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Sand Piles

In 1987, Bak, Tang, and Wiesenfeld published a paper in Physical Review Letters, “Self-organized criticality: An explanation of noise.” You can download it from http://prl.aps.org/abstract/PRL/v59/i4/p381_1.

The title takes some explaining. A system is critical if it is in transition between two phases; for example, water at its freezing point is a critical system.

A variety of critical systems demonstrate common behaviors:

  • Long-tailed distributions of some physical quantities: for example, in freezing water, the distribution of crystal sizes is characterized by a power law.

  • Fractal geometries: freezing water tends to form fractal patterns—the canonical example is a snowflake. Fractals are characterized by self-similarity; that is, parts of the pattern resemble scaled copies of the whole.


  

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