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 twelve of these configurations which preserve the full four-fold dihedral symmetry of the original grid. This image presents these twelve configurations.