Scaling and multiscaling behavior of the perimeter of a diffusion-limited aggregation generated by the Hastings-Levitov method

In this paper, we analyze the scaling behavior of a diffusion-limited aggregation (DLA) simulated by the Hastings-Levitov method. We obtain the fractal dimension of the clusters by direct analysis of the geometrical patterns, in good agreement with one obtained from an analytical approach. We compute the two-point density correlation function and we show that, in the large-size limit, it agrees with the obtained fractal dimension. These support the statistical agreement between the patterns and DLA clusters. We also investigate the scaling properties of various length scales and their fluctuations, related to the boundary of the cluster. We find that all of the length scales do not have a simple scaling with the same correction to scaling exponent. The fractal dimension of the perimeter is obtained equal to that of the cluster. The growth exponent is computed from the evolution of the interface width equal to β = 0.557(2). We also show that the perimeter of the DLA cluster has an asymptotic multiscaling behavior.