Anisotropic Laplacian growths: From diffusion-limited aggregates to dendritic fractals

The statistical properties of anisotropic diffusion-limited aggregates (DLA) grown in a strip are investigated. The mean shape of these aggregates being related to the corresponding smooth Saffman-Taylor solutions, a finite-size scaling analysis is applied. This scaling description shows that the anisotropy-induced crossover from isotropic DLA clusters (${\mathit{D}}_{\mathit{F}}$=5/3) to dendritic fractals (${\mathit{D}}_{\mathit{F}}$=3/2) is actually contained in the continuous shape transition of the stable solution, from isotropic fingers of relative width λ=0.5 to λ=0 needlelike fingers.