Exact enumeration method for diffusion-limited aggregation

The authors present a new method for growing and analysing diffusion-limited aggregates (DLA). The method is based on the exact enumeration approach which enables one to calculate exactly the probability density of a random walker starting from an outer circle (at r=r₁). The method yields the exact growth probabilities, p_i, of the perimeter sites, i, for a given configuration as a function of time. The authors study the histogram, n(p), i.e. the number of perimeter sites having growth probability p, as a function of time, for several different boundary conditions. Their results suggest that the fluctuations in the survival times of the particle are very small compared with the large fluctuations in the growth probabilities. They find that at times of the order of r₁² all growth probabilities are essentially converged. Very long survival particles have only a negligible effect on the histogram n(p) and thus on the DLA structure.