Percolation and Invasion Percolation As Fractal Growth Problems

We apply the fixed-scale transformation method, developed for Laplacian fractal growth, to compute the fractal dimension of standard percolating clusters and of clusters generated by invasion percolation with and without trapping. In all cases we obtain values within 1% from the exact or numerical results. This provides an important test for this theoretical framework, fundamentally different from the renormalization groups, as an alternative tool to study fractal structures generated by both equilibrium and irreversible growth processes.