01183nas a2200133   4500000000100000000000100001008004100002260001200043100002200055245010000077856003700177490000700214520082800221       2023                            d  c10/20231 aJaroslaw Miszczak00aRule switching mechanisms in the Game of Life with synchronous and asynchronous updating policy  uhttps://arxiv.org/abs/2310.059790 v983 a<p>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.</p>