My work is motivated by a fascination with the occurrence of mathematical and scientific imagery in traditional art forms, and the mystical, spiritual, or cosmological significance that is often attached to such imagery. Mathematical themes both overt and subtle appear in a broad range of traditional art: Medieval illuminated manuscripts, Buddhist mandalas, intricate tilings in Islamic architecture, restrained temple geometry paintings in Japan, complex patterns in African textiles, geometric ornament in archaic Greek ceramics. Often this imagery is deeply connected with the models and abstractions these cultures use to interpret and relate to the cosmos, in much the same way that modern scientific diagrams express a scientific worldview.
This image is part of a series exploring the threefold symmetries of repeating patterns in the plane. The box at the top left shows an uncolored pattern with symmetry group p31m (orbifold signature 3*3). The box on the right shows a particular threefold coloring of this pattern, with symmetry group p3m1 (orbifold signature *333). The box at the bottom left shows the same coloring with a single color isolated. In the center of the image is a stylized Cayley diagram of the symmetry group of the uncolored pattern, with its elements colored to identify the cosets of the single-color stabilizer subgroup (in this case, p3m1). The two small boxes at the center left define the homomorphism from p31m into S3 (the group which permutes the 3 colors).