Classifying Asynchronous Elementary Cellular Automata with the 0–1 Test for Chaos

We investigate the effect of asynchronous updating on the dynamical behavior of elementary cellular automata (ECA) by means of the 0–1 test for chaos. While the classical theory of cellular automata is based on synchronous evolution, many natural systems are inherently asynchronous. It is therefore interesting to understand how asynchrony affects their qualitative dynamics, in particular whether it induces transitions from chaotic to regular behavior or vice versa. We adopt the experimental framework introduced in [6] and extend it to fully asynchronous ECA (AECA): for each rule, we compute the 0–1 test statistic and compare the resulting classification with both its synchronous counterpart and Wolfram’s empirical classification [8]. Our results show that asynchronous updating can significantly alter the dynamical behavior of cellular automata. In particular, several rules that are regular in the synchronous setting exhibit chaotic behavior under asynchronous updates, while some chaotic rules become regular.