On Wave-Based Majority Gates with Cellular Automata

TL;DR

This paper presents a novel wave-based majority gate implementation using cellular automata, leveraging pattern symmetry and propagation in chaotic automata to perform logical majority operations.

Contribution

It introduces a discrete, wave-based majority gate in cellular automata, demonstrating multiple input configurations and potential substrate implementations.

Findings

Successfully implemented 3-input majority gate in cellular automata

Extended to 5-input and cascade majority gates

Demonstrated gate operation via pattern symmetry and propagation

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.