Fractal Lightning

Another naturally occurring fractal pattern is a lightning bolt. As Benoit Mandelbrot noted in the opening quotation, lightning does not travel in straight lines. Rather, it follows a chaotic, jagged path, formed as the huge charge separation built up in the sky suddenly breaks down.

The majority of a lightning bolt is generally hidden in a cloud, much as an iceberg hides beneath the ocean. Lightning can be very large, spanning several kilometers, but it is formed in microseconds. Thunder is a fractal sound. It is caused by the superheating of air. Because the pathway of the lightning bolt is a jagged fractal in 3D space, the time it takes to reach your ear varies, and the thunder rumbles in a corresponding fractal pattern.


Lightning over Albuquerque, New Mexico. Photo courtesy of Jef Duncan.

Lightning can also be created in a laboratory, at small scale. By using a particle accelerator to charge up a piece of acrylic material electrons, and then suddenly discharging it, a lightning-like discharge path is created and burns a trace in the material. It appears like frozen lightning.


A Lichtenberg Figure, or simulated lightning, created by rapidly discharging electrons on a block of acrylic. Scale = 10 cm.
Photo courtesy of Bert Hickman, Teslamania.com.