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## The BTW mechanism on a self-similar image of a square: A path to unexpected exponents

Physica A: Statistical Mechanics and its Applications. 2012. Vol. 391. No. 1-2. P. 15-20.
Shapoval A.B., Shnirman M.

We define the BTW mechanism on a two-dimensional heterogeneous self-similar lattice. Our model exhibits the power distribution of avalanches with the exponent $\nu is the similarity exponent of the lattice. The inequality$$\tau <1, for the first time detected in this paper inside a broad class of sand-piles, is ensured by random loading uniformly distributed over the lattice.$