An additive cellular automaton is a cellular automaton whose rule is compatible with an addition of states. Typically, this addition is derived from modular arithmetic. Additive rules allow the evolution for different initial conditions to be computed independently, then the results combined by simply adding. The results for arbitrary starting conditions can therefore be computed very efficiently by convolving the evolution of a single cell with an appropriate convolution kernel (which, in the case of two-color automata, would correspond to the set of initially "active" cells).