A theory of intrinsic simulations and universality for families of automata networks is developed and a short proof that the family of networks were each node obeys the rule of the ’game of life’ cellular automaton is strongly universal is given.Expand

The maximum rank and the maximum periodic rank of a finite dynamical system with a given interaction graph over any non-Boolean alphabet are determined and it is proved that the average rank is relatively close (as the size of the alphabet is large) to the maximum.Expand

It is shown that the minimum rank decreases with the alphabet size, thus yielding the definition of an absolute minimum rank, and lower and upper bounds on thisabsolute minimum rank are obtained.Expand

Graph-Grammars and Their Application to Computer Science and Biology

1978

TLDR

It can be shown that a cellular d-graph automaton can measure various properties of its underlying graph; can detect graph or subgraph isomorphism; and can recognize various basic types of graphs.Expand

To every one-sided one-dimensional cellular automatonF with neighbourhood radiusr we associate its canonical factor defined by considering only the firstr coordinates of all the images of points… Expand

It is shown that there exists a right-expansive reversible cellular automaton that has a non-sofic trace and thus does not have the pseudo-orbit tracing property.Expand