Chapter 9: Fundamental Physics

Section 12: Evolution of Networks

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.

Network mobile automata image 1

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.

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]