The authors 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 {l_brace}1,...,n{r_brace} where each vertex has a binary state, (b) functions F{sub i}:F{sub 2}{sup n} {r_arrow} F{sub 2}{sup n} and (c) an update ordering {pi}. The functions F{sub i} 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. They derive a decomposition result, characterize invertible SDS and study fixed points. In particular they analyze how many different SDS that can be obtained by reordering a given multiset of update functions and give a criterion for when one can derive concentration results on this number. Finally, some specific SDS are investigated
