A Quantitative Approach for Detecting Symmetries and Complexity in 2D Plane

  • Mohammad Ali Javaheri JavidEmail author
  • Robert Zimmer
  • Anna Ursyn
  • Mohammad Majid al-Rifaie
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9477)


Aesthetic evaluation of computer generated patterns is a growing filed with several challenges. This paper focuses on the quantitative evaluation of order and complexity in multi-state two-dimensional (2D) cellular automata (CA). CA are known for their ability to generate highly complex patterns through simple and well defined local interaction of rules. It is suggested that the order and complexity of 2D patterns can be quantified by using mean information gain. This measure, also known as conditional entropy, takes into account conditional and joint probabilities of the elements of a configuration in a 2D plane. A series of experiments is designed to demonstrate the effectiveness of the mean information gain in quantifying the structural order and complexity, including the orientation of symmetries of multi-state 2D CA configurations.


Symmetry Complexity Entropy Information gain  Cellular automata 2D patterns 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mohammad Ali Javaheri Javid
    • 1
    Email author
  • Robert Zimmer
    • 1
  • Anna Ursyn
    • 2
  • Mohammad Majid al-Rifaie
    • 1
  1. 1.Department of ComputingGoldsmiths, University of LondonLondonUK
  2. 2.School of Art & DesignUniversity of Northern ColoradoGreeleyUSA

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