We uploaded a bunch of additional videos, including the first video showing fifth-order harmonic sandpile identity dynamics. The other videos mainly show the sandpile dynamics for lower order harmonics when starting with some interesting fractal patterns found in the videos of certain harmonics.
Harmonic sandpile dynamics:
Moritz Lang and Mikhail Shkolnikov (2019).
Harmonic dynamics of the abelian sandpile.
Proceedings of the National Academy of Sciences (online first). DOI: 10.1073/pnas.1812015116
Sandpile monomorphisms:
Moritz Lang and Mikhail Shkolnikov (2019).
Sandpile monomorphisms and harmonic functions.
ArXiv preprint arXiv:1904.12209.
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