A Study of Stochastic Noise and Asynchronism in Elementary Cellular Automata

This work focuses on the set of 32 legal Elementary Cellular Automata. We perform an exhaustive study of the systems’ response under: (i) α-asynchronous dynamics, from full asynchronism to perfect synchrony; (ii) φ-noise scheme, a perturbation that causes a cell to miscalculate the new state when it is updated. We propose a new classification in three classes under asynchronous conditions: α-invariant, α-robust and α-dependent. We classify the 32 legal automata according to the degree of behavioural modification. We demonstrate that, in the α-dependent class, asynchrony behaves as a form of noise in timing. We identify models tolerant to both noise and asynchrony. While the majority of the α-invariant class is robust to noise, a subset is not able to recover its original behaviour.