# Conan Chadbourne

My work is motivated by a fascination with the occurrence of mathematical and scientific imagery in traditional art forms, and the frequently mystical or cosmological significance that can be attributed to such imagery. Mathematical themes both subtle and overt appear in a broad range of traditional art, from Medieval illuminated manuscripts to Buddhist mandalas, intricate tilings in Islamic architecture to restrained temple geometry paintings in Japan, complex patterns in African textiles to geometric ornament in archaic Greek ceramics. Often this imagery is deeply connected with how these cultures interpret and relate to the cosmos, in much the same way that modern scientific diagrams express a scientific worldview.

The Steiner triple system S(2,3,7) is the unique combinatorial design in which three-element subsets (or blocks) are drawn from a seven element set such that any pair of elements occurs in exactly one block, and any two blocks have exactly one element in common. The permutations of the elements which leave the system invariant form a group isomorphic to PSL(2,7), the second smallest non-abelian simple group. In this image, the blocks of three symbols are shown in the center of the image, surrounded by a frame with 168 symbols which correspond to the 168 automorphisms of the system.

The Klein Quartic is a genus 3 Riemann surface whose conformal automorphism group is isomorphic to PSL(2,7). In this image, a projection of the Klein Quartic into the Poincare disk is shown, with a heptagonal tessellation.