GALLERY -Visual Version- :

NON DETERMINISTIC FRACTAL GEOMETRY
AND
NATURAL PHENOMENON SYNTHESIS

[Géométrie Fractale Non Déterministe
et
Synthèse de Phénomènes Naturels ]

Jean-François COLONNA

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

tel = +33.(0)1.69.33.46.45
jean-francois.colonna@polytechnique.edu

http://www.lactamme.polytechnique.fr

http://www.cmap.polytechnique.fr/~colonna

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(this page was created on 03/15/2000)
(this page -belonging to the CMAP28 site- was last updated on 07/17/2010 20:14:12 -CEST-)

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

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] :

[more information ]

Principles [Principes] :

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

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

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

Clouds [Nuages] :

Light cloud dynamics -this sequence being periodical-

Light cloud dynamics at sunset -this sequence being periodical-

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)

Fractal synthesis of mountains with vegetation and clouds

Fractal synthesis of mountains with vegetation and stormy clouds

$Snowy multifractal mountains$

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-

$A set of 4x3 stereograms of a fractal mountain$

$Earthquake with multifractal mountains$

$Periodical earthquake with multifractal mountains (bird's-eye view)$

$Periodical earthquake with multifractal mountains$

$Periodical earthquake with multifractal mountains (bird's-eye view)$

$Periodical earthquake with multifractal mountains$

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

Long term evolution of a landscape (bird's-eye view)

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

Tridimensional texture animation by means of the Generalized Product (bird's-eye view)

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

$Synthesis of tridimensional textures by means of a fractal process and of a fourth degree Verhulst-like dynamics$

Mountains with slight linear structures and discontinuities (bird's-eye view)

Mountains with slight linear structures (bird's-eye view)

Mountains with large linear structures and discontinuities (bird's-eye view)

$Multifractal mountains (bird's-eye view)$

A set of 4x3 stereograms of a few Babel Towers

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

Mountains and cloud dynamics -this sequence being periodical-

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

more information

Waltzing Monument Valley (bird's-eye view)

Erosion in Monument Valley (bird's-eye view)

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)

Soft Archimedes mountains (bird's-eye view)

Landscape Interpolation [Interpolation de Paysages] :

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

Artistic view of the surface of 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-] :

Tridimensional Structures [Structures Tridimensionnelles] :

$Self-similar zoom in on tridimensional fractal structure$

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

$Tridimensional fractal structure$

$An interpolation between two fractal networks$

$Dynamics of a bidimensional fractal structure$

$Rotation of a static tridimensional fractal structure$

$Tridimensional fractal structure$

$Tridimensional fractal structure in a tridimensional torus$

$Translation along the three axes of a tridimensional fractal structure in a tridimensional torus$

$Tridimensional heterogeneous fractal structure in a tridimensional torus$

$Tridimensional fractal structure$

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] :

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 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,gree,cyan)are an increasing function of the time- and its 'external border' -white-

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,gree,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

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

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] :

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

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

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

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

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

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

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

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

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

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

Cauliflowers, seaweeds, shells,... with fog

GALLERY -Visual Version- :

NON DETERMINISTIC FRACTAL GEOMETRY
AND
NATURAL PHENOMENON SYNTHESIS

[Géométrie Fractale Non Déterministe
et
Synthèse de Phénomènes Naturels ]

Jean-François COLONNA

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

tel = +33.(0)1.69.33.46.45
jean-francois.colonna@polytechnique.edu

http://www.lactamme.polytechnique.fr

http://www.cmap.polytechnique.fr/~colonna

http://www.lactamme.polytechnique.fr

http://www.cmap.polytechnique.fr/~colonna

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

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] :

Copyright (c) Jean-François Colonna, 2000-2010.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) / Ecole Polytechnique, 2000-2010.

Copyright (c) Jean-François Colonna, 2000-2010.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) / Ecole Polytechnique, 2000-2010.

GALLERY -Visual Version- : NON DETERMINISTIC FRACTAL GEOMETRY AND NATURAL PHENOMENON SYNTHESIS [Géométrie Fractale Non Déterministe et Synthèse de Phénomènes Naturels ]

Jean-François COLONNA

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

tel = +33.(0)1.69.33.46.45 jean-francois.colonna@polytechnique.edu http://www.lactamme.polytechnique.fr http://www.cmap.polytechnique.fr/~colonna

http://www.lactamme.polytechnique.fr

http://www.cmap.polytechnique.fr/~colonna

Copyright (c) Jean-François Colonna, 2000-2010. Copyright (c) CMAP (Centre de Mathématiques APpliquées) / Ecole Polytechnique, 2000-2010.

GALLERY -Visual Version- :

NON DETERMINISTIC FRACTAL GEOMETRY
AND
NATURAL PHENOMENON SYNTHESIS

[Géométrie Fractale Non Déterministe
et
Synthèse de Phénomènes Naturels ]

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

tel = +33.(0)1.69.33.46.45
jean-francois.colonna@polytechnique.edu

http://www.lactamme.polytechnique.fr

http://www.cmap.polytechnique.fr/~colonna

Copyright (c) Jean-François Colonna, 2000-2010.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) / Ecole Polytechnique, 2000-2010.