Diffusion-limited aggregation and regular patterns: fluctuations versus anisotropy

The authors show that the patterns in diffusion-limited aggregation (DLA) on a lattice emerge from the interplay of lattice anisotropy and fluctuations. These fluctuations can be damped by Monte Carlo averaging. Increasing its amount, the effective anisotropy becomes larger and a crossover from tip splitting typical for continuum DLA to stable tips is observed, in analogy with a number of recent experiments. The simulations suggest the following scenario for the transitions which take place as a function of the increasing effective anisotropy: disordered patterns to dendritic structures to needle crystals. It is shown that DLA clusters go through the same sequence of transitions as a function of their size. Therefore, diffusion-limited aggregates on a lattice are asymptotically not fractals.