I use computational software to design artwork inspired by the inherent beauty of mathematics. I push boundaries of skills and knowledge to learn something new in each piece. As with my teaching, I strive for audience participation and engagement. The final pieces aim to inspire a curiosity about the mathematical nugget underlying the visualization.
This year’s pieces bring ideas from the two-dimensional realm into higher dimensions. Knight’s tours are traditionally on a two-dimensional chessboard; this piece explores a four-dimensional variant. The multiplication of permutations can bewilder; this piece gives the audience an opportunity to clarify the behavior with physical three-dimensional braid representations.
Artworks
Playing 4D Chess
15.0 x 15.0 x 15.0 cm
3D Printed Nylon through a multi jet fusion process
2025
Playing 4D Chess is a visualization of a knight’s tour on a four-dimensional chessboard. The 80 chambers on the 3x3x3x3 chessboard (removing the central chamber) are each represented by a vertex; a knight’s move is a displacement of two units in one direction and one unit in an orthogonal direction. The first three dimensions (x,y,z) are shown in a standard 3D grid. A unit move in the fourth dimension is represented by a translation of (1/4,1/4,1/4); vertices for a fixed 3D slice have a consistent form (cube, sphere, octahedron) to aid in the visualization. As the viewer plays four-dimensional chess by following this Hamiltonian cycle around all 80 vertices, they will see that two consecutive moves involve the same two coordinates.
Experiential Braid Relations
24.0 x 16.0 x 6.0 cm
Laser cut wood, Optical Cable, 3D printed parts, LED lights, and magnets
2025
Experiential Braid Relations is an interactive light display that explores the structure of the permutation group S4. A group element is visualized by a permutation of four colors. Each box is a conduit that permutes the input colors according to a predefined permutation. Viewers build towers of boxes to explore multiplication of permutations. Viewers can discern that permutation multiplication is not commutative, that every permutation is the product of adjacent transpositions, and that adjacent transpositions satisfy the expected braid relations. Engravings on the boxes provide for a "beginner mode" in which viewers can be guided by the braid relations, and an "advanced mode" in which viewers use their permutation multiplication skills.
