Complex dynamics of cellular automata emerging in chaotic rules
Martinez, G. J. , Adamatzky, A. and Alonso-Sanz, R. (2009) Complex dynamics of cellular automata emerging in chaotic rules. In: The 3rd International Conference on Complex Systems and Applications, Le Havré University, Normandy, France, 29th June - 1st July, 2009.
Publisher's URL: http://litis.univ-lehavre.fr/~bertelle/iccsa2009/i...
We show novel techniques of analysing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order and disorder. A number of attempts have been made to classify CA functions on their spatio-temporal dynamics and to predict behaviour of any given function. Examples include mechanical computation, $\lambda$ and $Z$-parameters, mean field theory, differential equations and number conserving features. We propose 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 rules enriched with memory quickly transform a chaotic system converging to a complex global behaviour from almost any initial condition. Thus just in few steps we can select chaotic rules without exhaustive computational experiments or recurring to additional parameters. We provide analysis of well-known chaotic functions in one-dimensional CA, and decompose dynamics of the automata using majority memory.
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