Cellular automata over generalized Cayley graphs
It is well-known that cellular automata can be characterized as the set of translation-invariant
continuous functions over a compact metric space; this point of view makes it easy to extend …
continuous functions over a compact metric space; this point of view makes it easy to extend …
Reversibility vs Local Creation/Destruction
Consider a network that evolves reversibly, according to nearest neighbours interactions.
Can its dynamics create/destroy nodes? On the one hand, since the nodes are the principal …
Can its dynamics create/destroy nodes? On the one hand, since the nodes are the principal …
Generalized Cayley graphs and cellular automata over them
Cayley graphs have a number of useful features: the ability to graphically represent finitely
generated group elements and their relations; to name all vertices relative to a point; and the …
generated group elements and their relations; to name all vertices relative to a point; and the …
An intrinsically universal family of causal graph dynamics
Abstract Causal Graph Dynamics generalize Cellular Automata, extending them to bounded
degree, time varying graphs. The dynamics rewrites the graph in discrete time-steps, with …
degree, time varying graphs. The dynamics rewrites the graph in discrete time-steps, with …
Universality of causal graph dynamics
Causal Graph Dynamics generalize Cellular Automata, extending them to bounded degree,
time varying graphs. The dynamics rewrite the graph at each time step with respect to two …
time varying graphs. The dynamics rewrite the graph at each time step with respect to two …