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Dynamic fractals in spatial evolutionary games

Author

Listed:
  • Kolotev, Sergei
  • Malyutin, Aleksandr
  • Burovski, Evgeni
  • Krashakov, Sergei
  • Shchur, Lev

Abstract

We investigate critical properties of a spatial evolutionary game based on the Prisoner’s Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue that the cluster boundary is a random fractal. Our simulations are consistent with the fractal dimension of the boundary being equal to 2, and the cluster boundaries are hence asymptotically space filling as the system size increases.

Suggested Citation

  • Kolotev, Sergei & Malyutin, Aleksandr & Burovski, Evgeni & Krashakov, Sergei & Shchur, Lev, 2018. "Dynamic fractals in spatial evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 142-147.
    • Handle: RePEc:eee:phsmap:v:499:y:2018:i:c:p:142-147
    DOI: 10.1016/j.physa.2018.02.007
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    References listed on IDEAS

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    1. Adler, Joan, 1991. "Bootstrap percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 171(3), pages 453-470.
    2. Shiguo Jiang & Desheng Liu, 2012. "Box-Counting Dimension of Fractal Urban Form: Stability Issues and Measurement Design," International Journal of Artificial Life Research (IJALR), IGI Global, vol. 3(3), pages 41-63, July.
    3. Dirk Helbing, 2013. "Globally networked risks and how to respond," Nature, Nature, vol. 497(7447), pages 51-59, May.
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