Robustness of Elementary Cellular Automata to Asynchronous Transitions and Communications

The robustness of elementary cellular automata (ECAs) in response to asynchronous updating of cells has been extensively studied by Fates et al. In this paper, we introduce a further level of asynchronism into the ECAs, by which each cell not only takes a probability to undergo state transitions at every time step, but also may communicate with its neighboring cells independently in a random order. Though asynchronous communication may affect distinct dynamics to emerge from any specific ECA model, numerical experiments demonstrate that the whole class of ECAs tend to exhibit robustness to both asynchronous communication and asynchronous transitions that is remarkably similar to the observations of Fates et al.