# Conan Chadbourne

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.

A regular k-coloring of a symmetric pattern can be described by the symmetry group of the uncolored pattern together with a homomorphism from the group in to the symmetric group on k elements. This image describes one of the three distinct 2-colorings of a pattern with symmetry group p4g (or orbifold signature 4•2). The uncolored pattern appears at the lower left of the image, while the colored pattern, with color-preserving symmetry group cmm (orbifold signature 2•22), appears at the lower right of the image. At the top of the image is a stylized Cayley diagram of the group p4g, with elements colored to correspond to the cosets of the color-preserving subgroup.

A regular k-coloring of a symmetric pattern can be described by the symmetry group of the uncolored pattern together with a homomorphism from the group in to the symmetric group on k elements. This image describes one of the three distinct 2-colorings of a pattern with symmetry group p4g (or orbifold signature 4•2). The uncolored pattern appears at the lower left of the image, while the colored pattern, with color-preserving symmetry group pgg (orbifold signature 22x), appears at the lower right of the image. At the top of the image is a stylized Cayley diagram of the group p4g, with elements colored to correspond to the cosets of the color-preserving subgroup.