Julia sets are created by entering a complex number into a recursive function. The images below represent how the recursive function behaved. The Mandelbrot set is sort of a catalog of all the possible Julia sets. The Mandelbrot set is the most famous fractal because it is extremely complex and was first discovered by the founder of fractal geometry: Benoit Mandelbrot.
If you'd like to find out some more about the Mandelbrot set or Sierpinski's gasket, here are two Java applets created by a literary and mathematical genius, Christine Wong.