Asynchronous cellular automata

Nazim A. Fatès (1)

1 MOCQUA - Designing the Future of Computational Models

This text is intended as an introduction to the topic of asynchronous cellular automata. We start from the simple example of the Game of Life and examine what happens to this model when it is made asynchronous (Sec. 1). We then formulate our definitions and objectives to give a mathematical description of our topic (Sec. 2). Our journey starts with the examination of the shift rule with fully asynchronous updating and from this simple example, we will progressively explore more and more rules and gain insights on the behaviour of the simplest rules (Sec. 3). As we will meet some obstacles in having a full analytical description of the asynchronous behaviour of these rules, we will turn our attention to the descriptions offered by statistical physics, and more specifically to the phase transition phenomena that occur in a wide range of rules (Sec. 4). To finish this journey, we will discuss the various problems linked to the question of asynchrony (Sec. 5) and present some openings for the readers who wish to go further (Sec. 6).

Domaines: Automates cellulaires et gaz sur réseau [nlin.CG]

Nazim A. Fatès. Asynchronous cellular automata. Robert Meyers. Encyclopedia of Complexity and Systems Science, Springer, pp.21, 2018, 978-3-642-27737-5. ⟨10.1007/978-3-642-27737-5_671-1⟩. ⟨hal-01653675⟩