Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations

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 computat iona l t ask . Packard examined the frequency of evolved CA rules as a function of Langton's A par amet er [17]; he interpret ed t he results of his experiment as giving evidence for two hypotheses: (1) CA rules that are able to perform complex comp utat ions are most likely to be found near "crit ical" Avalues (which have been claim ed to correlate with a phase transition between ord ered and chaot ic behavioral regimes for CAs) ; (2) Wh en CA rules are evolved to perform a compl ex comput at ion, evolut ion will t end t o select rules with Avalues close to the critical values. Our experiment produced quit e different results , and we suggest that the int erpretation of the original results is not correct. We also review and discuss issues related to A, dyn ami cal-b ehavior classes, and computation in CAs. The primary constructive results of our study are the identification of the emergence and competition of comput ational strategies, and the analysis of the central role of symmetries in an evolut ionary system. In pa rticular, we demonstrat e how symmetry breaking can impede evolut ion toward higher computational