Monument Valley au coucher de soleil, 1997

This picture of Monument Valley at sunset is a synthetic creation. It was computed using an iterative process in order to generate fractal fields: a fractal bi-dimensional height field obtained by means of this process, a distorted version of this field, a fractal texture map obtained by means of the distorted fractal bi-dimensional height field, a tri-dimensional visualization of the distorted fractal bi-dimensional height field with texture mapping, then sun effects and fractal clouds were added.

In this image, there are two types of fractals: clouds and mountains. To define the later, supposing there is no overhangs, one gives to each point an altitude Z {X,Y} on a reference plane, with a function Z (X,Y) which translates the property of auto-similarity mathematically. Used directly, it would give rise to a relief of the alpine type. But it is possible to transform the values it produces: this is the case here where only the low and high altitudes were preserved in order to simulate the relief's characteristic of Monument Valley (Utah, USA). The colors selected were natural and the lighting corresponds to that of a sunset.

http://www.lactamme.polytechnique.fr/Mosaic/descripteurs/MonumentValley.01.Ang.html

Eclats, 1996

Jeener's triple Klein bottle

The brightness of this image is on purpose: it forms a two-dimensional table L(X, Y) of numerical values, giving each point a level of gray. Then, they are smoothed (thanks to a filtering of Fourier preserving only the space's low frequencies) in order to avoid too sharp variations. It is possible of consider that this new table of values Z (X,Y) resides in a horizontal plane of coordinates {X,Y} and that it defines for each of its points an altitude Z. Z(X,Y) creates a surface without overhangs which can then be visualized while sticking above (mapping) the original image re-colored, as if it was an elastic cover.

http://www.lactamme.polytechnique.fr/Mosaic/images/BKLN.52.M.D/display.html

Dans la forêt magique, 2001

Bi-dimensional Diffusion Limited Aggregations and Fractal Aggregates.

A (two-dimensional) rectangular vertical box immersed in a field of gravitation contains massive particles. Initially, they fill the box uniformly; their speeds are random in direction, constants in module. Where the field of gravitation attracts them downwards, they can strike the walls or shocked each other. At the time of these shocks, half of the particles (initially selected randomly) can stick to each others (they appear in white) as the others rebound). Gradually, the white particles form an fractal aggregate above the lower wall of the box. The other colored particles, either stay free inside the box, or are trapped by the aggregate box. The curves show the trajectories of each particle since the initial fractal moment.

http://www.lactamme.polytechnique.fr/Mosaic/descripteurs/