Gallery :

Non Deterministic Fractal Geometry
and
Natural Phenomenon Synthesis

[Galerie : Géométrie Fractale Non Déterministe
et
Synthèse de Phénomènes Naturels ]

Jean-François COLONNA

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS
91128 Palaiseau Cedex, France

http://www.lactamme.polytechnique.fr

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(CMAP28 WWW site : this page was created on 03/15/2000 and last updated on 05/09/2012 17:26:11 -CEST-)

• Principles [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-] :
• Tridimensional Structures [Structures Tridimensionnelles] :
• Bidimensional Erosion Process according to the Sapoval-Baldassarri-Gabrielli Theory [Processus d'Erosion Bidimensionnel suivant la Théorie de Sapoval-Baldassarri-Gabrielli] :
• Bidimensional Etching Process according to the Sapoval-Kolwankar Theory [Processus d'Attaque Chimique Bidimensionnel suivant la Théorie de Sapoval-Kolwankar] :
• Tridimensional Erosion Process according to the Sapoval-Baldassarri-Colonna-Gabrielli Theory [Processus d'Erosion Tridimensionnel suivant la Théorie de Sapoval-Baldassarri-Colonna-Gabrielli] :
• Diffusion Processes [Processus de Diffusion] :
• Bidimensional Brownian Motion [Mouvement Brownien Bidimensionnel] :
• Tridimensional Brownian Motion [Mouvement Brownien Tridimensionnel] :
• Bidimensional Diffusion Limited Aggregations and Fractal Aggregates [DLAs 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 and Fractal Aggregates [DLAs et Agrégats Fractals Tridimensionnels] :
• Iterated Function Systems (IFS) [Systèmes de Fonctions Itérées (IFS)] :
• Recursive "Living" Structures [Structures "Vivantes" Récursives] :

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

Principles [Principes] :

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).	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] :

Light cloud dynamics -this sequence being periodical-.	Light cloud dynamics -this sequence being periodical-.	Clouds.	Light clouds.	Light cloud dynamics at sunset -this sequence being periodical-.
Light clouds at sunset.	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.	Mystery mountain.
Mystery mountain at sunrise.	Bloody mountain.	Pinky mystery mountain.	Meteor Crater.	Archipelago.
Foggy Islands.	Islands at sunset.	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 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.	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.	Snowy Rocky Mountains.	Grand Canyon (bird's-eye view).
Foggy Grand Canyon.	Opencast mine (bird's-eye view).	Foggy opencast mine.	The erection of the Babel Tower.	The erosion of the Babel Tower.
A set of 4x3 stereograms of a few Babel Towers.	Foggy Babel Tower.	Foggy Cliffs.	Mystery cliffs at sunrise.	Foggy Cliffs.
Foggy Cliffs.	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 with craters at sunrise.	Monument Valley at sunrise.	Cloudy Monument Valley.	Paradoxal Monument Valley at sunset.	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.	Artistic view of Monument Valley.
Artistic view of Monument Valley.	Monument Valley (bird's-eye view).	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.




Fractal Euclidian Landscapes [Paysages Fractals et Euclidiens] :

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.	Botticelli anomaly on the Moon.	Artistic view of the surface of the Moon.
Alien spacecrafts on the Moon.	First clouds on the Moon.	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.

Shore.

Planet.

Boy planet.

Boy planet with a sea.




Tridimensional Structures [Structures Tridimensionnelles] :

Self-similar zoom in on 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.
Tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.	Tridimensional fractal structure.




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

Foggy cliffs.	Cliffs at sunset.	Foggy cliffs.	Cliffs at sunset.	Foggy seaboard.
Foggy 'anti-seaboard'.	The foggy Earth planet.	The foggy Earth 'anti-planet'.	Foggy Brittany.	Foggy 'anti-Brittany'.
Foggy island.	Foggy 'anti-island'.	Foggy steep island.	Steep island at sunset.	Foggy island.
Foggy 'anti-island'.	Foggy steep island.	Steep island at sunset.	Foggy island.	Foggy 'anti-island'.
Foggy steep island.	Steep island at sunset.




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

Foggy cliffs.




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

The bottom of the sea.




Diffusion Processes [Processus de Diffusion] :

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.

Bidimensional fractal aggregates obtained by means of two families of interacting particles with the following initial conditions about velocity : V for the Red ones and V/5 for the Blue ones.

Tridimensional fractal aggregate with variable fractal dimension -increasing from front to back-.




Bidimensional Brownian Motion [Mouvement Brownien Bidimensionnel] :

Brownian motion of a few heavy slow particles inside a gaz of fast light particles.	Brownian motion of a few heavy slow particles inside a gaz of fast light particles.	Brownian motion of a few heavy slow particles inside a gaz of fast light particles with increasing mass ratio (heavy/light=1,10,100,1000).	Bidimensional brownian motion -dark green- and its 'external border' -white-.	Bidimensional brownian motion -the colors used (magenta,red,yellow,green,cyan) are an increasing function of the time- and its 'external border' -white-.
Bidimensional brownian motion -the colors used (magenta,red,yellow,green,cyan) are an increasing function of the time- and its 'external border' -white-.	Bidimensional brownian motion with a uniform distribution law regarding the radial coordinate.	Bidimensional brownian motion with a gaussian distribution law regarding the radial coordinate.	Bidimensional brownian motion with a gaussian-like (with two bells) distribution law regarding the radial coordinate.	Bidimensional brownian motion with three different distribution laws regarding the radial coordinate -20 points starting from the white point at the picture center-.
Bidimensional brownian motion with three different distribution laws regarding the radial coordinate -60 points starting from the white point at the picture center-.




Tridimensional Brownian Motion [Mouvement Brownien Tridimensionnel] :

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-.




Bidimensional Diffusion Limited Aggregations and Fractal Aggregates [DLAs 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 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 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.




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




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 and Fractal Aggregates [DLAs 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.	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 aggregate obtained by means of a 50% 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 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 tridimensional Sierpinski 'carpet' computed by means of an 'Iterated Function System' -IFS-.




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

[more information about the Recursive "Living" Structures -in french-]



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

Copyright (c) Jean-François Colonna, 2000-2012.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2012.