Structural information in two-dimensional patterns: entropy convergence and excess entropy.
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.
Feldman
David P
DP
College of the Atlantic, Bar Harbor, Maine 04609, USA. dpf@santefe.edu
Crutchfield
James P
JP