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Sandpile toppling on Penrose tilings: identity and isotropic dynamics

We present experiments of sandpiles on grids (square, triangular, hexagonal) and Penrose tilings. The challenging part is to program such simulator; and our javacript code is available online, ready to play! We first present some identity elements of the sandpile group on these aperiodic structures, and then study the stabilization of the maximum stable configuration plus the identity, which lets a surprising circular shape appear. Roundness measurements reveal that the shapes are not approaching perfect circles, though they are close to be. We compare numerically this almost isotropic dynamical phenomenon on various tilings.

preprint2020arXivOpen access
Jérémy FersulaCamille NoûsKévin Perrot
nlin.CG
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Open access3 authors1 topic
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
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Jérémy FersulaCamille NoûsKévin Perrot

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