Newton's method is a way to solve equations, invented by the famous Isaac Newton. When it works, it works quickly - and it usually works. It works equally well for equations in complex numbers. However it doesn't always work.
To make the movies on this page I applied Newton's method to the equation (z2+1)(z-a) for different complex numbers a. The colour depends on which of the three complex solution the method converged to, and how fast. As well as movies, you can also get posters of these fractal images.
I find it amazing that within these fractals you can find the familiar Mandelbrot set in all its glorious complexity!