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The Complexity of Sequences Generated by the Arc-Fractal System

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  • Hoai Nguyen Huynh
  • Andri Pradana
  • Lock Yue Chew

Abstract

We study properties of the symbolic sequences extracted from the fractals generated by the arc-fractal system introduced earlier by Huynh and Chew. The sequences consist of only a few symbols yet possess several nontrivial properties. First using an operator approach, we show that the sequences are not periodic, even though they are constructed from very simple rules. Second by employing the ϵ-machine approach developed by Crutchfield and Young, we measure the complexity and randomness of the sequences and show that they are indeed complex, i.e. neither periodic nor random, with the value of complexity measure being significant as compared to the known example of logistic map at the edge of chaos. The complexity and randomness of the sequences are then discussed in relation with the properties of associated fractal objects, such as their fractal dimension, symmetry and orientations of the arcs.

Suggested Citation

  • Hoai Nguyen Huynh & Andri Pradana & Lock Yue Chew, 2015. "The Complexity of Sequences Generated by the Arc-Fractal System," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-21, February.
    • Handle: RePEc:plo:pone00:0117365
    DOI: 10.1371/journal.pone.0117365
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    References listed on IDEAS

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    1. 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.
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