Complex Systems

Complex Shift Dynamics of Some Elementary Cellular
Automaton Rules Download PDF

Junbiao Guan
School of Science, Hangzhou Dianzi University
Hangzhou, Zhejiang 310018, P.R. China
junbiaoguan@gmail.com

Kaihua Wang
School of Mathematics and Statistics
Hainan Normal University
Haikou, Hainan 571158, P.R. China

Abstract

This paper presents a discussion of complex shift dynamics of some elementary cellular automaton rules (rules 30, 41, and 110). Equations that show some degree of self-similarity are obtained. It is demonstrated that rules 30, 41, and 110 exhibit Bernoulli shifts and are topologically mixing on one of their own closed invariant subsystems. Furthermore, many complex Bernoulli shifts are explored for finite symbolic sequences with periodic boundary conditions.