Cellular automata and self-organisation phenomena

Cellular automata are dynamical systems for which time and space are discrete. They are used to model the evolution of a set of components, the cells , that interact locally with each other: over time, each cell updates its state according to what it perceives in its neighbourhood. Some cellular automata exhibit a self-organisation behaviour: from an initial disordered state, successive updates of the cells by the local rule lead to the emergence of a macroscopic structure. Conversely, given a desired global behaviour, we can ask ourselves which local rules allow to achieve this collective behavior, in a decentralised way. In this article, we will address several such inverse problems (synchronisation, density classification, self-correction of tilings), and study the influence that the introduction of randomness can have on the dynamics.