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Pattern formation in growth of snow crystals occurring in the surface kinetic process and the diffusion process.

We propose a model of pattern formation in the growth of snow crystals that takes into account the actual elemental processes relevant to the growth of crystals, i.e., a surface kinetic process for incorporating molecules into a crystal lattice and a diffusion process. This model gives a clear correspondence between the patterns produced and the actual growth conditions such as supersaturation and the diffusion coefficient. Circular patterns due to kinetic roughening, hexagonal patterns, and dendritic patterns are obtained starting from a circular crystal under various growth conditions. We analyze these patterns and discuss the mechanisms of appearance of round patterns, the development of hexagonal patterns, and the formation of dendritic patterns of snow crystals. Finally, it is shown that the dimensionless crystal size with reference to the mean free path of a water molecule plays an important role in the pattern formation of growing snow crystals.