Limit dynamics of elementary cellular automaton 18

TL;DR

This paper investigates the long-term behavior of elementary cellular automaton 18 by analyzing its limit sets, revealing the role of local patterns called kinks and distinguishing the three types of limit sets.

Contribution

It provides a detailed characterization of the generic limit set of rule 18, especially configurations with up to two kinks, and distinguishes the three limit sets.

Findings

The three limit sets of rule 18 are distinct.

Configurations with at most two kinks are characterized within the generic limit set.

Persistent local patterns called kinks govern the dynamics.

Abstract

We study the the asymptotic dynamics of elementary cellular automaton 18 through its limit set, generic limit set and $\mu$-limit set. The dynamics of rule 18 are characterized by persistent local patterns known as kinks. We characterize the configurations of the generic limit set containing at most two kinks. As a corollary, we show that the three limit sets of rule 18 are distinct.