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We show techniques of analyzing complex dynamics of cellular automata (CA)with chaotic behaviour. CA are well known computational substrates for studyingemergent collective behaviour, complexity, randomness and interaction betweenorder and chaotic systems. A number of attempts have been made to classify CAfunctions on their space-time dynamics and to predict behaviour of any givenfunction. Examples include mechanical computation, \lambda{} and Z-parameters,mean field theory, differential equations and number conserving features. Weaim to classify CA based on their behaviour when they act in a historical mode,i.e. as CA with memory. We demonstrate that cell-state transition rulesenriched with memory quickly transform a chaotic system converging to a complexglobal behaviour from almost any initial condition. Thus just in few steps wecan select chaotic rules without exhaustive computational experiments orrecurring to additional parameters. We provide analysis of well-known chaoticfunctions in one-dimensional CA, and decompose dynamics of the automata usingmajority memory exploring glider dynamics and reactions.

Complex dynamics of elementary cellular automata emerging from chaotic rules