James Mai

Professor of Art
Illinois State University
United States

Mathematics and visual art converge in their mutual preoccupation with pattern and structure. In mathematics, patterns and structures are usually approached cognitively and symbolically; in visual art, they are experienced perceptually and palpably. The former approach is largely quantitative in nature, the latter largely qualitative. My work results from a combination of these approaches. Current work includes exhaustive permutations derived from octagons, from which I choose subsets for compositions. By selective arrangement and coloration, the final compositions allude to such figurative subjects as the macroscopic universe of stars and galaxies and the microscopic world of atoms and molecules.

Stellar (Octets - Rotational)
Stellar (Octets - Rotational)
archival digital print

The 9 forms in this work are a subset of a much larger set of forms derived from octagons, each form a different configuration of a circuitous line that touches the 8 vertices of an octagon only once. Eliminating symmetrical "redundancies" (forms that, by rotation, reflection, or translation, are the same as another), there are over 200 unique forms in the full set. Within this full set, there are only 9 forms that possess rotational symmetry. In this work, coloration of the 9 forms indicates the number of remaining external edges of the original regular convex octagon: 2 yellow forms possess 4 of the outer edges; 5 red forms possess 2 outer edges; 2 blue forms possess 0 outer edges. The 9 rotationally symmetrical forms are composed in a rotationally symmetrical array within a square diamond.