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The emergence of complex structures in the systems governed by a simple setof rules is among the most fascinating aspects of Nature. The particularlypowerful and versatile model suitable for investigating this phenomenon isprovided by cellular automata, with the Game of Life being one of the mostprominent examples. However, this simplified model can be too limiting inproviding a tool for modelling real systems. To address this, we introduce andstudy an extended version of the Game of Life, with the dynamical processgoverning the rule selection at each step. We show that the introducedmodification significantly alters the behaviour of the game. We alsodemonstrate that the choice of the synchronization policy can be used tocontrol the trade-off between the stability and the growth in the system.

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