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

Abstract

Abstract. We study Life-like cellular automaton rule B2/S2345. This automaton exhibits a chaotic behavior yet capable for purposeful computation. The automaton implements Boolean gates via patterns which compete for the space when propagate in channels. Values of Boolean variables are encoded into two types of patterns -symmetric (False) and asymmetric (True). We construct basic logical gates and elementary arithmetical circuits by simulating logical signals using glider reactions taking place in the channels built of non-destructible still lifes. We design a binary adder of majority gates realised in rule B2/S2345.

Computation with competing patterns in Life-like automaton

“…6). Such type of circuitry has been already used to implement xor gate in chemical laboratory precipitating reaction-diffusion systems [3], and precipitating logical gates imitated in CA [26,28]. A minimal width of each channel equals three widths of the still life block (Fig.…”

“…The still life patterns [29,11] represent precipitation of an abstract reaction-diffusion chemical system imitated by rule B2/S2345 automaton. The still life blocks are not affected by their environment however they do affect their environment [26,28]). Therefore the still life patterns can be used to build channels, or wires, for signal propagation.…”

“…Conventional logic circuit and truth table of a binary half-adder are shown in Fig. 14a (true tables were derived from [28]). 7 Schematic representation of the half-adder via T -junctions between channels is shown in Fig.…”

“…We develop a model where the channels are constructed using static patterns and computation is implemented by propagating patterns of precipitation. The results are based on our previous studies of reaction-diffusion analogs B2/S23456 [26] and B2/S2345678 [28].…”

Universal One-Dimensional Cellular Automata Derived for Turing Machines and its Dynamical Behaviour

“…Frequently the construction of computers in cellular automata are handled just with primitive signals (classic examples include von Neumann rule [27], Codd [3], Banks [2]) or with non-trivial patterns known as gliders, particles, waves or self-localizations (classic examples include the Game of Life [6], Rule 110 [4,30]), and recently by packages of signals ( [18,10]). Actually, we have some Turing machines implemented in cellular automata, one of them in the Game of Life by Paul Rendell [23] and in one dimension by Smith [25] and other by Lindgren and Nordahl [9].…”