Classifying 1D elementary cellular automata with the 0–1 test for chaos
Mohammed Terry-Jack, Simon O’Keefe · Physica D Nonlinear Phenomena · 2023
We utilise the 0–1 test to automatically classify elementary cellular automata. The quantitative results of the 0–1 test reveal a number of advantages over Wolfram’s qualitative classification. For instance, while almost all rules classified as chaotic by Wolfram were confirmed as such by the 0–1 test, there were two rules which were revealed to be non-chaotic. However, their periodic nature is hidden by the high complexity of their spacetime patterns and not easy to see without looking very carefully. Comparing each rule’s chaoticity (as quantified by the 0–1 test) against its intrinsic complexity (as quantified by its Chua complexity index) also reveals a number of counter-intuitive discoveries; i.e. non-chaotic dynamics are not only found in simpler rules, but also in rules as complex as chaos.