Harmonic measure of DLA and percolation clusters

The problem of efficiently finding the harmonic measure of DLA and percolation clusters is addressed. Deep inside fjords and inlets of irregular surfaces, traditional methods of solving Laplace's equation become very inefficient. A new numerical algorithm that efficiently solves for those measures is developed. The technique uses a step-by-step approach that adds a shell at each time step to the diffusion front, and is essentially linear in the number of sites considered. The method works for lattice systems and discretized versions of continuum systems. With it, we have solved for the multifractal exponents of the fractal surfaces. For DLA, we address the controversy of the behavior of the harmonic measure deep inside the fjord. For percolation, we consider both the relatively smooth accessible hull (D = 4/3), and the very invaginated regular hull (D = 7/4).