# Mathematics of Lightning

Here’s a fun challenge suggested by Matt Henderson: can you find a mathematical model for the path of a bolt of lightning?

You can check out this video of a lightning strike to get the ideas flowing:

http://www.youtube.com/watch?v=2XwFF5idD_0

The tree structure suggests graph theory, the bifurcations suggest dynamical systems, and the inherent physics suggest that some complicated differential equations might be involved.

* *

## 2 Comments

## Ben · July 25, 2013 at 12:08 pm

Given the fact that the leaders involved in the production of lightning travel in a discontinuous manner, some finite element methods could be involved. I’d also imagine it would be reasonable to assume that, given that the electric current will follow a path of least resistance, there may be call some sort of application of the calculus of variations.

## Ben · July 25, 2013 at 12:13 pm

Typo, the end of my last sentence should read:

call for some sort of application of the calculus of variations.