  The dynamics of a 2D site percolation model on a square lattice is studied
using the hierarchical approach introduced by Gabrielov et al., Phys. Rev. E,
60, 5293-5300, 1999. The key elements of the approach are the tree
representation of clusters and their coalescence, and the Horton-Strahler
scheme for cluster ranking. Accordingly, the evolution of percolation model is
considered as a hierarchical inverse cascade of cluster aggregation. A
three-exponent time-dependent scaling for the cluster rank distribution is
derived using the Tokunaga branching constraint and classical results on
percolation in terms of cluster masses. Deviations from the pure scaling are
described. An empirical constraint on the dynamics of a rank population is
reported based on numerical simulations.
