This is oddly satisfying.https://observablehq.com/@mbostock/abelian-sandpile …
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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