A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

Robustness of Cellular Automata in the Light of Asynchronous Information Transmission

International audienceCellular automata are classically synchronous: all cells are simultaneously updated. However, it has been proved that perturbations in the updating scheme may induce qualitative changes of behaviours. This paper presents a new type of asynchronism, the beta -synchronism, where cells still update at each time step but where the transmission of information between cells is disrupted randomly. We experimentally study the behaviour of beta-synchronous models. We observe that, although many eff ects are similar to the perturbation of the update, novel phenomena occur. We particularly study phase transitions as an illustration of a qualitative variation of behaviour triggered by continuous change of the disruption probability beta

Probing robustness of cellular automata through variations of asynchronous updating

International audienceTypically viewed as a deterministic model of spatial computing, cellular automata are here considered as a collective system subject to the noise inherent to natural computing. The classical updating scheme is replaced by stochastic versions which either randomly update cells or disrupt the cell-to-cell transmission of information. We then use the novel updating schemes to probe the behaviour of Elementary Cellular Automata, and observe a wide variety of results. We study these behaviours in the scope of macroscopic statistical phenomena and microscopic analysis. Finally, we discuss the possibility to use updating schemes to probe the robustness of complex systems

Coalescence in fully asynchronous elementary cellular automata

International audienceCellular automata (CA) are discrete mathematical systems formed by a set of cells arranged in a regular fashion. Each of these cells is in a particular state and evolves according to a local rule depending on the state of the cells in its neighbourhood. In spite of their apparent simplicity, these dynamical systems are able to display a complex emerging behaviour, and the macroscopic structures they produce are not always predictable despite complete local knowledge. While studying the robustness of CA to the introduction of asynchronism in their updating scheme, a phenomenon called coalescence was observed for the first time: for some asynchronous CA, the application of the same local rule on any two di↵erent initial conditions following the same sequence of updates quickly led to the same non-trivial configuration. Afterwards, it was experimentally found that some CA would always coalesce whilst others would never coalesce, and that some of them exhibit a phase transition between a coalescing and non-coalescing behaviour. However, a formal explanation of non-trivial rapid coalescence has yet to be found, and this is the purpose of this project, where we try to characterise and explain this phenomenon both qualitatively and analytically. In particular, we analytically study trivial coalescence, find lower bounds for the coalescence time of ECA 154 and ECA 62, and give some first steps towards finding their upper bounds in order to prove that they have, respectively, quadratic and linear coalescence time

Autômatos celulares com inércia

Resumo: Desde que os autômatos celulares (AC) foram criados, vêm sendo muito utilizados em diversas áreas de conhecimento, pois são sistemas simples e de fácil implementação computacional. Em geral, AC são compostos por redes de células, onde cada célula assume um valor numérico que determina seu estado. O tempo é discreto e o valor do estado de cada célula num tempo posterior depende do valor dos estados de seus vizinhos no tempo anterior. A exata conexão entre estas quantidades é estabelecida por uma regra dinâmica específica (a regra de atualização). Existem milhares de regras distintas para AC. Em nosso trabalho utilizaremos uma regra simples, onde o estado da célula no tempo t + 1 depende da soma dos estados de seus vizinhos no tempo t. Consideramos 3 estados, sendo 2 ativos (+1, -1), que competem dinamicamente, um passivo (zero), que não influencia a regra de mudança. Definimos também um “estado interno”, a inércia, que é um ingrediente novo no AC. Essa inércia (que pode variar de 0 ao número máximo de vizinhos) confere a cada célula uma resistência à mudança de seu estado. Discutimos então, no caso de um AC bidimensional, como a inércia modifica os padrões de evolução e as propriedades dinâmicas do sistema. Estudamos diferentes aspectos do problema, populações das configurações finais, tempos de convergência, dinâmica de invasão, geração de padrões espaciais, dinâmica da competição entre os estado ativos e assim por diante. De forma geral encontramos que a inércia pode alterar de forma bastante significativa a dinâmica e o comportamento médio típico de um mesmo AC