Evolutive sandpiles

TL;DR

This paper explores an evolving graph version of the Abelian sandpile model, revealing new phenomena like persistent instability, fractal formations, and power laws, expanding understanding of self-organized critical systems.

Contribution

It introduces a dynamic topology in sandpile models, demonstrating novel behaviors and fractal patterns not seen in classical static graph models.

Findings

Configurations can remain unstable indefinitely on evolving graphs.

Evolutive graphs produce interesting fractal structures.

Power laws are observed in certain evolutive graph configurations.

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 the topology at each stage. This turns out in the occurrence of phenomena impossible in the classical sandpile models. For instance, configurations over evolutive graphs that are always unstable. 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 some power laws associated with some evolutive graphs.