Phenomenology of Reaction–diffusion Binary-State Cellular Automata

Abstract

We study a binary-cell-state eight-cell neighborhood two-dimensional cellular automaton model of a quasi-chemical system with a substrate and a reagent. Reactions are represented by semi-totalistic transitions rules: every cell switches from state 0 to state 1 depending on if the sum of neighbors in state 1 belongs to some specified interval, cell remains in state 1 if the sum of neighbors in state 1 belong to another specified interval. We investigate space-time dynamics of 1296 automata, establish morphology-bases classification of the rules, explore precipitating and excitatory cases and scrutinize collisions between mobile and stationary localizations (gliders, cycle life and still-life compact patterns). We explore reaction–diffusion like patterns produced as a result of collisions between localizations. Also, we propose a set of rules with complex behavior called Life 2c22.

On logical gates in precipitating medium: Cellular automaton model

“…Previously we have proposed a detailed classification of two-dimensional semitotalistic cellular automaton functions [5], which imitates the processes of dissociation and association in spatially extended nonlinear media. Every cell of the automaton array has eight neighbours and takes two states, 0 and 1.…”

“…Cells update their states simultaneously in discrete time, depending on the sum of the states of their neighbours, and by the same cell-state transition rule. We have demonstrated that this family of cellular automata is capable of constructing Voronoi diagrams [4], information transfer in the form of mobile self-localizations [15] and self-development of sophisticated patterns from minimal seed conditions [5].…”

Majority Adder Implementation by Competing Patterns in Life-Like Rule B2/S2345

“…On the way, we have reported in phenomenological studies of semi-totalistic CA [5], a selected set rules named as Life 2c22, identified by periodic structures [28]. The clan closest to the family 2c22 and the Diffusion Rule (Life rule B2/S7) [21], all they also into of a big cluster named as Life dc22.…”

Computation with Competing Patterns in Life-Like Automaton

“…In its original form, GoL automaton is a discrete analog of sub-excitable chemical media [8,24]. Localized wave-fragments (reaction-diffusion dissipative solitons) in sub-excitable Belousov-Zhabotinsky reaction [8,24] are represented by gliders [14,45,16,33,38,4] in GoL cellular automaton. See examples of direct comparisons between experimental chemical laboratory results and cellular automaton models in [12].…”

“…The LwD family of cell-state transition rules is an automaton equivalent of the precipitating chemical systems. This is demonstrated in our phenomenological studies of semi-totalistic and precipitating CA [4], where we selected a set of rules Life 2c22, identified by periodic structures [35]. The clans closest to the family 2c22 are Diffusion Rule (Life rule B2/S7) [27], all they also into of a big cluster named as Life dc22.…”