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In this paper, we analyze the scaling behavior of \emph{Diffusion LimitedAggregation} (DLA) simulated by Hastings-Levitov method. We obtain the fractaldimension of the clusters by direct analysis of the geometrical patterns in agood agreement with one obtained from analytical approach. We compute thetwo-point density correlation function and we show that in the large-sizelimit, it agrees with the obtained fractal dimension. These support thestatistical agreement between the patterns and DLA clusters. We alsoinvestigate the scaling properties of various length scales and theirfluctuations, related to the boundary of cluster. We find that all of thelength scales do not have a simple scaling with same correction to scalingexponent. The fractal dimension of the perimeter is obtained equal to that ofthe cluster. The growth exponent is computed from the evolution of theinterface width equal to $\beta=0.557(2)$. We also show that the perimeter ofDLA cluster has an asymptotic multiscaling behavior.

Scaling and Multiscaling Behavior of the Perimeter of Diffusion-Limited Aggregation (DLA) Generated by the Hastings-Levitov Method