James Crutchfield, Peter Hraber, Melanie Mitchell

Paper #: 93-06-040

In this paper we review previous work and present new work concerning the relationship between dynamical systems theory and computation. In particular, we review work by Langton [22] and Packard [29] on the relationship between dynamical behavior and computational capability in cellular automata (CA). We present results from an experiment similar to the one described in [29], that was cited there as evidence for the hypothesis that rules capable of performing complex computations are most likely to be found at a phase transition between ordered and chaotic behavioral regimes for CA (the “edge of chaos”). Our experiment produced very difficult results from the original experiment, and we suggest that the interpretation of the original results is not correct. We conclude by discussing general issues related to dynamics, computation, and the “edge of chaos” in cellular automata.