My entry to the contest is Iterlab, a program for doing graphical iteration of functions. I hope this type of program is appropriate for the contest. It's one is for the math enthusiasts, it probably goes in the educational/academic category.
Graphical iteration is a simple way of visualizing the process of function iteration. It helps you to see if the sequence of the iterates converges or diverges.
With this program one can iterate on any function of the