Network mobile automata

The analog of a mobile automaton can be defined for networks by setting up a single active node, then having rules which replace clusters of nodes around this active node, and move its position. The pictures below show two simple examples.

The total number of replacements that can be used in the rules of a network mobile automaton and which involve clusters with up to four nodes and have from 1 to 4 dangling connections is {14, 10, 2727, 781}. Despite looking at several hundred thousand cases I have not been able to find network mobile automata with especially complicated behavior.

Note that by having a cluster of nodes with a unique form it is possible to emulate a network mobile automaton using an ordinary network substitution system.