Fractal analysis of electrical trees

Recently, fractal characteristics in pattern formation have been attracting much attention. A number of books and papers have been published on the fractal analysis of random patterns or structures occurring in nature. The geometrical patterns of dielectric breakdown, which include lightning, surface discharges and electrical trees, are known to be of a fractal nature. Their fractal patterns can be analyzed numerically using fractal dimensions. In this paper, a survey of the fractal analysis of electrical trees, both in experiment and in computer simulation, is given. Several methods for estimating the fractal dimension are summarized. The stochastic models for discharge patterns based on computer simulation are also summarized. Fractal analysis of real electrical trees in polymeric insulating materials is reviewed. For the experimental tree patterns, the fractal analysis of the projected 2-D and the reconstructed 3-D patterns is presented