Non-deterministic approach to anisotropic growth patterns with continuously tunable morphology: the fractal properties of some real snowflakes

The authors demonstrate that a tunable family of patterns resembling a range of experimentally observed snowflakes is obtained from a simple but somewhat ad hoc non-deterministic growth model-an extension of the Niemeyer-Pietronero-Wiesmann eta model in which they (i) use 'noise reduction' to enable the asymptotic behaviour to become more readily apparent from simulations of reasonable size, (ii) replace the eta model boundary conditions by the boundary conditions of the diffusion-limited aggregation (DLA) model and (iii) include a surface tension parameter. They measure the fractal dimension of some real snowflakes and obtain quantitative agreement with certain cases of the model. They conclude that the model, although somewhat ad hoc, gives patterns that are in both qualitative and quantitative agreement with a range of real snowflake patterns.