# 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.

There are 212,987 distinct ways to partition a 4x4 grid of square tiles into component shapes composed of contiguous tiles, assuming any two such partitions are considered equivalent if they differ only by a symmetry transformation such as a rotation or reflection. There are exactly thirteen of these configurations which have four-fold rotational symmetry, but no mirror symmetry. This image presents this set of thirteen configurations, sorted by the minimum number of colors that each requires to color the component shapes such that adjacent shapes have different colors (2 colors for the four configurations at the corners, 3 colors for the eight in the middle ring, and 4 colors for the one in the center).

Seven points may be arranged in a configuration having hexagonal symmetry by placing one point at the center and arranging the remaining six points uniformly around this center point. There are exactly 46 geometrically distinct ways of partitioning this configuration into subsets of adjacent points, assuming that any two such partitions are considered equivalent if they differ only by a symmetry transformation, such as reflection or rotation. This image presents these 46 different partitions, arranged in concentric rings according to the subgroup of the full hexagonal symmetry of the configuration that stabilizes the partition.