There are an infinite amount of Julia sets, one for each complex constant number we choose. The set of all Julia sets is the Mandelbrot set. As the equation for each Julia set is iterated over and over, the computer colors the output according to whether it goes to zero ("inside" points which are colored black) or goes to infinity ("outside points" which are colored in bands of color depending on how fast it goes to infinity). Function values that cause the output to cycle through several points, or jump all over the place, are part of the colorful bands along the boundary of the black center of each Julia set and the Mandelbrot set.

There is a lot to explore with the Mandelbrot set. You can investigate the equations and relationship of the Julia sets to the Mandelbrot set, or the different types of fractals that can be generated using these methods. You can also zoom into the Mandelbrot set. We will next examine several simple fractals that can be drawn for the first few iterations. Then we will investigate IFS fractals and Sierpinski fractals.