Cellular Automata Transforms

Consider a three-site neighborhood, dual-state, one-dimensional CA. The state of each cell is given by the Boolean variable a. When the state is on, a=1. Otherwise it is off and a=0. The quantity a it represents the state (Boolean) of the i-th cell, at discrete time t, whose two neighbors are in the following states: a i-1t,ai+1t . In general, we seek a rule that will be used to synchronously calculate the state a it+1 from the state of the cells in the neighborhood at the t-th time level (Figure 2.1).

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