Pattern Formation in Diffusion-Limited Aggregation

The diffusion-limited-aggregation model is generalized in order to take into account the surface effects playing an essential role during most of the growth processes. With variation of a parameter of the model the geometry of the clusters generated in the Monte Carlo simulations gradually changes from the randomly branched diffusion-limited-aggregation clusters into compact, nearly regular, snowflakelike patterns. The deposition of particles along a line results in patterns similar to those observed in the experiments on directional solidification.