# Apollonian structure in the Abelian sandpile

@article{Levine2012ApollonianSI,
title={Apollonian structure in the Abelian sandpile},
author={Lionel Levine and Wesley Pegden and Charles K. Smart},
journal={Geometric and Functional Analysis},
year={2012},
volume={26},
pages={306-336}
}
• Published 23 August 2012
• Geology
• Geometric and Functional Analysis
The Abelian sandpile process evolves configurations of chips on the integer lattice by toppling any vertex with at least 4 chips, distributing one of its chips to each of its 4 neighbors. When begun from a large stack of chips, the terminal state of the sandpile has a curious fractal structure which has remained unexplained. Using a characterization of the quadratic growths attainable by integer-superharmonic functions, we prove that the sandpile PDE recently shown to characterize the scaling…
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