Computing Aggregate Properties of Preimages for 2D Cellular Automata
Cellular Automata and Lattice Gases
2017-12-01 v1
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 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.
Keywords
Cite
@article{arxiv.1711.04563,
title = {Computing Aggregate Properties of Preimages for 2D Cellular Automata},
author = {Randall D. Beer},
journal= {arXiv preprint arXiv:1711.04563},
year = {2017}
}