Sandpile

Any square holding four grains or more gives one away to each of its four neighbours, and that is the whole rule. Drop a million grains on one square, watch the toppling spread outwards, then zoom in on the straight edges and the triangles nobody put there.

Board, pace and image size
Board

A pile of n grains settles into a disc of radius about the square root of n over six and a half, so the board has to be wider than that or the edges eat the picture. Grains that fall off the edge are gone, which is what stops the board filling up.

Pace

A round topples every unstable square at once. The order never matters, which is the abelian part of the name, so a round is a legal shortcut for toppling them one at a time and lands on the same picture.

Saved image

Written from the grid rather than off the screen, so every square lands on a whole number of pixels and no edge is blurred.

Drag on the picture to drop grains where you point · scroll or pinch to zoom, two fingers to pan · F for fullscreen