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Computing properties of the set of precursors of a given configuration is acommon problem underlying many important questions about cellular automata.Unfortunately, such computations quickly become intractable in dimensiongreater than one. This paper presents an algorithm --- incremental aggregation--- that can compute aggregate properties of the set of precursorsexponentially faster than na{\"i}ve approaches. The incremental aggregationalgorithm is demonstrated on two problems from the two-dimensional binary Gameof Life cellular automaton: precursor count distributions and higher-order meanfield theory coefficients. In both cases, incremental aggregation allows us toobtain new results that were previously beyond reach.

Computing Aggregate Properties of Preimages for 2D Cellular Automata