Elements of a theory of simulation II: sequential dynamical systems

We study a class of discrete dynamical systems that is motivated by the generic structure of simulations. The systems consist of the following data: (a) a finite graph Y with vertex set 1,…,n where each vertex has a binary state, (b) functions and (c) an update ordering Ï. The functions Fi update the binary state of vertex i as a function of the state of vertex i and its Y-neighbors and leave the states of all other vertices fixed. The update ordering is a permutation of the Y-vertices. By composing the functions Fi in the order given by Ï one obtains the sequential dynamical system (SDS):