Typical cellular automaton rules have a predefined pattern of connectivity between cells, as well as a specific orientation of those cells implied in the way they are constructed. Therefore, a one-dimensional rule would have little use operating in three dimensional space, and if there were no way to ascertain any sense of direction in this space, then it could do even less.

This poster presents a more general cellular automaton rule setup that allows an arbitrary number of neighbors with no set orientation. In this way, any network topology can be preconstructed for use with any one of these cellular automaton rules. A set of sample networks was chosen, and an enumeration of a set of "elementary" network cellular automaton rules was made for each of them.

Network cellular automata seem to have wide applicability due to the
broad range of different network topologies they can run on.