This is oddly satisfying.https://observablehq.com/@mbostock/abelian-sandpile …
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Here’s the WebGL version at much higher resolution.https://observablehq.com/@mbostock/abelian-sandpile/2 …
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Replying to @mbostock
it's interesting that growth appears to slow down, though the radius is probably increasing linearly like here - https://t.d3fc.io/status/707687796199309313 … - maybe we expect growth to appear as if some physical object was approaching us with a fixed speed
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In fact, Pegden and Smart proved in 2013 that the radius grows like the _square root_ of the number of added grains (radius scales like 1/d in d dimensions): https://arxiv.org/abs/1105.0111 I learned this from this paper by Levine and Pereshttp://www.ams.org/journals/bull/2017-54-03/S0273-0979-2017-01573-X/ …
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This makes sense intuitively if you think of the grains as ending up spread out uniformly in a disk - proving it to be so is another matter though!
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