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

TL;DR

This study reevaluates the relationship between cellular automata's lambda parameter and their computational capabilities, challenging previous hypotheses and highlighting the importance of symmetries in evolution.

Contribution

It provides new experimental evidence that questions earlier claims about lambda's role in evolving computationally capable CA rules and emphasizes symmetry breaking effects.

Findings

Different results from Packard's original experiment.

Symmetry breaking can hinder evolution of computational ability.

Emergence and competition of computational strategies observed.

Abstract

We present results from an experiment similar to one performed by Packard (1988), 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 (Langton, 1990), 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.