The sandpile identity element on an ellipse
Analysis of PDEs
2023-07-04 v2 Cellular Automata and Lattice Gases
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.
Cite
@article{arxiv.2007.05792,
title = {The sandpile identity element on an ellipse},
author = {Andrew Melchionna},
journal= {arXiv preprint arXiv:2007.05792},
year = {2023}
}