Rapid left expansivity, a commonality between Wolfram's Rule 30 and powers of p/q

Abstract

<p>We define the class of rapidly left expansive cellular automata, which contains Wolfram's Rule 30, fractional multiplication automata, and many others. Previous results on aperiodi-city of columns in space-time diagrams of certain cellular automata generalize to this new class. We also present conditions that imply periodic behavior in cellular automata and use these to prove new results on rapidly left expansive cellular automata that originate from the theory of distribution modulo 1.<br></p><p>(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).</p>