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arXiv · 2007.05792

The sandpile identity element on an ellipse

Andrew Melchionna
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Abstract

We consider certain elliptical subsets of the square lattice. The recurrent representative of the identity element of the sandpile group on this graph consists predominantly of a biperiodic pattern, along with some noise. We show that as the lattice spacing tends to 0, the fraction of the area taken up by the pattern in the identity element tends to 1.

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Andrew Melchionna. 2020-07-11. The sandpile identity element on an ellipse. https://arxiv.org/abs/2007.05792

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