Abstract

We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies. We show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension. We compare and contrast entropy-convergence with mutual-information and structure-factor techniques for quantifying and detecting spatial structure.

Citation

D. P. Feldman and J. P. Crutchfield Structural Information in Two-Dimensional Patterns:
Entropy Convergence and Excess Entropy. Physical Review E 67 (2003) 051104.
Santa Fe Institute Working Paper 02-12-065. arXiv.org/abs/cond-mat/0212078.

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