Fractal dimension of long electrical discharges

The fractal dimension of 500 mm long electrical discharges is presented by analyzing a set of photographic images. Three popular fractal dimension estimation techniques, box counting, sandbox and correlation function methods were used to estimate the fractal dimension of the discharge channels. To remove the apparent thickness due to varying magnitudes of current in the discharge channels, edge detection algorithms were utilized. The estimated fractal dimensions for box counting, sandbox and correlation function for long laboratory sparks were 1.20 ± 0.06, 1.66 ± 0.05 and 1.52 ± 0.12 respectively. Within statistical uncertainties, the estimated fractal dimensions of positive and negative polarities agreed very well.