Scaling in the Diffusion Limited Aggregation Model

We present a self-consistent picture of diffusion limited aggregation (DLA) growth based on the assumption that the probability density P(r,N) for the next particle to be attached within the distance r to the center of the cluster is expressible in the scale-invariant form P[r/R_dep(N)]. It follows from this assumption that there is no multiscaling issue in DLA and there is only a single fractal dimension D for all length scales. We check our assumption self-consistently by calculating the particle-density distribution with a measured P(r/R_dep) function on an ensemble with 1000 clusters of 5×10⁷ particles each. We also show that a nontrivial multiscaling function D(x) can be obtained only when small clusters (N<10000) are used to calculate D(x). Hence, multiscaling is a finite-size effect and is not intrinsic to DLA.