Statistical properties of fractal dendrites and anisotropic diffusion-limited aggregates

Crystalline dendrites, growing in a two-dimensional diffusion field at small Péclet numbers, are investigated. It is shown that, far from the tip, the distribution in size of the side branches gives them a fractal structure of dimension ${\mathit{d}}_{\mathit{f}}$≊1.58±0.03. In spite of the fluctuations, their overall area is the same as the underlying stable parabola observed at the tip. Similarly, anisotropic diffusion-limited aggregation patterns grown in a strip have a mean occupancy profile with a parabolic tip and a selection mechanism similar to that of stable anomalous Saffman-Taylor fingers.