits -base 10-.

Tridimensional artistic view of 'pi'.	Tridimensional artistic view of 'pi'.	Tridimensional artistic view of 'pi'.	Tridimensional artistic view of 'pi'.	Tridimensional artistic view of 'pi'.
Tridimensional artistic view of 'pi'.

The 'pi' island -1-.

Untitled 0252.

Untitled 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.	Untitled 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.	Untitled 0112.	Untitled 0113.	Intertwining.
Intertwining.	Intertwining.	Interpolated intertwining.	Fractal intertwining.	Fractal intertwining.
Fractal network.	Fractal intertwining.	Recursive intertwining.	Untitled 0131.	Untitled 0114.
The Mathematics are the key of the Multiverse.	Recursive intertwining.	Intertwining.	Recursive intertwining.	Intertwining.
Intertwining.	Intertwining.	Intertwining.	Intertwining.	Intertwining.
Intertwining.	Chessboard.	Recursive chessboard.	Untitled 0115.	Intertwining.
Intertwining.

La diagonale du Flou.

Untitled 0116.

Untitled 0120.

Untitled 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 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).
Untitled 0123.	The Bonan-Jeener's 12-bottle before a paradoxal field.	Untitled 0207.	The Bonan-Jeener's 12-bottle before a paradoxal field.

An aperiodic Penrose tiling of the plane.	An aperiodic Penrose tiling of the plane.	An aperiodic Penrose tiling of the plane.	The Penrose city.	Tridimensional display of an aperiodic Penrose tiling of the plane with a fractal noise.
A tridimensionally distorded aperiodic Penrose tiling of the plane.

A 'triple stack' of two aperiodic Penrose tilings of the plane.

Tridimensional visualization of an aperiodic Penrose tiling of the Golden Decagon.

Artistic view of an aperiodic Penrose tiling of the Golden Decagon.

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

A tridimensional structure made of six Golden Decagons with aperiodic Penrose tilings.

Untitled 0299.

Untitled 0626.	Untitled 0627.	Untitled 0628.	Untitled 0629.	Untitled 0631.
Untitled 0630.	Untitled 0632.	Untitled 0635.	Untitled 0633.	Untitled 0634.

Untitled 0362.	Untitled 0363.	Untitled 0364.	Untitled 0365.	Untitled 0366.
Untitled 0367 -with an illusion of depth (the red seems to be in the foreground and the blue in the background)-.	Untitled 0368.

Untitled 0351.

Untitled 0352.

Untitled 0353.	Untitled 0354.	Untitled 0355.	Untitled 0356.	Untitled 0357.
Untitled 0358.	Untitled 0359.	Untitled 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.	Untitled 0300.

Untitled 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.

Untitled 0614.

Untitled 0615.

Untitled 0202 -a Tribute to Henri Matisse-.

The golden binary tree.	Artistic view of a binary tree with 256 leaves.	Untitled 0239.	Untitled 0244.	Untitled 0245.
Untitled 0246.	Untitled 0247.	Untitled 0369.

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Copyright © Jean-François COLONNA, 2000-2025.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2025.

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.	Untitled 0306.	Untitled 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.	Untitled 0304.	Untitled 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.	Untitled 0308.
Untitled 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.
Untitled 0310.	Untitled 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.	Untitled 0312.	Untitled 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.	Untitled 0314.
Untitled 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.
Untitled 0318.	Untitled 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.	Untitled 0332.	Untitled 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.	Untitled 0334.	Untitled 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.	Untitled 0339.	Untitled 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.	Untitled 0338.
Untitled 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.
Untitled 0336.	Untitled 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.	Untitled 0330.	Untitled 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.	Untitled 0320.	Untitled 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.	Untitled 0316.	Untitled 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.	Untitled 0329.
Untitled 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.
Untitled 0324.	Untitled 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.	Untitled 0321.

Gallery (679 different pictures): Art and Science [Galerie (679 images différentes) : Art et Science]

Jean-François COLONNA [Contact me]

www.lactamme.polytechnique.fr

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France france telecom, France Telecom R&D

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, 2000-2025. Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2025.

Copyright © Jean-François COLONNA, 2000-2025. Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2025.

Gallery (679 different pictures):

Art and Science

[Galerie (679 images différentes) : Art et Science]

Jean-François COLONNA
[Contact me]

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France
france telecom, France Telecom R&D

Copyright © Jean-François COLONNA, 2000-2025.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2025.

Copyright © Jean-François COLONNA, 2000-2025.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2025.