Computation and Universality: Class IV versus Class III Cellular Automata

TL;DR

This paper investigates whether Class III cellular automata, known for chaotic behavior, can perform universal computation, challenging the traditional association of universality primarily with Class IV automata.

Contribution

It explores the potential for Turing universality in Class III cellular automata, expanding the understanding of computational capabilities across Wolfram's classes.

Findings

Some chaotic CA may be candidates for universal computation

Discussion on Turing universality in both Class III and IV automata

Challenges the assumption that only Class IV CA are computationally universal

Abstract

This paper examines the claim that cellular automata (CA) belonging to Class III (in Wolfram's classification) are capable of (Turing universal) computation. We explore some chaotic CA (believed to belong to Class III) reported over the course of the CA history, that may be candidates for universal computation, hence spurring the discussion on Turing universality on both Wolfram's classes III and IV.