Saturday, June 7, 2008

Dynamic plane symmetry groups

I have two running themes. One is to identify artists who were trained in some other field, particularly math or science. The other theme has been a gratuitous display of my arc shaped digital prints.

My artists list now includes: the chemist Jess Collins, the biologist Jo Baer, the mechanical engineer Alexander Calder, the inventor Hans Hofmann, and the lawyer and professor Wassily Kandinsky.

My image below, from my latest project, represents a dynamic, arc shaped plane symmetry (wallpaper) group. The arc shape for the grid was arbitrarily chosen. It has no particular significance though it slightly complicates the math. It's a pleasing shape. The cells are arranged like discs in sectors and tracks around a center point, with axes dividing sectors and concentric circles dividing tracks. The animations of images are done by one of two transformations. When an image moves to an adjacent sector it amounts to a mathematical reflection about an axis. When a image moves to an adjacent track it represents an oblique or scaling reflection.

The cell images are designed to be rotated to one of four orientations. An animation may contain multiple related images which are rotated in quarter-turns to three other orientations. The image selection is random, but the initial orientation is calculated using the greatest common divisor method described above.

Plane symmetry groups show up naturally, in mathematics, in architecture, and art. The recent Portland Art Museum presentation, Every Picture Tells a Story: Persian Narrative Painting, includes several fine examples.

Gratuitous still image from the animated GCD (dynamic plane symmetry group) project:

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