Wolfram Computation Meets Knowledge

Wolfram Summer School


Joshua Bonner

Summer School

Class of 2005


Joshua Bonner is a recent graduate of Indiana University, having majored in computer science and mathematics and minored in Japanese, and is continuing on there for graduate school. His academic interests include ubiquitous computing, networks, and artificial intelligence. He also enjoys mathematics, reading, and gaming, and has made a hobby of translating Japanese animation.

Project: Simple Games with Cellular Automata

In the NKS book, Note 1105a considers simple games between cellular automata, and presents a basic plot of how each of the two-color nearest-neighbor automata perform against each other in a short iterated game similar to the Prisoner’s Dilemma. The book notes that considerable complexity is evident, but does not go beyond a surface analysis of the system. The purpose of this project is to examine the data produced by another simple game between cellular automata, Penny Matching (a.k.a. Evens and Odds), in greater detail and investigate any interesting features that emerge. The project also aims to determine whether competition between cellular automata can result in a consistent ranking of rules, and whether such a ranking correlates with a rule’s ability to succeed against non-CA players.

Favorite Four-Color, Nearest-Neighbor, Totalistic Rule

Rule chosen: 587348

My favorite four-color totalistic cellular automaton is rule 587348, which I found while playing around with

With[{rule=RandomInteger[{0, 4^10 - 1}], init = Table[RandomInteger[{0, 3}], {250}]}, {ArrayPlot[CellularAutomaton[{rule, {4, 1}, 1}, init, 500]], rule, init}]

If you just start it with a single cell on an infinite background, it seems boring unless you’re careful about picking the foreground and background colors. However, if you start it with a random initial condition it has an interestingly complex pattern that sort of looks rounded and three dimensional, as if there were both a foreground and background layer of patterns.