Finite-size effects in diffusion-limited aggregation

Abstract

This paper discusses a large variety of numerical results on diffusion-limited aggregation (DLA) to support the view that asymptotically large DLA is self-similar and the scaling of the geometry can be specified by the fractal dimension alone. Deviations from simple scaling observed in many simulations are due to finite-size effects. I explain the relationship between the finite-size effects in various measurements and how they can arise due to a crossover of the noise magnitude in the growth process. Complex scaling hypotheses including anomalous scaling of the width of the growing region, multiscaling of the cluster radial density, infinite drift of the ε-neighborhood filling ratio, nonmultifractal scaling of the growth probability measure, and geometrical multifractality, are shown to lead to physically unacceptable predictions.