Evaluating the Influence of Network Structure on Boolean Networks and Cellular Automata

Abstract

While there have been many papers respectively on the qualities of Boolean networks and Cellular Automata, little work has been done on comparing these networks to each other. Network parameters such as input count and choice of Boolean functions are often fixed in preparation of the experiments with less regard to what effect that choice has. In this paper a broader overview of how the choice of network structure and network parameters will affect the behavior of the network is given. Metrics such as iterations until stabilization (intermediary state count) and complexity of network behavior over time (functional complexity) are proposed, and evaluated for a set of 15 different network configurations. CA networks are observed to have much less functional complexity than BN, and in general BN seems to have more potential for complex behavior. It is also observed that for increasing values of dimension count/input count the functional complexity decreases.