So I got my program to work last night and was doing some number crunching today along with some background research. Here are some interesting bifurcation diagrams I've made so far.

This one (below) demonstrates when you have a particular set symmetrical equations. As I mess around with the parameters it does some of this (notice that the region in the lower left hand corner of the graph towards the origin)...And this, where it would appear as if the region bulges outwards and forms a quarter of a circle...

At a certain point, however, the entire graph turns suddenly blue. I'm toying around with the numbers to see what happens. Also, I'm going to modify my program so it has different colors indicating not only which line terminates the system, but also if it crosses 0r not. I'll upload some images with the formal equations tomorrow (right now I'm using a computer without LaTex on it).

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