STATISTICAL-MECHANICS OF LAPLACIAN FRACTALS

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