Beautiful Abelian Sandpiles
I can't remember where I first saw them, but ever since, I have been unable to forget them: abelian sandpiles. I'm far from the only one. They're remarkably simple, yet produce lovely symmetric patterns. I loved them so much that I adorned the title banner of this blog with an animation of an abelian sandpile. But what exactly are abelian sandpiles? How do they work? And how many pretty, mesmerizing pictures can we make with these things?