The SYMMETRY CELL (SC) produces images very varied by applying a sequence of symmetries.

   - 2D - In two dimensions it is axial symmetry:

   When applied to a set of about ten randomly selected axes in the order of their index, they create a pattern organized in cells. Their walls are multiple replicas of axes generators. The red dot (CENTER) indicates the direction of thinking.

   The patterns obtained may be colored by multiple ways: tapes or colored circles, colored walls, shading, etc.

   With about a hundred axes the set of the cells can't be represented legibly in the screen: it is necessary to select an area and a scale suitable.

   The gallery SC-PLA shows some examples of the images obtained.

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   - 3D - in three dimensions it is planar-symmetry:

   The cells are then polyhedral (foam soap). It is difficult to represent them in pictures, unless the cuts by an animation. Or by the replicas of an object placed at the centre, such as a ball. 

   These images 3D can also make an animation !....

   If all the planes of symmetry are passing through by the middle of a sphere, the SC product designs on the surface of it. The projection of an area creates an image plane. A program can scroll the area around the sphere. 

   The gallery SC-SPH shows some examples of the images obtained with plans chosen at random but from a law optimal distribution. These images evoke the designs of oriental tapestry works. They can be progressive.

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   - GEOM 2D - In two dimensions, but the successive axes are tangent to a equiangular spiral.

   The images obtained are then very regular and evoke geometric or natural shapes. Some are strictly fractal.

   The gallery SC-EXP shows some examples of these images.

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   - 2D FRAC-In two dimensions, but the lines become hyperbolas by a transformation similar to that which generate fractals of JULIA. The images obtained are similar to previous ones. But they are limited by a fractal line and harmoniously redued on the periphery.

   The gallery SC-FRA shows some examples of these images. The last were obtained by a "graft" onto the spherical cells.   

Copyright © Hugues Amiard 2004 2008 Tous droits réservés.