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

Melanie Mitchell, Peter T. Hraber, and James P. Crutchfield

93-03-014

We present results from an experiment similar to one performed by Packard [23], in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA rules as a function of Langton's $\lambda$ parameter [16], and interpreted the results of his experiment as giving evidence for the following two hypotheses: (1) CA rules able to perform complex computations are most likely to be found near “critical” $\lambda$ values, which have been claimed to correlate with a phase transition between ordered and chaotic behavioral regimes for CA; (2) when CA rules are evolved to perform a complex computation, evolution will tend to select rules with $\lambda$ values close to the critical values. Our experiment produced very different results, and we suggest that the interpretation of the original results is not correct. We also review and discuss issues related to $\lambda$, dynamical-behavior classes, and computation in CA. The main constructive results of our study are identifying the emergence and competition of computational strategies and analyzing the central role of symmetries in an evolutionary system. In particular, we demonstrate how symmetry breaking can impede the evolution toward higher computational capability.