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.

翻译：在由简单规则集支配的系统中涌现出复杂结构，是自然界中最引人入胜的现象之一。细胞自动机为研究这一现象提供了强大且通用的模型，其中生命游戏是最著名的实例之一。然而，这一简化模型在作为真实系统建模工具时可能过于局限。为解决此问题，我们引入并研究了一种扩展版生命游戏，其规则选择过程由动态机制主导。研究表明，所引入的修改显著改变了游戏的行为。我们还证明，同步策略的选择可用于控制系统稳定与增长之间的权衡。