Unlike the Mandelbrot set, there are many different kinds of Julia sets. For every complex number C in the complex plane, there is a corresponding Julia set. The most interesting such sets are found when C is chosen near the borders of the Mandelbrot set. Anyhow, a Julia set is found as the set of all complex numbers Z that cannot escape an infinite number of orbits through the recursive equation Z -> Z2 + C. Such a Z is said to never escape if its magnitude has an upper bound over all recursive iterations. It can be shown that if |Z| ever becomes greater than a certain size, then it will escape. More information can be found here.