Gallery (537 different pictures):

Non Deterministic Fractal Geometry
and
Natural Phenomenon Synthesis

[Galerie (537 images différentes) : Géométrie Fractale Non Déterministe
et
Synthèse de Phénomènes Naturels]

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

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Non Deterministic Fractal Geometry and Natural Phenomenon Synthesis [Géométrie Fractale Non Déterministe et Synthèse de Phénomènes Naturels]:

Generation of Fractal Fields, Principles [Génération de Champs fractals, Principes]	Clouds [Nuages]	Landscapes [Paysages]	One Landscape and Various Meteorological Conditions [Un seul Paysage dans des Conditions Météorologiques Variées]	How the West was won [La Conquête de l'Ouest]
Fractal Euclidian Landscapes [Paysages Fractals et Euclidiens]	Landscape Interpolation [Interpolation de Paysages]	Deep Space [Au plus Profond de l'Espace]	Some of my first fractal pictures made in 1980 -very low resolution: 256x256, 8 colors- [Quelques une de mes premières images fractales faites en 1980 -très basse résolution: 256x256, 8 couleurs-]	Random Surfaces [Surfaces Aléatoires]
Tridimensional Structures [Structures Tridimensionnelles]	Bidimensional Erosion Process according to the Sapoval-Baldassarri-Gabrielli Theory [Processus d'Erosion Bidimensionnelle suivant la Théorie de Sapoval-Baldassarri-Gabrielli]	Bidimensional Etching Process according to the Sapoval-Kolwankar Theory [Processus d'Attaque Chimique Bidimensionnelle suivant la Théorie de Sapoval-Kolwankar]	Tridimensional Erosion Process according to the Sapoval-Baldassarri-COLONNA-Gabrielli Theory [Processus d'Erosion Tridimensionnelle suivant la Théorie de Sapoval-Baldassarri-COLONNA-Gabrielli]	Pseudo-Erosion Processes [Processus de pseudo-érosion]
Diffusion Processes [Processus de Diffusion]	Bidimensional Brownian Motion [Mouvement Brownien Bidimensionnel]	Tridimensional Brownian Motion [Mouvement Brownien Tridimensionnel]	Bidimensional Diffusion Limited Aggregations, Bidimensional Fractal Dendrites and Fractal Aggregates [DLAs, Dendrites Fractales Bidimensionnelles et Agrégats Fractals Bidimensionnels]	Fractal Diffusion Front in a Bidimensional Medium [Front Fractal de Diffusion dans un Milieu Bidimensionnel]
Fractal Diffusion Front in a Tridimensional Medium [Front Fractal de Diffusion dans un Milieu Tridimensionnel]	Tridimensional Diffusion Limited Aggregations, Tridimensional Fractal Dendrites and Fractal Aggregates [DLAs, Dendrites Fractales Tridimensionnelles et Agrégats Fractals Tridimensionnels]	Iterated Function Systems (IFS) [Systèmes de Fonctions Itérées (IFS)]	Recursive "Living" Structures [Structures "Vivantes" Récursives]	Trees [Arbres]
Miscellaneous [Divers]

Non Deterministic Fractal Geometry and Natural Phenomenon Synthesis [Géométrie Fractale Non Déterministe et Synthèse de Phénomènes Naturels]:

[More information]

Generation of Fractal Fields, Principles [Génération de Champs fractals, Principes]:

The iterative process used to generate bidimensional fractal fields (large mesh).

The iterative process used to generate bidimensional fractal fields (medium mesh).

The iterative process used to generate bidimensional fractal fields (small mesh).

The iterative process used to generate bidimensional fractal fields (16 iterations).

The iterative process used to generate fractal mountains (16 iterations and bird's-eye view).

The iterative process used to generate fractal mountains (16 iterations).

The iterative process used to generate bidimensional fractal fields (large mesh).

The iterative process used to generate bidimensional fractal fields (medium mesh).

The iterative process used to generate bidimensional fractal fields (small mesh).

Bidimensional clouds or height field.

A fractal mountain using a gaussian model with various standard deviation values -decreasing from 0.06 to 0.02- (bird's-eye view).

A fractal mountain using a gaussian model with various standard deviation values (decreasing from 0.06 to 0.02).

Clouds [Nuages]:

Clouds.	Light clouds.	Light clouds.	Light clouds.	Light clouds at sunset.
Light clouds at sunset.

Light cloud dynamics -this sequence being periodical-.	Light cloud dynamics -this sequence being periodical-.	Light cloud dynamics -this sequence being periodical-.	Light cloud dynamics at sunset -this sequence being periodical-.	Zoom in on light clouds.
Zoom in on self-similar light clouds.

Landscapes [Paysages]:

Zoom in on mountains (with 3D clipping, bird's-eye view).	Zoom in on self-similar mountains (with 3D clipping, bird's-eye view).	Mountains at sunrise.	Animation of a sunrise on mountains.	Mountains at sunrise.
Fractal synthesis of mountains with vegetation and clouds.	Fractal synthesis of mountains with vegetation and stormy clouds.	Snowy multifractal mountains.	Snowy multifractal mountains.	Snowy multifractal mountains.
Snowy multifractal mountains.	Snowy day.	Mountains and fog.	Mountains and fog.	Magical forest.
Mountains and fog.	Mountains and fog.	Mystery mountain.	Mystery mountain at sunrise.	Bloody mountain.
Pinky mystery mountain.	Meteor Crater.

Archipelago.

Foggy islands.

Paradoxal islands at sunset.

Multifractal mountains (side view).

Multifractal mountains (bird's-eye view).

Cloud dynamics -this sequence being periodical- (bird's-eye view).	Mountains and light clouds (bird's-eye view).	Mountains and light cloud dynamics -this sequence being periodical-.	Mountains and light cloud dynamics -this sequence being periodical-.	Mountains and light clouds.
Mountains and clouds.

A set of 4x3 stereograms of a fractal mountain.	Earthquake (bird's-eye view).	Earthquake.	Earthquake.	Earthquake with multifractal mountains.
Earthquake with multifractal mountains.	Periodical earthquake with multifractal mountains (bird's-eye view).	Periodical earthquake with multifractal mountains.	Periodical earthquake with multifractal mountains (bird's-eye view).	Periodical earthquake with multifractal mountains.
Dynamical mountains (bird's-eye view).

Dynamics of an erosion process (bird's-eye view).

Erosion process.

Dynamics of an erosion process with fog.

Long term evolution of a landscape (bird's-eye view).	Long term evolution of a landscape.	Synthesis of periodical tridimensional textures by means of a fractal process.	Tridimensional texture animation by means of the Generalized Product (bird's-eye view).	Synthesis of tridimensional textures by means of a fractal process.
Synthesis of tridimensional textures by means of a fractal process.	Synthesis of tridimensional textures by means of a fractal process and of a fourth degree Verhulst-like dynamics.	Mountains with slight linear structures and discontinuities (bird's-eye view).	Mountains with slight linear structures (bird's-eye view).	Mountains with slight linear structures (bird's-eye view).
Mountains with large linear structures and discontinuities (bird's-eye view).	Multifractal mountains (bird's-eye view).

Waltzing snowy Rocky Mountains.

Snowy Rocky Mountains.

Grand Canyon (bird's-eye view).	Foggy Grand Canyon.	Opencast mine (bird's-eye view).	Foggy opencast mine.	Foggy Cliffs.
Mystery cliffs at sunrise.	Foggy Cliffs.	Foggy Cliffs.

The foggy Babel Tower -a Tribute to Brueghel the Elder-.

The erection of the Babel Tower.

The erosion of the Babel Tower.

A set of 4x3 stereograms of a few Babel Towers.

The foggy Babel Pyramid.

The tide.

Octonionic mountains with extended arithmetics.

One Landscape and Various Meteorological Conditions [Un seul Paysage dans des Conditions Météorologiques Variées]:

Painted Desert.	Mountains and clouds at sunset.	Mountains and clouds.	Mountains and cloud dynamics -this sequence being periodical-.	Mountains and clouds.
Mountains and fog.	Mountains and fog.	Mountains and snowfall.

How the West was won [La Conquête de l'Ouest]:

More information

Monument Valley at sunrise.	Artistic view of Monument Valley at sunrise with the Great Bear.	Monument Valley at sunrise.	Monument Valley at sunrise.	Artistic view of Monument Valley at sunrise with the Great Bear.
Monument Valley at sunrise.

Monument Valley.	Paradoxal Monument Valley at sunset.	Monument Valley.	Paradoxal Monument Valley at sunset.	Monument Valley.
Paradoxal Monument Valley at sunset.	Monument Valley.	Paradoxal Monument Valley at sunset.

Monument Valley.	Paradoxal Monument Valley at sunset.	Monument Valley.	Paradoxal Monument Valley at sunset.	Monument Valley.
Paradoxal Monument Valley at sunset.	Monument Valley.	Paradoxal Monument Valley at sunset.	Monument Valley.	Paradoxal Monument Valley at sunset.
Monument Valley.	Paradoxal Monument Valley at sunset.	Monument Valley.	Paradoxal Monument Valley at sunset.	Monument Valley.
Paradoxal Monument Valley at sunset.	Monument Valley.	Paradoxal Monument Valley at sunset.

Monument Valley with craters at sunrise.	Monument Valley at sunrise.	Cloudy Monument Valley.	Paradoxal Monument Valley at sunset, 'World of Tiers' -a Tribute to Philip José Farmer-.	Cloudy Monument Valley.
Foggy Monument Valley.	Paradoxal Monument Valley at sunrise.	Paradoxal Monument Valley at sunset.	Snowy Monument Valley.	Cloudy Monument Valley.
Foggy Monument Valley.	Paradoxal Monument Valley at sunrise.	Paradoxal Monument Valley at sunset.	Snowy Monument Valley.	Cloudy Monument Valley.
Foggy Monument Valley.	Sunny Monument Valley.	Spring Time in Monument Valley.	Artistic view of Monument Valley.	Artistic view of Monument Valley.
Monument Valley (bird's-eye view).

Monument Valley at sunrise with light cloud dynamics -this sequence being periodical-.	Waltzing Monument Valley (bird's-eye view).	Waltzing Monument Valley.	Erosion in Monument Valley (bird's-eye view).	Erosion in Monument Valley.
Erosion in Monument Valley with fog.

The Gate.

Inside the Gate.

Beyond the Gate.

The end of the World.

Fractal Euclidian Landscapes [Paysages Fractals et Euclidiens]:

Mysterious structures in the desert.	Mountains with an unnatural star-like structure (bird's-eye view).	Interpolation between a fractal field and a gaussian field (tridimensional visualization).	Dynamics of archimedian mountains (bird's-eye view).	Archimedian mountains (bird's-eye view).
Archimedes mountains (bird's-eye view).	Foggy Archimedes mountains.	Soft Archimedes mountains (bird's-eye view).	Foggy soft Archimedes mountains.	Archimedes mountains (bird's-eye view).
Foggy Archimedes mountains.	Soft Archimedes mountains (bird's-eye view).	Foggy soft Archimedes mountains.	Foggy Archimedes mountains.	Archimedes mountains (bird's-eye view).
Foggy soft Archimedes mountains.	Soft Archimedes mountains (bird's-eye view).

Landscape Interpolation [Interpolation de Paysages]:

Linear landscape interpolation.

Linear landscape interpolation with fog.

Deep Space [Au plus Profond de l'Espace]:

More and more craters on the Moon.	More and more craters on the Moon.	The surface of the Moon.	The fractal Moon.	Botticelli anomaly on the Moon.
Botticelli anomaly on the Moon.	Artistic view of the surface of the Moon.	Alien spacecrafts on the Moon.	First clouds on the Moon.	The terraforming of the Moon.

Beyond Pluto.

A dying Borg starship on Pluto.

The City and the Stars -a Tribute to Arthur C. Clarke-.

Some of my first fractal pictures made in 1980 -very low resolution: 256x256, 8 colors- [Quelques une de mes premières images fractales faites en 1980 -très basse résolution: 256x256, 8 couleurs-]:

Shore.

Planet.

Boy planet.

Boy planet with a sea.

Random Surfaces [Surfaces Aléatoires]:

Tridimensional fractal surface (bird's-eye view).

Tridimensional 'smooth' fractal surface.

Two tridimensional 'smooth' fractal surfaces.

Tridimensional 'smooth' fractal surface with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-.

Untitled 0359.

Untitled 0360.

Untitled 0368.

'Fractal set of ropes' based on a plane.

Fractal 'celestial body' based on a sphere.

Fractal 'celestial body' based on a sphere with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.

Fractal 'celestial body' based on a sphere.

Fractal 'celestial body' based on a sphere with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.

Fractal 'celestial body' based on a sphere.

Fractal 'celestial body' based on a sphere with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.

'Fractal set of ropes' based on a plane.

'Fractal set of ropes' based on a plane with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.

Fractal 'celestial body' based on a torus.

Fractal 'celestial body' based on a torus with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.

Fractal 'celestial body' based on a torus.

Fractal 'celestial body' based on the Bonan-Jeener-Klein triple bottle.

Fractal 'celestial body' based on the Bonan-Jeener-Klein triple bottle with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.

Tridimensional Structures [Structures Tridimensionnelles]:

A random Menger Sponge -iteration 2-.

A random Menger Sponge -iteration 3-.

A random Menger Sponge -iteration 4-.

A random Menger Sponge -iteration 5-.

Tridimensional fractal structure.	Tridimensional fractal structure.	Synthesis of tridimensional textures by means of a fractal process.	Synthesis of tridimensional textures by means of a fractal process.	Synthesis of tridimensional textures by means of a fractal process.
Synthesis of tridimensional textures by means of a fractal process.	Filament dynamics.	Tridimensional fractal structure.	Tridimensional fractal structure.	An interpolation between two fractal networks.
Dynamics of a bidimensional fractal structure.

Rotation of a static tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.
Tridimensional fractal structure in a tridimensional torus.	Tridimensional fractal structure in a tridimensional torus.	Translation along the three axes of a tridimensional fractal structure in a tridimensional torus.	Tridimensional heterogeneous fractal structure in a tridimensional torus.	Tridimensional heterogeneous fractal structure in a tridimensional torus.

Untitled 0359.

Untitled 0360.

Untitled 0368.

Tridimensional fractal structure.

Tridimensional fractal structure.	Bidimensional cross-sections inside a fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.
Bidimensional cross-sections inside a fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.
Dynamical tridimensional fractal structure.	Dynamical tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.

Tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.
Tridimensional fractal structure.	Tridimensional fractal structure.

Tridimensional fractal structure.

Tridimensional fractal structure -the space-time foam?-.

A 'mixing' between a tridimensional fractal structure and a close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.

A fractal-fractal tree.	Tridimensional spherical fractal structure.	Tridimensional filamentous fractal structure.	Tridimensional filamentous fractal structure.	Tridimensional filamentous fractal structure.
Tridimensional filamentous fractal structure.	Tridimensional filamentous fractal structure.	Tridimensional filamentous fractal structure.	Tridimensional filamentous fractal structure.	A fractal sphere.
A fractal sphere.	A fractal torus.	A fractal Möbius strip.	A fractal Möbius strip.	A fractal Klein bottle.
A fractal Klein bottle.	Sixteen interlaced fractal torus.	Sixty-four interlaced fractal torus.	Sixty-four interlaced fractal torus.	Fractal 3-foil torus knot.
Fractal 5-foil torus knot.	Fractal 7-foil torus knot.	A fractal polyhedron.	A fractal Lorenz attractor.	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 hypercube.	A fractal hypercube.	Fractal tridimensional cubic mesh.	Fractal tridimensional cubic mesh.
Tridimensional representation of a fractal quadridimensional Calabi-Yau manifold.	Fractal quaternionic shell.	Fractal intertwining.	Fractal periodical impossible structure.	Fractal paradoxal structure.
A fractal aperiodic Penrose tiling.	Fractal Notre-Dame de la Garde, Marseilles.	Fractal Notre-Dame de Paris -a tribute-.

Tridimensional fractal structure.

Bidimensional Erosion Process according to the Sapoval-Baldassarri-Gabrielli Theory [Processus d'Erosion Bidimensionnelle suivant la Théorie de Sapoval-Baldassarri-Gabrielli]:

Foggy cliffs.

Erosion of a bidimensional random (with small and large scale correlations) medium.

Cliffs at sunset.

Foggy cliffs.	Foggy seaboard.	Erosion of a bidimensional random (with small and large scale correlations) medium.	Foggy 'anti-seaboard'.	Foggy seaboard.
Foggy 'anti-seaboard'.	Foggy seaboard.	Foggy 'anti-seaboard'.	Cliffs at sunset.

Foggy island.	Foggy steep island.	Erosion of a bidimensional random island.	Erosion of a bidimensional random (with small scale correlations) island.	Erosion of a bidimensional random (with large scale correlations) island.
Erosion of a bidimensional random (with small and large scale correlations) island.	Foggy 'anti-island'.	Steep island at sunset.

Foggy island.	Foggy steep island.	Erosion of a bidimensional random island.	Erosion of a bidimensional random (with small scale correlations) island.	Erosion of a bidimensional random (with large scale correlations) island.
Erosion of a bidimensional random (with small and large scale correlations) island.	Foggy 'anti-island'.	Steep island at sunset.

Foggy island.	Foggy steep island.	Erosion of a bidimensional random island.	Erosion of a bidimensional random (with small scale correlations) island.	Erosion of a bidimensional random (with large scale correlations) island.
Erosion of a bidimensional random (with large scale correlations) island.	Erosion of a bidimensional random (with small and large scale correlations) island.	Foggy 'anti-island'.	Foggy island.	Foggy 'anti-island'.
Steep island at sunset.

The foggy Earth planet.

The foggy Earth 'anti-planet'.

Foggy Brittany.

Foggy 'anti-Brittany'.

Bidimensional Etching Process according to the Sapoval-Kolwankar Theory [Processus d'Attaque Chimique Bidimensionnelle suivant la Théorie de Sapoval-Kolwankar]:

Foggy steep cliffs.

Tridimensional Erosion Process according to the Sapoval-Baldassarri-COLONNA-Gabrielli Theory [Processus d'Erosion Tridimensionnelle suivant la Théorie de Sapoval-Baldassarri-COLONNA-Gabrielli]:

The bottom of the sea.

Tridimensional eroded medium.

Bidimensional brownian motion.	Bidimensional brownian motion on a sphere.	Bidimensional brownian motion on a torus.	Bidimensional brownian motion on the Möbius strip.	Bidimensional brownian motion on the Klein bottle.
Bidimensional brownian motion on the Bonan-Jeener-Klein triple bottle.	Bidimensional brownian motion on the Boy surface.

Bidimensional closed self-avoiding brownian motion.	Bidimensional closed self-avoiding brownian motion on a sphere.	Bidimensional closed self-avoiding brownian motion on a torus.	Bidimensional closed self-avoiding brownian motion on the Möbius strip.	Bidimensional closed pseudo-self-avoiding brownian motion on the Klein bottle.
Bidimensional closed pseudo-self-avoiding brownian motion on the Bonan-Jeener-Klein triple bottle.	Bidimensional closed pseudo-self-avoiding brownian motion on the Boy surface.	5x5 identical bidimensional closed self-avoiding brownian motions on a tridimensional representation of a quadridimensional Calabi-Yau manifold.

Bidimensional closed self-avoiding brownian motion.	Bidimensional closed self-avoiding brownian motion on a sphere.	Bidimensional closed self-avoiding brownian motion on a torus.	Bidimensional closed self-avoiding brownian motion on the Möbius strip.	Bidimensional closed pseudo-self-avoiding brownian motion on the Klein bottle.
Bidimensional closed pseudo-self-avoiding brownian motion on the Bonan-Jeener-Klein triple bottle.	Bidimensional closed pseudo-self-avoiding brownian motion on the Boy surface.	5x5 identical bidimensional closed self-avoiding brownian motions on a tridimensional representation of a quadridimensional Calabi-Yau manifold.	5x5 various bidimensional closed self-avoiding brownian motions on a tridimensional representation of a quadridimensional Calabi-Yau manifold.

Tridimensional Brownian Motion [Mouvement Brownien Tridimensionnel]:

Tridimensional brownian motion.

Tridimensional brownian motion -dark green- and the 'external border' of its bidimensional projection -white-.

Tridimensional brownian motion -the colors used (magenta,red,yellow,green,cyan) are an increasing function of the time- and the 'external border' of its bidimensional projection -white-.

Tridimensional brownian motion -the colors used (magenta,red,yellow,green,cyan) are an increasing function of the time- and the 'external border' of its bidimensional projection -white- with display of the evolution of the distance to the origin -grey, from left to right-.

Tridimensional brownian motion on a cubic lattice based on a random process -the colors used (magenta,red,yellow,green,cyan) are an increasing function of the time-.

Tridimensional brownian motion on a cubic lattice based on the Verhulst dynamics -the colors used (magenta,red,yellow,green,cyan) are an increasing function of the time-.

Tridimensional accumulation of the bidimensional projections of 512 correlated tridimensional brownian motions -1000 time steps-.

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

Tridimensional accumulation of 512 correlated tridimensional brownian motions -1000 time steps-.

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

Tridimensional accumulation of 10 strongly correlated tridimensional brownian motions -50000 time steps-.

Tridimensional accumulation of 50 strongly correlated tridimensional brownian motions -50000 time steps-.

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

Tridimensional accumulation of 10 non correlated tridimensional brownian motions -50000 time steps-.

Tridimensional accumulation of 50 non correlated tridimensional brownian motions -50000 time steps-.

Bidimensional brownian motion on a sphere.	Bidimensional brownian motion on a torus.	Bidimensional brownian motion on the Möbius strip.	Bidimensional brownian motion on the Klein bottle.	Bidimensional brownian motion on the Bonan-Jeener-Klein triple bottle.
Bidimensional brownian motion on the Boy surface.

Bidimensional closed self-avoiding brownian motion on a sphere.	Bidimensional closed self-avoiding brownian motion on a torus.	Bidimensional closed self-avoiding brownian motion on the Möbius strip.	Bidimensional closed pseudo-self-avoiding brownian motion on the Klein bottle.	Bidimensional closed pseudo-self-avoiding brownian motion on the Bonan-Jeener-Klein triple bottle.
Bidimensional closed pseudo-self-avoiding brownian motion on the Boy surface.

Bidimensional closed self-avoiding brownian motion on a sphere.	Bidimensional closed self-avoiding brownian motion on a torus.	Bidimensional closed self-avoiding brownian motion on the Möbius strip.	Bidimensional closed pseudo-self-avoiding brownian motion on the Klein bottle.	Bidimensional closed pseudo-self-avoiding brownian motion on the Bonan-Jeener-Klein triple bottle.
Bidimensional closed pseudo-self-avoiding brownian motion on the Boy surface.

Bidimensional Diffusion Limited Aggregations, Bidimensional Fractal Dendrites and Fractal Aggregates [DLAs, Dendrites Fractales Bidimensionnelles et Agrégats Fractals Bidimensionnels]:

Bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.

The particle trajectories of bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.

Bidimensional fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.

Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to an attractive central field of gravity.

The particle trajectories of bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to an attractive central field of gravity.

Bidimensional fractal aggregate obtained by means of a 50% pasting process during collisions of particles submitted to an attractive central field of gravity.

Bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity.

The trajectories of bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity.

Bidimensional fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity.

Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity.

The trajectories of bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity.

Bidimensional fractal aggregate obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity.

Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity.

The trajectories of bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity.

Bidimensional fractal aggregate obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity.

Bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.

The particle trajectories of bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.

Bidimensional fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.

Tridimensional display of the particle trajectories of bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.

Fractal Diffusion Front in a Bidimensional Medium [Front Fractal de Diffusion dans un Milieu Bidimensionnel]:

Fractal diffusion front in a bidimensional medium obtained by means of a random walk process.

Tridimensional display (bird's-eye view) of the density of particles during a bidimensional diffusion process.

Fractal diffusion front in a bidimensional medium obtained by means of identical interacting particles.

Fractal diffusion front in a bidimensional medium obtained by means of identical interacting particles with spatial Fourier filtering.

The first documentary -1985- about the Fractal Structure of the Diffusion Front
[Le premier documentaire -1985- sur la structure fractale d'un front de diffusion]

Fractal Diffusion Front in a Tridimensional Medium [Front Fractal de Diffusion dans un Milieu Tridimensionnel]:

A gradient of 114299 particles obtains by means of a tridimensional diffusion process.

A gradient of 128312 particles obtains by means of a tridimensional diffusion process.

Tridimensional Diffusion Limited Aggregations, Tridimensional Fractal Dendrites and Fractal Aggregates [DLAs, Dendrites Fractales Tridimensionnelles et Agrégats Fractals Tridimensionnels]:

Tridimensional fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.

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

Tridimensional fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.

Tridimensional fractal aggregate obtained by means of a 50% pasting process during collisions of particles submitted to an attractive central field of gravity.

Tridimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity.

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 fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity.

Tridimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity.

The trajectories of tridimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity.

Tridimensional fractal aggregate obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity.

Iterated Function Systems (IFS) [Systèmes de Fonctions Itérées (IFS)]:

A bidimensional fern computed by means of an 'Iterated Function System' -IFS-.

A bidimensional Sierpinski Carpet computed by means of an 'Iterated Function System' -IFS-.

A pyramidal Menger Sponge computed by means of an 'Iterated Function System' -IFS-.

Artistic view of a pyramidal Menger Sponge computed by means of an 'Iterated Function System' -IFS-.

Recursive "Living" Structures [Structures "Vivantes" Récursives]:

More information about the Recursive "Living" Structures

A fractal vegetal structure.

A fractal vegetal structure -'the Knowledge Tree'-.

Cauliflowers, seaweeds, shells,... with fog.	Cauliflowers, seaweeds, shells,....	Untitled 0361.	Animation of a natural form.	Alien.
Alien.	Animation of a natural form.	Animation of a natural form.

Trees [Arbres]:

A random tridimensional fractal tree.

A random tridimensional fractal tree and the self-similarity.

A random bidimensional fractal tree and the self-similarity.

A random tridimensional binary tree.

Magical forest.

A random tridimensional binary tree.

Miscellaneous [Divers]:

Untitled 0613.

Fractal Texture Dynamics.

A random tridimensional graph.

Artistic view of a fractal Multiverse.

Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 1.083.984 galaxies) obtained by means of a non deterministic fractal process.

Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 637.312 galaxies) obtained by means of a non deterministic fractal process.

Artistic view of the Cosmic Web (nodes, galaxy clusters, filaments,... including 304.116 galaxies) obtained by means of a non deterministic fractal process -with an illusion of depth (the red seems to be in the foreground and the blue in the background)-.

Birds and fishes.

[More information and visual access to more Non Deterministic Fractal Geometry pictures [Plus d'informations et accès visuel à plus d'images de Géométrie Fractale Non Déterministe]]
[See the Non Deterministic Fractal Geometry Slide Show [Visionnez le Diaporama de Géométrie Fractale Non Déterministe]]

Copyright © Jean-François COLONNA, 2000-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.

Gallery (537 different pictures): Non Deterministic Fractal Geometry and Natural Phenomenon Synthesis [Galerie (537 images différentes) : Géométrie Fractale Non Déterministe et Synthèse de Phénomènes Naturels]

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

Non Deterministic Fractal Geometry and Natural Phenomenon Synthesis [Géométrie Fractale Non Déterministe et Synthèse de Phénomènes Naturels]:

Non Deterministic Fractal Geometry and Natural Phenomenon Synthesis [Géométrie Fractale Non Déterministe et Synthèse de Phénomènes Naturels]:

Generation of Fractal Fields, Principles [Génération de Champs fractals, Principes]:

Clouds [Nuages]:

Landscapes [Paysages]:

One Landscape and Various Meteorological Conditions [Un seul Paysage dans des Conditions Météorologiques Variées]:

How the West was won [La Conquête de l'Ouest]:

Fractal Euclidian Landscapes [Paysages Fractals et Euclidiens]:

Landscape Interpolation [Interpolation de Paysages]:

Deep Space [Au plus Profond de l'Espace]:

Some of my first fractal pictures made in 1980 -very low resolution: 256x256, 8 colors- [Quelques une de mes premières images fractales faites en 1980 -très basse résolution: 256x256, 8 couleurs-]:

Random Surfaces [Surfaces Aléatoires]:

Tridimensional Structures [Structures Tridimensionnelles]:

Bidimensional Erosion Process according to the Sapoval-Baldassarri-Gabrielli Theory [Processus d'Erosion Bidimensionnelle suivant la Théorie de Sapoval-Baldassarri-Gabrielli]:

Bidimensional Etching Process according to the Sapoval-Kolwankar Theory [Processus d'Attaque Chimique Bidimensionnelle suivant la Théorie de Sapoval-Kolwankar]:

Tridimensional Erosion Process according to the Sapoval-Baldassarri-COLONNA-Gabrielli Theory [Processus d'Erosion Tridimensionnelle suivant la Théorie de Sapoval-Baldassarri-COLONNA-Gabrielli]:

Pseudo-Erosion Processes [Processus de pseudo-érosion]:

Diffusion Processes [Processus de Diffusion]:

Bidimensional Brownian Motion [Mouvement Brownien Bidimensionnel]:

Tridimensional Brownian Motion [Mouvement Brownien Tridimensionnel]:

Bidimensional Diffusion Limited Aggregations, Bidimensional Fractal Dendrites and Fractal Aggregates [DLAs, Dendrites Fractales Bidimensionnelles et Agrégats Fractals Bidimensionnels]:

Fractal Diffusion Front in a Bidimensional Medium [Front Fractal de Diffusion dans un Milieu Bidimensionnel]:

Fractal Diffusion Front in a Tridimensional Medium [Front Fractal de Diffusion dans un Milieu Tridimensionnel]:

Tridimensional Diffusion Limited Aggregations, Tridimensional Fractal Dendrites and Fractal Aggregates [DLAs, Dendrites Fractales Tridimensionnelles et Agrégats Fractals Tridimensionnels]:

Iterated Function Systems (IFS) [Systèmes de Fonctions Itérées (IFS)]:

Recursive "Living" Structures [Structures "Vivantes" Récursives]:

Trees [Arbres]:

Miscellaneous [Divers]:

Copyright © Jean-François COLONNA, 2000-2024. Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.

Copyright © Jean-François COLONNA, 2000-2024. Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.

Gallery (537 different pictures):

Non Deterministic Fractal Geometry
and
Natural Phenomenon Synthesis

[Galerie (537 images différentes) : Géométrie Fractale Non Déterministe
et
Synthèse de Phénomènes Naturels]

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, 2000-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.

Copyright © Jean-François COLONNA, 2000-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.