Rule switching mechanisms in the Game of Life with synchronous and asynchronous updating policy

TL;DR

This paper explores an extended version of Conway's Game of Life where rules can switch dynamically, demonstrating how different synchronization policies influence system stability and growth, thus offering a more versatile modeling tool.

Contribution

It introduces a rule-switching mechanism in the Game of Life and analyzes how synchronization policies affect the system's behavior and stability.

Findings

Rule switching significantly alters system dynamics.

Synchronization policy controls stability and growth trade-off.

Extended model offers better tools for real system modeling.

Abstract

The emergence of complex structures in the systems governed by a simple set of rules is among the most fascinating aspects of Nature. The particularly powerful and versatile model suitable for investigating this phenomenon is provided by cellular automata, with the Game of Life being one of the most prominent examples. However, this simplified model can be too limiting in providing a tool for modelling real systems. To address this, we introduce and study an extended version of the Game of Life, with the dynamical process governing the rule selection at each step. We show that the introduced modification significantly alters the behaviour of the game. We also demonstrate that the choice of the synchronization policy can be used to control the trade-off between the stability and the growth in the system.