The Sandpile at Criticality

Plate 83 speaks for itself: “One grain at a time, until one grain moves a mountain.”

The Physics

In the Bak–Tang–Wiesenfeld sandpile, any site with four or more grains topples onto its neighbours. Driven grain by grain, the pile organises itself to a critical state where avalanches of all sizes occur.

z ≥ 4 ⇒ z → z − 4

• z: number of grains at a site, integer

A toppling site sends one grain to each neighbour. Avalanche sizes follow a power law.

Sources

• P. Bak, C. Tang, K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987).

On the poster

Plate 083, “The Sandpile at Criticality”: the pixel-art plate with its slogan “One grain at a time, until one grain moves a mountain.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.