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