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Published on: June 27, 2013
Structural information in two-dimensional patterns: entropy convergence and excess entropy
David P Feldman1, James P Crutchfield
1College of the Atlantic, Bar Harbor, Maine 04609, USA. dpf@santefe.edu
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.
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