In recent posts I’ve presented the complex numbers and the complex plane. Those were just stepping stones to this post, which involves a basic fact about the Mandelbrot set. It’s something that I stumbled over recently (after tip-toeing around it many times, because math).

This is one of those places where something that seems complicated turns out to have a fairly simple (and kinda cool) way to see it when approached the right way. In this case, it’s the way multiplication *rotates* points on the complex plane. This allow us to actually visualize certain equations.

With that, we’re ready to move on to the “heart” of the matter…