Parameter characterization of two-dimensional cellular automata rule space

Cellular automata (CA) are discrete dynamical systems formed by a great number of identical and simple components, with local connectivity. It has been proved that the problem of forecasting the dynamical behavior of CA is undecidable. Based upon parameterizations of CA rule space, several approximations have been investigated. The majority of these studies are focused on the one-dimensional CA. The present work generalizes for the two-dimensional space the definition of three parameters previously published in the one-dimensional context: sensitivity, neighborhood dominance and activity propagation. As an example of the application of such generalized parameters some simulations about the computational task known as the density classification task are reported.