Complex Systems

Particle Structures in Elementary Cellular Automaton Rule 146 Download PDF

Paul-Jean Letourneau
Wolfram Research, Inc.
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Champaign, IL 61820, USA
paul-jean@wolfram.com

Abstract

Stochastic particle-like persistent structures are found in the class 3 elementary cellular automaton rule number 146. These particles arise as boundaries separating regions with black cells occupying sites at spacetime points (x, t) of constant parity xt. The particles execute random walks and annihilate in pairs, with particle density decaying with time in a power-law fashion. It is shown that the evolution of rule 146 closely resembles that of the additive rule 90, with persistent localized structures.