Complexity of two-dimensional patterns
Moscow State University, Physics Department, Moscow 119899, Russia
2 Physics Department, University Potsdam, Am Neuen Palais, 14415 Potsdam, Germany
Published online: 15 June 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.
PACS: 05.20.-y – Classical statistical mechanics / 05.90.+m – Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000