A Study of Chaos in Cellular Automata

Abstract

This paper presents a study of chaos in one-dimensional cellular automata (CAs). The communication of information from one part of the system to another has been taken into consideration in this study. This communication is formalized as a binary relation over the set of cells. It is shown that this relation is an equivalence relation and all the cells form a single equivalence class when the cellular automaton (CA) is chaotic. However, the communication between two cells is sometimes blocked in some CAs by a subconfiguration which appears in between the cells during evolution. This blocking of communication by a subconfiguration has been analyzed in this paper with the help of de Bruijn graph. We identify two types of blocking — full and partial. Finally a parameter has been developed for the CAs. We show that the proposed parameter performs better than the existing parameters.