Complexity-entropy causality plane as a complexity measure for two-dimensional patterns |
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Authors: | Haroldo V Ribeiro Luciano Zunino Ervin K Lenzi Perseu A Santoro Renio S Mendes |
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Institution: | Departamento de Física and National Institute of Science and Technology for Complex Systems, Universidade Estadual de Maringá, Maringá, Brazil. |
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Abstract: | Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to Formula: see text] fractal landscapes generated numerically where we compare our measures with the Hurst exponent; Formula: see text] liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; Formula: see text] 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; Formula: see text] and Ising surfaces where our method identified the critical temperature and also proved to be stable. |
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