On the Dynamics of Cellular Automata with Memory

Elementary cellular automata ECA are linear arrays of finite-state machines cells which take binary states, and update their states simultaneously depending on states of their closest neighbours. We design and study ECA with memory ECAM, where every cell remembers its states during some fixed period of evolution. We characterize complexity of ECAM in a case study of rule 126, and then provide detailed behavioural classification of ECAM. We show that by enriching ECA with memory we can achieve transitions between the classes of behavioural complexity. We also show that memory helps to 'discover' hidden information and behaviour on trivial uniform, periodic, and non-trivial chaotic, complex dynamical systems.

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