Thursday, August 27, 2009

Tessellations: Math and Art

I have been reading about and studying mathematical symmetry, the theories of tiling on the plane, and pattern in Islamic art and attempting to create images using my knowledge.

The mathematics is fascinating, one of the greatest accomplishment of 20th century mathematics was the classification of the finite simple groups. From the French revolutionary and mathematician Evariste Galois, through a quirk of numbers, 12 + 22 + ... + 242 = 702 that enables 24 dimensional grocers to pack their oranges in a small box, to the discovery of a strange and beautiful 196, 883 dimensional snowflake, it's a fantastic world. I would very much recommend the book Symmetry: A Journey into the Patterns of Nature, Marcus du Sautoy.
The art can be beautiful, I spent a lovely week in Granada, visiting the Alhambra, which is tiled with patterns of great complexity and beauty. (and on Saturday night pretty Spanish girls walk down the street, past clubs and discos, hand and hand, singing songs and laughing - hola)
In New York, I spent many an hour in the usually empty Islamic art section of the Met.
And in Istanbul, not enough time at the fantastic museum of Islamic art on Sultanahmet Square. I still can picture in my mind a piece of calligraphy, that seemed to spiral and twist from meaning, to pure mathematical form, with pattern that I could not resolve, but must have come from a deep understanding of possibility and application.

Anyway, with all this behind me and in my mind, I tried to make something. I figured out how to do it, threw myself into the fugue of creation, using what I had, and what I could do, made about 35 pieces so far, these two turned out.
If you save these images, you can set them as your desktop image, set it to tile, and the Zhalih's lips, or the spinning head of corrosion and Aimee will tile an infinite plane.

or watch this full screen. The music is Mozart. Queen of the Night. I made this with After Affects

Or even more, a gallery of these and more of my patterns.