Charlie Brummitt recently graduated from the University of Wisconsin-Madison, where he studied mathematics and physics and wrote a thesis about finding the simplest chaotic partial differential equation. In fall 2009 he will begin graduate study at the University of California-Davis, where he intends to study complexity science for a PhD in applied mathematics. His other interests include cycling, foreign languages, cooking, and traveling.
Project: Classifying Boundaries of Cellular Automata
A fundamental question regarding cellular automata is the shape of their boundaries. The boundaries are more tractable than the interior because they are guaranteed to have the same background on one side. Most boundaries grow linearly, but some grow in more unusual ways—such as according to power laws or logarithms. This project will attempt to determine what kinds of boundaries are possible. It would be interesting to find boundaries that grow in ways that involve transcendental numbers like pi or Log(2). This project will search the space of k=2, r=2 cellular automata, which is sufficiently vast to determine what kinds of boundaries are possible. Heuristics will be used to find the nonlinear boundaries, and curve fitting will then be applied to describe the asymptotic forms of the boundaries.
Favorite Three-Color Cellular Automaton