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We report on numerical evidence for a statistical mechanics description of the probability distribution of clusters grown on a square lattice with the {η} model. The morphology selection mechanism in Laplacian growth phenomena is formulated in terms of two functions {α}({η}) and {β}({η}), 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.
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Elezgaray et al. (1993) studied this question.
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