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

► We define the BTW mechanism on a two-dimensional heterogeneous self-similar lattice. ► We find the dependence of the critical exponent on the similarity exponent of the lattice. ► The size-frequency relation in the model admits to universal representations with respect to the lattice area. ► The results are ensured by random loading uniformly distributed over the lattice.