Any Shape Can Ultimately Cross Information on Two-Dimensional Abelian Sandpile Models

Abstract : We study the abelian sandpile model on the two-dimensional grid with uniform neighborhood (a number-conserving cellular automata), and prove that any family of discrete neighborhoods defined as scalings of a continuous non-flat shape can ultimately perform crossing.
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Viet-Ha Nguyen, Kévin Perrot. Any Shape Can Ultimately Cross Information on Two-Dimensional Abelian Sandpile Models. 24th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2018, Ghent, Belgium. pp.127-142, ⟨10.1007/978-3-319-92675-9_10⟩. ⟨hal-01824872⟩

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