Glider Collisions in Hybrid Cellular Automaton with Memory Rule (43,74)

Abstract

In the case of one-dimensional cellular automaton (CA), a hybrid CA (HCA) is the member whose evolution of the cells is dependent on nonunique global functions. The HCAs exhibit a wide range of traveling and stationary localizations in their evolution. We focus on HCA with memory (HCAM) because they produce a host of gliders and complicated glider collisions by introducing the hybrid mechanism. In particular, we undertake an exhaustive search of gliders and describe their collisions using quantitative approach in HCAM[Formula: see text]. By introducing the symbol vector space and exploiting the mathematical definition of HCAM, we present an analytical method of complex asymptotic dynamics of the gliders.

On Patterns and Dynamics of Rule 22 Cellular Automaton

“…Memory functions were developed and extensively studied by Alonso-Sanz in [73]. Memory in ECA have been studied, showing its potential to produce complex behavior from chaotic systems and beyond in [37,72], and recently in [74] authors have included hybrid versions. Thus, we can conjecture that a memory function can produce complex behavior [72] as follows:…”