Complex dynamics of elementary cellular automata emerging in chaotic rules

Martinez, G. J., Adamatzky, A. and Alonso-Sanz, R. (2010) Complex dynamics of elementary cellular automata emerging in chaotic rules. International Journal of Bifurcation and Chaos, 22 (2). ISSN 0218-1274

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Publisher's URL: http://dx.doi.org/10.1142/S021812741250023X

Abstract

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 behavior 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 in just a 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.

Item Type:Article
Additional Information:International Journal of Bifurcation and Chaos © 2010 [copyright World Scientific Publishing Company]http://www.worldscinet.com/ijbc/
Uncontrolled Keywords:cellular automata, memory, complex dynamics, chaos, self-organization and filters
Faculty/Department:Faculty of Environment and Technology
ID Code:7881
Deposited By: A. Lawson
Deposited On:02 Jun 2010 15:34
Last Modified:05 Oct 2013 15:26

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