Computation with Competing Patterns in Life-Like Automaton

Abstract

Summary. We study a Life-like cellular automaton rule B2/S2345 where a cell in state '0' takes state '1' if it has exactly two neighbors in state '1' and the cell remains in the state '1' if it has between two and five neighbors in state '1.' This automaton is a discrete analog spatially extended chemical media, combining both properties of sub-excitable and precipitating chemical media. When started from random initial configuration B2/S2345 automaton exhibits chaotic behavior. Configurations with low density of state '1' show emergence of localized propagating patterns and stationary localizations. We construct basic logical gates and elementary arithmetical circuits by simulating logical signals with mobile localizations reaction propagating geometrically restricted by stationary non-destructible localizations. Values of Boolean variables are encoded into two types of patterns -symmetric (False) and asymmetric (True) patterns -which compete for the 'empty' space when propagate in the channels. Implementations of logical gates and binary adders are illustrated explicitly.

On Emulation of Flueric Devices in Excitable Chemical Medium

“…Examples include interaction of wave-fragments in light-sensitive Belousov-Zhabotinsky media [94], swarms of soldier crabs [95], growing lamellipodia of slime mould Physarum polycephalum [43, 96], crystallisation patterns in ‘hot ice’ [97], peristaltic waves in protoplasmic tubes [98], and jet streams in fluidic devices [99], competing patterns propagation in channels of communication with a Life-like CA [100]. When Boolean values are represented by localised, finite size, patterns—the accuracy of synchronisation depends on the size of the patterns.…”

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

“…The still life pattern [23,11] in B2/S2345 has a relevant characteristic. They are not affected by their environment however they do affect their environment [20,22]). Therefore the still life patterns can be used to build channels, or wires, for signal propagation.…”

“…3). Such type of circuitry has been already used to implement xor gate in chemical laboratory precipitating reaction-diffusion systems [4], and precipitating logical gates imitated in CA [20,22]. A minimal width of each channel equals three widths of the still life block (Fig.…”

“…In this paper we will exploit previous results on the constructions of feedback channels with still life patterns (previous studies since B2/S23456 [20] and B2/S2345678 [22]), reducing the number of cells in state 1 on the evolution rule. Hence every pattern propagation is stimulated since a glider reaction that will produce a specific static geometric pattern, thus their interactions when they compete shall yield a binary value representation.…”

Logic Gates Formed by Perturbations in an Asynchronous Game of Life

“…To date, various logic gates have been constructed for the GL. For example, there are logic gates that use collisions of gliders [1][2][3][4] or geographical constraints with fixed objects [5]. These logic gates are based on synchronous updating.…”