Diffusion-Limited Aggregation

Dielectric Breakdown

Dielectric breakdown refers to the formation of electrically conducting regions in an insulating material exposed to a strong electric field.
For example, the intense electric fields during thunderstorms can produce a conducting path in the air along which many electrons flow (lightning).
A formal model, ignoring the physical details of the processes, was proposed in 1984 by Niemeyer, Pietronero, and Weismann.
Here is a brief mathematical description of DBM.
Dielectric breakdown patterns exhibit a branching, fractal pattern with a dimension of about 1.7.

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