Quasi-fractals: new possibilities in describing of the self-similar clusters

In this paper we propose a method for parameterization of fractal clusters which allows us to represent as quasi-fractals. The quasi-fractals are self-similar objects with a slower (logarithmic) scaling in comparison with conventional fractals. The proposed method on flat clusters, obtained by the model of Witten-Sander in which dipole-dipole and charge-dipole interactions between particles were additionally introduced is tested. The results suggest that these clusters can be interpreted as fractals and as quasi-fractals but in the second case we have a clear connection between external conditions of growth and geometry of the clusters (in terms of new fitting parameters).