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.