Fractal geometry of lightning strokes

Fractal dimension is defined, and methods of approximating it are presented. Several pictures of lightning and a picture of an electric arc from a point charge were digitized, and the fractal dimension of the resultant arrays was computed. The use of the diffusion limited aggregation (DLA) fractal growth method to model dielectric breakdown of a point charge is discussed. To simulate lightning breakdowns in insulators, which are assisted by space charge, a surface charge model that uses an Eden cluster as a two-dimensional molecular substrate on which lightning charges can form without violating any rules of electrodynamics, is discussed. It is shown that lightning flashes produced on the Eden cluster have qualities similar to those measured in actual lightning, including the spectrum and fractal dimension.<
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