How full does the pile get before losses at the edges balance the grains being added? Toppling patches show near-white against the indigo-to-amber grain colors (amber is 3 grains), and an avalanche spreads as a white front, one patch per tick.
Try this Set drop-mode to random and grains-per-tick to 5 (both are read every tick). The pile fills five times faster, but mean-grains doesn't stop at 2.13 as it does with one grain per tick. It climbs to about 2.36 with some 1,700 patches toppling at once, because grains arrive faster than avalanches can carry them out.
About this model Where it ends up
The sandpile of Bak, Tang and Wiesenfeld (1987), the first model of self-organized criticality. A pile that gains grains slowly and loses them at its edges settles, with no parameter tuned, at a density where one grain can set off an avalanche of any size. This version shows the pile filling and the avalanches spreading; it does not measure their sizes.
Setup gives every patch 0 to 3 grains at random. Each tick, grains-per-tick grains land on the center patch (or on a random patch when drop-mode is random), every patch holding 4 or more is marked toppling, and then all toppling patches fire at once, each losing 4 grains and giving 1 to each of its 4 neighbors. Grains pushed past the edge of the 97 × 97 box are lost. A patch with 8 or more grains still fires only once per tick. Both params are read every tick.
The main difference from the BTW model: there, the next grain is added only after the pile has stopped toppling. Here a grain lands every tick and each tick runs one round of toppling, so once the pile is full several avalanches are always in progress and toppling-now never returns to 0. Nothing records avalanche sizes, so their size distribution, the headline result of the BTW paper, is not shown here.
