STATISTICAL-MECHANICS OF LAPLACIAN FRACTALS

We report on numerical evidence for a statistical mechanics description of the probability distribution of clusters grown on a square lattice with the eta model. The morphology selection mechanism in Laplacian growth phenomena is formulated in terms of two functions alpha(eta) and beta(eta), which play the role of a free energy and an inverse temperature, respectively. Invariants of the growth process such as the fractal dimension of a typical cluster and the singularity spectrum of its harmonic measure are computed from these thermodynamic quantities.