Complexity of two-dimensional patterns

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Andrienko, Y.A., Brilliantov, N.V., Kurths, J.: Complexity of two-dimensional patterns. Eur. Phys. J. B 15(3), 539–546 (2000)



To describe quantitatively the complexity of two-dimensional patterns we introduce a complexity measure based on a mean information gain. Two types of patterns are studied: geometric ornaments and patterns arising in random sequential adsorption of discs on a plane (RSA). For the geometric ornaments analytical expressions for entropy and complexity measures are presented, while for the RSA patterns these are calculated numerically. We compare the information-gain complexity measure with some alternative measures and show advantages of the former one, as applied to two-dimensional structures. Namely, this does not require knowledge of the “maximal” entropy of the pattern, and at the same time sensitively accounts for the inherent correlations in the system.

Extended Abstract


author="Andrienko, Yu.A. and Brilliantov, N.V. and Kurths, J.",
title="Complexity of two-dimensional patterns",
journal="The European Physical Journal B - Condensed Matter and Complex Systems",
url=" "

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