Complex Shift Dynamics of Some Elementary
Cellular Automaton Rules
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.
