# 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.

The Fano plane is the smallest finite projective plane, and consists of seven points and seven lines, such that any two points uniquely determine a line and any two lines intersect at exactly one point. It is combinatorially equivalent to the Steiner triple system on seven elements, STS(7), in which triples of elements are chosen from a set of seven elements such that any pair occurs in exactly one triple.

This image emphasizes the connection between these two structures by labeling the points and lines of the Fano plane with symbols and colors, respectively. The lines of the Fano plane, shown here as ellipses, are equivalent to the triples of STS(7), which appear around the outside of the image in corresponding colors.

The Klein Quartic is a genus-three Riemann surface which can be covered by a regular tessellation of 24 heptagons. In this image, the Klein quartic is projected into the Poincaré disk, and this heptagonal tessellation is given a regular 8-coloring. Each triplet of heptagons of any given color is fixed by a subgroup of order 21 of the full automorphism group of the surface.