Electric Discharge and Fractals

Abstract

Electric discharge simulations, especially those of streamers, are usually based on the Liouville equation. However, there have been extremely few studies of the morphology of electric discharges. Morphological research methods have the advantage of allowing common characteristics over different fields, e.g., biology, physical geography etc., to be extracted. In this work, a fractal dimension analysis of streamers simulated by computer with random numbers, the dimension being on feature of the morphology, was performed to obtain the fractal dimension of streamer-modeled figures. The fractal dimension is about 1.23 to 1.54 for figures having many streamers (300-streamer channels) and fluctuates for streamers having slight branching. The overall geometrical changes of the patterns formed by the streamer development cause the fractal dimension to change rapidly.