Cosmology and Art

The images shown above are based on tiling of the hyperbolic plane with equilateral triangles having angles not of 60^o but rather 360/7 degrees, so 7 such triangles fit around a point.

The image on the left shows the triangles and circles drawn from the vertices that each touch 7 other points. On the right, the pattern formed by these circles has been filled with blue and gold. When this image was made, the 7 fold symmetry was appropriate to mark the 7 straight victories of UCLA over USC in football, but that streak has now grown to 8 straight wins. This filled image is shown at larger scale below:

These images are of course very similar to works by M. C. Escher. This kind of tiling the hyperbolic plane is similar to the 3-D tilings of H³ described in the April 1999 Scientific American by Luminet, Starkman and Weeks.

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