Dynamics, Computation, and the "Edge of Chaos": A Re-Examination

TL;DR

This paper re-examines the relationship between dynamical systems and computation, challenging previous evidence that complex computation occurs at the phase transition between order and chaos in cellular automata.

Contribution

It presents new experimental results that question earlier findings on the 'edge of chaos' hypothesis in cellular automata and discusses broader implications for dynamics and computation.

Findings

New experiment contradicts previous evidence for the 'edge of chaos' hypothesis.

Questions the interpretation of earlier results linking complexity and phase transitions.

Discusses broader issues in dynamics and computational capability in cellular automata.

Abstract

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 \cite{Langton90} and Packard \cite{Packard88} 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 \cite{Packard88}, 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 different 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.