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

In this paper we present a two-dimensional chaotic cellular automaton, the Life rule B2/S2345, able to simulate the action of an adder with majority gates, stimulated by gliders collisions transformed as competing patterns. 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. We construct basic logical gates and elementary arithmetical circuits by simulating logical signals with gliders reaction propagating geometrically restricted by stationary non-destructible still life. Therefore an implementation of universal logical gates and a majority binary adder is constructe