I chose to use Stephen Wolfram's ``Mathematica'' environment as my tool to implement the numerical
simulations. While using Matlab or programming directly would be much faster in terms of the time
it takes to run a simulation, the development time would be orders of magnitude greater. Mathematica allows
one to code at a high level, focussing more on the Mathematics than on some arcane syntax - though of course,
Mathematica has its share of silly tricks and frustrations. I am including my source code (temporarily uncommented,
this will soon be rectified) along with the pictures it has generated and some examples of how this was done so
that interested readers with access to Mathematica can play around on their own. The code is also available
as a Latex file on my Thesis Web Site at http://www2.ucsc.edu/people/scotfree/.