Artificial Life VI


Edges and Computation in Excitable Media

Andrew Adamatzky
Research Associate
www.uwe.ac.uk

Owen Holland
Reader in Electronics
www.uwe.ac.uk


Abstract

Using two-dimensional cellular automata with an 8-cell neighbourhood and a ternary cell state set, we have described all possible transition rules for a class of simple lattice-based excitable media, and have carried out an exhaustive investigation of the spatio-temporal dynamics of excitation in such lattices. We have subdivided the 256 possible rules of local excitation into 11 classes as a function of morphological characteristics of the resultant excitation configurations far beyond the transient period. Spatial factors (number and size diversity of clusters of excited states) and dynamic characteristics (length of transient period and activity level) were also examined. We present a parametrisation of the function space according to a measure equivalent to Langton's lambda parameter, and offer a classification of the morphological characteristics and potential computational capabilities as a function of lambda. For much of the function space, the values of lambda are in accordance with Langton's predictions; in particular, some identifiable computational capabilities are located at the boundaries between order and disorder.


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