  In this paper, we analyze the scaling behavior of \emph{Diffusion Limited
Aggregation} (DLA) simulated by Hastings-Levitov method. We obtain the fractal
dimension of the clusters by direct analysis of the geometrical patterns in a
good agreement with one obtained from 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 cluster. We find that all of the
length scales do not have a simple scaling with 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 $\beta=0.557(2)$. We also show that the perimeter of
DLA cluster has an asymptotic multiscaling behavior.
