# Gary Greenfield

Professor Emeritas of Mathematics & Computer Science

University of Richmond

Richmond, Virginia, USA

Most of my computer generated artworks arise from visualizations of mathematical, physical, or biological processes. I want to focus the viewer's attention on the complexity and intricacy underlying such processes. Most recently, I have been exploiting the tension that arises when generating minimalist art using complex processes.

Chip Firing Transient

23 x 15 cm

Digital print

2018

After placing a finite number of chips at each vertex of a finite graph, a chip firing cellular automaton is defined by iterating the rule: every vertex that has at least as many chips as neighbors distributes one chip to each of its neighbors. When the graph is a cycle with thirty vertices, and initially a vertex can have at most three chips, then after the transient phase the period is always one, two, or thirty. Therefore the question of interest is: how many iterations can the transient phase last? This period two automata is an example where the transient phase lasts for the conjectured maximum of ninety iterations. Vertices are colored white, yellow, orange, or red according as they have 0, 1, 2 or 3 chips.