Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations
Melanie Mitchell
Peter T. Hraber
Santa Fe Institute,
1660 Old Pecos Trail, Suite A,
Santa Fe, NM 87501, USA
James P. Crutchfield
Physics Department, University of California,
Berkeley, CA 94720, USA
Abstract
We present results from an experiment similar to one performed by Packard [24], in which a genetic algorithm is used to evolve cellular automata (CAs) to perform a particular computational task. Packard examined the frequency of evolved CA rules as a function of Langton's 
parameter [17]; he interpreted the results of his experiment as giving evidence for two hypotheses: (1) CA rules that are able to perform complex computations are most likely to be found near "critical'' values (which have been claimed to correlate with a phase transition between ordered and chaotic behavioral regimes for CAs); (2) When CA rules are evolved to perform a complex computation, evolution will tend to select rules with values close to the critical values. Our experiment produced quite different results, and we suggest that the interpretation of the original results is not correct. We also review and discuss issues related to , dynamical-behavior classes, and computation in CAs. The primary constructive results of our study are the identification of the emergence and competition of computational strategies, and the analysis of the central role of symmetries in an evolutionary system. In particular, we demonstrate how symmetry breaking can impede evolution toward higher computational capability.
