Informally, self-similar objects with parameters N and s are described by a power law such as N = s^d, where d = (ln N)/(ln s) is the "dimension" of the scaling law, known as the Hausdorff dimension. Formally, let A be a subset of a metric space X. Then the Hausdorff dimension D(A) of A is the infimum of d>=0 such that the d-dimensional Hausdorff measure of A is 0 (which need not be an integer).
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