An experimental study of noise and asynchrony in elementary cellular automata with sampling compensation

This article focuses on the set of 32 legal elementary cellular automata (ECA). We perform an exhaustive study of the systems’ response under: (i) α-asynchronous dynamics, from full asynchronism to perfect synchrony, (ii) κ-scaling, which extends α-asynchrony to compensate for less cell activity, and (iii) ϕ-noise scheme, a perturbation that affects the local transition function and causes a cell to probabilistically 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 ECA according to the degree of behavioural modification, and we show that our classifying scheme provides results coherent with the density-based classification. We also show that κ-scaling provides results comparable to synchronous systems, both quantitatively and qualitatively. Subsequently, we analyse the effects of including different levels of noise in synchronous systems. We identify different responses to noise, including systems that are robust to asynchrony and susceptible to noise. To conclude, we investigate the behavioural changes caused by simultaneous asynchrony and noise in models tolerant to both perturbations. We describe a number of effects caused by the interplay of noise and asynchrony, thus further reinforcing that both aspects are pertinent for future studies.