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Evolutive sandpiles

Author

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  • Alfaro, Carlos A.
  • Serrano, Juan Pablo
  • Villagrán, Ralihe R.

Abstract

The Abelian sandpile model was the first example of a self-organized critical system studied by Bak, Tang and Wiesenfeld. The dynamics of the sandpiles occur when the grains topple over a graph. In this study, we allow the graph to evolve over time and change its topology at each stage. This turns out in the occurrence of phenomena impossible in the classical sandpile models. For instance, unstable configurations over evolutive graphs with a sink that never stabilize. We also experiment with the stabilization of configurations with a large number of grains at the center over evolutive graphs, this allows us to obtain interesting fractals. Finally, we obtain power laws associated with some evolutive sandpiles.

Suggested Citation

  • Alfaro, Carlos A. & Serrano, Juan Pablo & Villagrán, Ralihe R., 2025. "Evolutive sandpiles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 657(C).
    • Handle: RePEc:eee:phsmap:v:657:y:2025:i:c:s037843712400757x
    DOI: 10.1016/j.physa.2024.130248
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    References listed on IDEAS

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    1. Ostojic, Srdjan, 2003. "Patterns formed by addition of grains to only one site of an abelian sandpile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(1), pages 187-199.
    2. Jeff Alstott & Ed Bullmore & Dietmar Plenz, 2014. "powerlaw: A Python Package for Analysis of Heavy-Tailed Distributions," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-11, January.
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    4. Alan Kirman, 1997. "The economy as an evolving network," Journal of Evolutionary Economics, Springer, vol. 7(4), pages 339-353.
    5. Alfaro, Carlos A. & Valencia, Carlos E. & Vargas, Marcos C., 2023. "Computing sandpile configurations using integer linear programming," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    6. Dhar, Deepak, 1999. "The Abelian sandpile and related models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 4-25.
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