Exactly soluble hierarchical clustering model: inverse cascades, self-similarity, and scaling.

We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling, as an intermediate asymptotic, which then truncates at the largest spatial scales. We show how this model can provide a general explanation for the behavior of several models that has been described as "self-organized critical," including forest-fire, sandpile, and slider-block models.