The Abelian Sandpile Model (ASM) was created by Dhar in 1990.  It is a generalization of the sandpile model proposed by Bak-Tang-Wiesenfeld (1987) as an example of self-organized criticality, having especially nice mathematical properties.  The ASM is connected to a wide range of mathematics: Markov processes and statistical mechanics, combinatorics (tilings, the Tutte polynomial, parking functions, the matrix-tree theorem), algebraic geometry (lattice ideals), graph analogues to Riemann surfaces, and tropical geometry.

This website provides resources for studying sandpiles. Make sure to check out the Gallery and Bryan Head's incredible application.

Sage Sandpiles  •  Literature  •  Algebraic Geometry  •  Applets/Java  •  Gallery
Last revised: 1/18/10