Fractal aggregation growth and the surrounding diffusion field

Silver metal trees grow and form a forest at the edge of a Cu plate in the AgNO3 water solution in a two-dimensional (d=2) cell. The local structure of the forest is similar to that of the diffusion-limited aggregation (DLA), but the whole pattern approaches a uniform structure. Its growth dynamics is characterized by the fractal dimension Df of DLA. Time-dependence of the tip height is found to satisfy the scaling relation with the solute concentration c, and the asymptotic growth velocity V is consistent with the power law V∼c1/(d-Df) expected from the theory. The thickness ξc of the diffusion boundary layer is measured by the Michelson interferometry, and the scaling relation is also confirmed.