The first part of this program investigated several different subjects. For me, the main problems to overcome were to learn the basics of PHP and the Unix operating system. Iteration is when the result from each use of the equation is used as the value for the variable in the next use of it. From my experiments, the first bifurcation occurs when k was equal to 2, and occurred again when k was equal to 3.
Bifurcation is when an equation begins to bounce between two separate paths on each iteration.
The second part of this program involved adding a menu which let you choose between four different equations to iterate. The challenge in this was to learn how to make menus in PHP and then send that information to a new page which processes it.