On Wave-Based Majority Gates with Cellular Automata

Abstract: We demonstrate a discrete implementation of a wave-based majority gate in a chaotic Life-like cellular automaton. The gate functions via controlling of patterns' propagation into stationary channels. The gate presented is realisable in many living and non-living substrates that show wave-like activity of its space-time dynamics or pattern propagation. In the gate a symmetric pattern represents a binary value 0 while a non-symmetric pattern represents a binary value 1. Origination of the patterns and their symmetry type are encoded by the particle reactions at the beginning of computation. The patterns propagate in channels of the gate and compete for the space at the intersection of the channels. We implement 3-inputs majority gates using a W topology showing additional implementations of 5-inputs majority gates and one tree (cascade) majority gate.