Glider Dynamics and Topological Dynamics of Bernoulli-shift Rule 61

Abstract

In this paper, the dynamics of elementary cellular automata rule 61 is investigated in the bi-infinite symbolic sequence space. This work provides the glider properties and the interactions in rule 61, including several natural gliders, a catalog of gliders and glider collisions, which were found in Wolfram’s complex rules 110 and 54 before. In addition, It is also proved that rule 61 defines three subsystems with complicated dynamical behaviors such as topologically mixing, topologically transitive and positive topological entropy. Finally, a relation between the collisions in rule 61 and a logical operation is established.