Critical properties of cellular automata with evolving network topologies

Abstract

Cellular automata (CAs) in their original form are laid out on regular structures such as rings or lattices. An unsophisticated evolutionary algorithm applied to the underlying structure of the CA's connectivity is capable to significantly improve its performance solving non-trivial tasks. In this work, we study the network properties that emerge in CAs with evolving topology for the density classification problem. We compare a simple rewiring mutation operator to a more sophisticated one that allows an increase in connectivity. We also analyze the effect of initial structure in the CAs before evolution, working over the entire spectrum of regular, irregular, and random networks. We conclude that, unsurprisingly, an increase in connectivity is the driver of fitness. This also result in an increase in the clustering coefficient, and decrease in assortativity. However, our study shows that artificial evolution can also achieve high fitness in CAs with constant degree by creating shortcuts through the network, lowing the characteristic path length, and keeping the assortativity and clustering coefficient constant.