Computation with competing patterns in Life-like automaton

Abstract: We study a Life-like cellular automaton rule $B2/S2345$ where a cell in state 0' takes state1' if it has exactly two neighbors in state 1' and the cell remains in the state1' 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 state1' 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.