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Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns

Author

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  • Haroldo V Ribeiro
  • Luciano Zunino
  • Ervin K Lenzi
  • Perseu A Santoro
  • Renio S Mendes

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 fractal landscapes generated numerically where we compare our measures with the Hurst exponent; liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; and Ising surfaces where our method identified the critical temperature and also proved to be stable.

Suggested Citation

  • Haroldo V Ribeiro & Luciano Zunino & Ervin K Lenzi & Perseu A Santoro & Renio S Mendes, 2012. "Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns," PLOS ONE, Public Library of Science, vol. 7(8), pages 1-9, August.
    • Handle: RePEc:plo:pone00:0040689
    DOI: 10.1371/journal.pone.0040689
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    Cited by:

    1. Zhang, Boyi & Shang, Pengjian & Zhou, Qin, 2021. "The identification of fractional order systems by multiscale multivariate analysis," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Zunino, Luciano & Ribeiro, Haroldo V., 2016. "Discriminating image textures with the multiscale two-dimensional complexity-entropy causality plane," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 679-688.
    3. Carlos F Alvarez & Luis E Palafox & Leocundo Aguilar & Mauricio A Sanchez & Luis G Martinez, 2016. "Using Link Disconnection Entropy Disorder to Detect Fast Moving Nodes in MANETs," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-15, May.
    4. Boaretto, Bruno R.R. & Budzinski, Roberto C. & Rossi, Kalel L. & Masoller, Cristina & Macau, Elbert E.N., 2023. "Spatial permutation entropy distinguishes resting brain states," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    5. Jauregui, M. & Zunino, L. & Lenzi, E.K. & Mendes, R.S. & Ribeiro, H.V., 2018. "Characterization of time series via Rényi complexity–entropy curves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 498(C), pages 74-85.
    6. Liu, Zhengli & Shang, Pengjian & Wang, Yuanyuan, 2020. "Characterization of time series through information quantifiers," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    7. Wang, Zhuo & Shang, Pengjian, 2021. "Generalized entropy plane based on multiscale weighted multivariate dispersion entropy for financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Pessa, Arthur A.B. & Zola, Rafael S. & Perc, Matjaž & Ribeiro, Haroldo V., 2022. "Determining liquid crystal properties with ordinal networks and machine learning," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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