The famous Sandpile model was originally developed by Per Bak and then generalized to the Bak-Tang-Wiesenfeld model, now apparently called the Abelian sandpile model. (I say apparently because I haven't followed it in a long time.)

Here are two article about it: http://www.natureincode.com/code/various/sandpile.html and https://www.scientificamerican.com/article/sand-pile-model-of-the-mind-grows-in-popularity/.

NetLogo has a version of the model under Chemistry and Physics. 

Sandpiles illustrate what Bak called self-organized criticality as well as power laws. 

Try running the NetLogo version with setup-uniform, grains-per-patch set to 3 (i.e. start with maximal sand), and drop location set to center.