Fractal characteristics of simulated electrical discharges

Abstract

A two dimensional stochastic dielectric breakdown
model was utilized to study the fractal properties of simulated
lightning discharges and surface discharges. The fractal
dimension of the simulated growth patterns varied depending
on the cell configuration chosen for the breakdown. The
inclusion of the cells in the diagonals with reference to the
growth site produced less branched trees with smaller fractal
dimensions. The production of branches in the electrical tree
growth depends highly on ‘η’, which is the exponent of the
breakdown probability distribution. For small η values, highly
complex tree patterns with many branches were observed. By
controlling the value of η, growth patterns similar to the
experimental observations could be produced. The average
fractal dimension estimated through the Correlation Function
method when η=1 for simulated lightning discharges and
surface discharges were 1.56±0.01 and 1.68±0.01
respectively. When η>4 the growth patterns effectively lose
their fractal structure and became a curve with dimension 1.