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Spatial Complexity Measure for Characterising Cellular Automata Generated 2D Patterns

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Progress in Artificial Intelligence (EPIA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9273))

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Abstract

Cellular automata (CA) are known for their capacity to generate complex patterns through the local interaction of rules. Often the generated patterns, especially with multi-state two-dimensional CA, can exhibit interesting emergent behaviour. This paper addresses quantitative evaluation of spatial characteristics of CA generated patterns. It is suggested that the structural characteristics of two-dimensional (2D) CA patterns can be measured using mean information gain. This information-theoretic quantity, also known as conditional entropy, takes into account conditional and joint probabilities of cell states in a 2D plane. The effectiveness of the measure is shown in a series of experiments for multi-state 2D patterns generated by CA. The results of the experiments show that the measure is capable of distinguishing the structural characteristics including symmetry and randomness of 2D CA patterns.

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Authors and Affiliations

  1. Department of Computing Goldsmiths, University of London, London, SE14 6NW, UK

    Mohammad Ali Javaheri Javid, Tim Blackwell, Robert Zimmer & Mohammad Majid Al-Rifaie

Authors
  1. Mohammad Ali Javaheri Javid
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  2. Tim Blackwell
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  3. Robert Zimmer
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  4. Mohammad Majid Al-Rifaie
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Corresponding author

Correspondence to Mohammad Ali Javaheri Javid .

Editor information

Editors and Affiliations

  1. ISEC - Coimbra Institute of Engineering, Polytechnic Institute of Coimbra, Coimbra, Portugal

    Francisco Pereira

  2. CIUSC, Department of Informatics Engineering, University of Coimbra, Coimbra, Portugal

    Penousal Machado

  3. CIUSC, Department of Informatics Engineering, University of Coimbra, Coimbra, Portugal

    Ernesto Costa

  4. CIUSC, Department of Informatics Engineering, University of Coimbra, Coimbra, Portugal

    Amílcar Cardoso

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Javaheri Javid, M.A., Blackwell, T., Zimmer, R., Al-Rifaie, M.M. (2015). Spatial Complexity Measure for Characterising Cellular Automata Generated 2D Patterns . In: Pereira, F., Machado, P., Costa, E., Cardoso, A. (eds) Progress in Artificial Intelligence. EPIA 2015. Lecture Notes in Computer Science(), vol 9273. Springer, Cham. https://doi.org/10.1007/978-3-319-23485-4_21

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  • DOI: https://doi.org/10.1007/978-3-319-23485-4_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23484-7

  • Online ISBN: 978-3-319-23485-4

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