Spatial Complexity Measure for Characterising Cellular Automata Generated 2D Patterns

  • Mohammad Ali Javaheri JavidEmail author
  • Tim Blackwell
  • Robert Zimmer
  • Mohammad Majid Al-Rifaie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9273)


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.


Cellular automata Spatial complexity 2D patterns 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mohammad Ali Javaheri Javid
    • 1
    Email author
  • Tim Blackwell
    • 1
  • Robert Zimmer
    • 1
  • Mohammad Majid Al-Rifaie
    • 1
  1. 1.Department of Computing GoldsmithsUniversity of LondonLondonUK

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