In this post we are going to look at a trick for figuring out what a whole type of fractals look like, before doing all the calculations needed to generate them. Occupy Math has posted on fractals before. The clue we will use to search for beautiful fractals is, itself, a very special fractal called the Mandelbrot set. Here is the core fact for today’s post. The Mandelbrot set lives in the complex numbers, which form a plane. Given that, the way the Mandelbrot set looks near a particular place (or number) in the plane of complex numbers is the way the Julia set based on that number looks all over. Another way to say this is that the Mandelbrot set *indexes* Julia sets.