# James Mai

Mathematics and visual art converge in their mutual preoccupation with pattern and structure. In mathematics, patterns and structures are usually understood cognitively and symbolically; in visual art, they are experienced perceptually and palpably. The former is largely quantitative in nature, the latter largely qualitative. My work results from both of these approaches. Current work includes exhaustive permutations of forms derived from octagonal point-arrays. These generate complete form-sets, from which I choose subsets for compositions. Compositions and coloration are guided by the inherent characteristics of the forms of a given subset, and those forms are often grouped by common features or arranged in gradients of increasing/decreasing features. Final composition and color decisions are sometimes intended to allude to such figurative subjects as the macroscopic universe of stars and galaxies and the microscopic world of atoms, molecules, and cells.

This composition employs the complete set of 17 octet-forms made from 4 straight line segments connecting pairs of points in an octagonal array. The octet-forms are arranged in horizontal rows in descending order from more to fewer outer edges (lines connecting adjacent points of the octagon); the top form possesses all 4 outer edges, while forms in the bottom row possess no outer edges. The forms are further ordered by color coding for degrees of reflective symmetry; the chromatic order, yellow - orange - red - blue, indicates a decreasing number of internal axes of reflective symmetry (yellow = 8 axes, descending to blue = 1 axis), while the single asymmetrical form is colored neutral.

These 29 forms include 2 complete form-sets: 17 octet-forms that are built from 4 straight line segments connecting pairs of points (yellow and red shells) and 12 octet-forms built from 2 closed shapes connecting 3, 4, or 5 points (blue shells). Starting from the inner shell and proceeding outward, the yellow shells hold forms that gradually lose their external edge-lines (lines that join adjacent vertexes of the octagon). The red shell holds linear forms with no outer edge-lines (no adjacent vertex lines). The inner blue shell holds forms made with triangles and pentagons; the outer blue shell has forms made with pairs of quadrangles. This composition employs the complete sets of octet-forms made from line + line combinations and shape + shape combinations.

This is one octet-form from a much larger set of forms, each of which is a closed, circuitous line that visits each vertex of an octagon only once. By varying the order in which the line visits the vertexes of the octagon, over 200 unique octet-forms result (this, after elimination of any forms that are symmetrically "redundant" by rotation or reflection). This composition includes each step of the line-segment construction of this single octet-form, completed as circuitous form in blue at the bottom of the composition.