A novel construction of chaotic dynamics base gliders in diffusion rule B2/S7

Abstract

The dynamical behaviors of gliders (mobile localizations) in diffusion rule B2/S7 are quantitatively analyzed from the theory of symbolic dynamics in two-dimensional symbolic sequence space. Their intrinsic complexity is demonstrated by exploiting the relationship between one-dimensional and two-dimensional subshifts. Based on this rigorous approach and technique, the underlying chaos of the extant gliders and their combinations is characterized in a subtle way. It is demonstrated that they can be identified to distinct subsystems with very rich and complicated dynamics; that is, diffusion rule is topologically mixing and possesses positive topological entropy on each subsystem. This analytical assertion provides the fact that diffusion rule is covered with complex subsystems “almost everywhere”. Finally, it is worth mentioning that the procedure proposed in this paper is also applicable to all other gliders arising from the two-dimensional cellular automata therein. It is an extended discovery in both cellular automata and chaos theory.