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Updated: Feb 17, 2026

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Published on: October 14, 2021
Computing aggregate properties of preimages for 2D cellular automata
1Cognitive Science Program, Indiana University, Bloomington, Indiana 47406, USA.
Abstract:
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 naïve 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.
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