Spatial and temporal ordering of events in discrete time cellular automata — An overview

Spatial processes are particularly suitable to being modelled by cellular automata. Ruxton (1996) showed the importance of the ordering of events in simple automata. Each cell within the array could be occupied by one entity (individual or population) or empty, and was subject to two events, a probability of extinction and a probability of colonising a neighbouring empty cell. Four orderings of these events were considered: (a) extinction was considered in numerical order within the array, and then colonisation was considered in the same order; (b) extinction was considered randomly without replacement, and then colonisation was considered randomly; (c) all events were considered in a random order without replacement, thus extinction and colonisation were considered to occur interdependently; (d) a similar number of events were considered randomly with replacement, so the location and type of event was random thus permitting each cell to be considered for more or less than one event of each type. The choice of ordering method used in the simulation had dramatic effects on the outcome, with more