Compact or fractal patterns in diffusion limited growth

Fractal viscous fingering patterns are observed in an infinite Hele-Shaw cell at long times when the capillary forces become negligible. On the contrary, growth of monocrystals from a punctual seed shows dendrites growing independently in 4 or 6 directions, according to the crystal symmetry. A close comparison of numerical and experimental data explains first the origin of the tip-splitting instability in radial growth and shows that it can be inhibited by the anisotropy of surface tension.