Wolfram's Classification and Computation in Cellular Automata Classes III and IV

TL;DR

This paper surveys Wolfram's classification of cellular automata, focusing on classes III and IV, and demonstrates that class III automata are capable of universal computation, challenging previous assumptions about their computational limitations.

Contribution

It provides evidence that class III cellular automata can achieve Turing universality, expanding understanding of their computational potential.

Findings

Class III automata are capable of computation.

Class III automata may reach Turing-completeness.

Class III automata are not inherently too 'hot' to control.

Abstract

We conduct a brief survey on Wolfram's classification, in particular related to the computing capabilities of Cellular Automata (CA) in Wolfram's classes III and IV. We formulate and shed light on the question of whether Class III systems are capable of Turing universality or may turn out to be "too hot" in practice to be controlled and programmed. We show that systems in Class III are indeed capable of computation and that there is no reason to believe that they are unable, in principle, to reach Turing-completness.