Abstract
Crystal growing in a diffusion field takes various patterns. Only with the diffusional instability, the aggregation grown has a self-similar structure, called fractal, up to a diffusion length. The growth rate is determined by the fractal dimension and the gas density. With the anisotropic surface tension, the regular dendritic morphology is stabilized, and the growth rate and the tip radius satisfies a universal scaling relation. Below a rounghening temperature of a certain interface, the singularity in the surface kinetics governs the growth and the crystal shape becomes polygonal.
