########### About the Mandelbrot and Julia Sets ##############
For every complex function f(z)=f(x+iy) there is an associated Mandelbrot set, generated by the iterated mapping
Zn+1=f(Zn)+Zo
Which is performed at every point Zo in the complex plane. After a large number of iterations, one checks to see how big Zn is. If Zn is below a certain cutoff (typically very large), we say it is in the mandelbrot set. Otherwise, it is not.
However, this doesn't make a very interesting picture, so it is nice to add some color by allowing points that diverged past the cutoff, but took a long time to do so, to be included as well. These points are then assigned a color based on how long they took to diverge, giving the set a little artistic flare.
While for a given function f(z) there is only one associated Mandelbrot set, there are an infinity of associated Julia sets, one for every point in the complex plane. They are generated in the same fashion as Mandelbrot sets only the mapping is changed to
Zn+1=f(Zn)+C
and is performed at every point Zo in the complex plane for a fixed complex value C.
Oh, and for e^z it turned out that the set of points that did diverge made a more interesting shape than those that didn't, so I plotted the inverse of the set and called it and Anti-set.