The critical sandpile

One falling grain may do nothing at all, or bring down a whole flank of the pile, and there is no telling which in advance. The rule of Bak, Tang and Wiesenfeld from 1987 is almost insultingly simple: any cell holding 4 grains topples, handing one grain to each of its 4 neighbours, and grains falling off the edge are gone for good. Keep dropping grains and the average load per cell settles near 2.1 with nobody tuning it, while avalanche sizes follow a power law: on log-log axes they line up almost straight, so no size counts as typical.

▸ Building the cell grid — each cell counts sand grains…

▸ Loading 1 single rule: cell ≥ 4 grains TOPPLES to 4 neighbours

▸ Grains fall, the system builds up gradually…

▸ One grain can ignite a chain AVALANCHE

▸ The system drives itself to the CRITICAL state (SOC)

▸ Ready — Online. ✅

Observation panel

🏖️ Đống cát

thumbnail of the whole grid

Mean grains / cell—

Total drops—

Last avalanche—

Largest avalanche—

Near-critical cells (≥3)—

State—

The idea

Just one rule: any cell stacking ≥ 4 grains topples, splitting 4 grains to 4 neighbours. Yet the system crawls to the critical point — where a small grain can cause an avalanche of any size. Most are tiny, rarely a giant one — exactly a power law.

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Cell color by grain count 0–3 (dark→bright) · cell ≥4 topples · click the grid to drop grains · yellow region = toppling. Try "Drop at center" or "Sand rain".

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Avalanche size over time · log-log distribution sizedistribution