# 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 Fano plane is the smallest finite projective plane, having seven points and seven lines, such that any two points uniquely determine a line and any two lines intersect at exactly one point. The 168 automorphisms of the Fano plane form a group isomorphic to PSL(2,7), the second smallest non-abelian simple group. In this image, the Fano plane is represented at the center of the image, in a projection which emphasizes the equivalence of its seven points (shown as small yellow disks) and its seven lines (shown as blue ellipses). It is surrounded by a frame containing symbols which represent the cycle structures of the 168 permutations in the automorphism group of the Fano plane.

This image presents a visualization of the Steiner triple system S(2,3,7). This system, which is combinatorially equivalent to the Fano plane, consists of seven three-element subsets (or blocks) drawn from a seven element set such that any pair of elements occur in exactly one block, and any two blocks have exactly one element in common.