A Chaotic Subsystem of Hyper Bernoulli Shift Rule 41

In this paper, the dynamics of elementary cellular automaton rule 41 is investigated in the bi-infinite symbolic sequence space. Rule 41, which is one of Chua´s hyper Bernoulli shift CA rule, possesses of rich and complex dynamical behaviors. By using blocking and releasing transformation, the topological conjugated relationship between rule 41 and rule 184 on their respective subsystems is established. Some interesting dynamical properties of the rule such as positive topological entropy, topological mixing, chaos in the sense of Li-Yorke and Devaney, are revealed.