# 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 grid of 16 symbols in this image represent a system of three mutually orthogonal Latin squares of order 4. Each symbol has three attributes which, considered alone, form a Latin square—color pairs (red-cyan, blue-orange, green-magenta, and yellow-violet), symmetry (one or two reflection axes, aligned either parallel to the sides of the square or on the diagonal), and proportion of the symbol which is filled with a particular pattern (2/9, 1/3, 2/3, or 7/9). The Latin square formed by considering any one of these attributes is orthogonal to that formed by either of the other two attributes.

Six circles can be arranged into a array with the symmetries of an equilateral triangle. This image presents the 23 geometrically distinct partitions of this array, assuming two configurations are considered equivalent if they differ only by a symmetry transformation. The partitions are arranged in concentric rings, according to the subgroup of the full triangular group that stabilizes the configuration: threefold rotational symmetry at the center (1 configuration), full triangular symmetry in the innermost ring (3 configurations), reflection symmetry only in the next ring (10 configurations), and no symmetry in the outermost ring (9 configurations).