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Emergence on Decreasing Sandpile Models

Abstract : Sand is a proper instance for the study of natural algorithmic phenomena. Idealized square/cubic sand grains moving according to ``simple'' local toppling rules may exhibit surprisingly ``complex'' global behaviors. In this paper we explore the language made by words corresponding to fixed points reached by iterating a toppling rule starting from a finite stack of sand grains in one dimension. Using arguments from linear algebra, we give a constructive proof that for all decreasing sandpile rules the language of fixed points is accepted by a finite (Muller) automaton. The analysis is completed with a combinatorial study of cases where the {\em emergence} of precise regular patterns is formally proven. It extends earlier works, and asks how far can we understand and explain emergence following this track?
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Submitted on : Friday, March 23, 2018 - 12:43:32 PM
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  • HAL Id : halshs-01212069, version 1


Kévin Perrot, Éric Rémila. Emergence on Decreasing Sandpile Models. MFCS 2015 40th International Symposium on Mathematical Foundations of Computer Science, Aug 2015, Milan, Italy. ⟨halshs-01212069⟩



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