Essential metrics for Life on graphs

TL;DR

This paper introduces a theoretical framework for Life-like network automata, generalizing cellular automata like the Game of Life, and demonstrates their application in solving synchronization problems with high success rates.

Contribution

It provides a formal foundation and essential metrics for Life-like network automata, enabling analysis and application to complex network dynamics.

Findings

Genotype and phenotype are correlated in these models.

The framework successfully addresses the firing squad synchronization problem.

Achieves over 90% success rate in synchronization tasks.

Abstract

We present a strong theoretical foundation that frames a well-defined family of outer-totalistic network automaton models as a topological generalisation of binary outer-totalistic cellular automata, of which the Game of Life is one notable particular case. These "Life-like network automata" are quantitatively described by expressing their genotype (the mean field curve and Derrida curve) and phenotype (the evolution of the state and defect averages). After demonstrating that the genotype and phenotype are correlated, we illustrate the utility of these essential metrics by tackling the firing squad synchronisation problem in a bottom-up fashion, with results that exceed a 90% success rate.