Glider Dynamics and Topological Dynamics of Bernoulli-shift Rule 61

Author

Wang, Yi ; Chen, Fangyue ; Han, Yunfang

Author_Institution

Sch. of Sci., Hangzhou Dianzi Univ., Hangzhou, China

fYear

2010

Firstpage

192

Lastpage

196

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.

Keywords

cellular automata; topology; Bernoulli-shift rule 61; Wolfram complex rule 110; Wolfram complex rule 54; biinflnite symbolic sequence space; elementary cellular automata rule 61; glider collisions; glider dynamics; glider properties; logical operation; natural gliders; positive topological entropy; topologically mixing; topologically transitive entropy; Automata; Bifurcation; Chaos; Entropy; Logic gates; Nonlinear dynamical systems; Orbits; cellular automata; chaos; glider; glider collision; logical operation; symbolic dynamics;

fLanguage

English

Publisher

ieee

Conference_Titel

Chaos-Fractals Theories and Applications (IWCFTA), 2010 International Workshop on

Conference_Location

Kunming, Yunnan

Print_ISBN

978-1-4244-8815-5

Type

conf

DOI

10.1109/IWCFTA.2010.36

Filename

5671284