Consider the following two-dimensional mapping , by Gumolski and Mira, for modeling the dynamics of a particle accelerator:
where a and b are constants and
Note that the argument of f on the right-hand-side of the second equation above depends on . Write a script for iterating with these equations. You will need to write a function program to calculate and a script for displaying a graph of all iterations of the equations. In order to obtain striking pictures, you should try to perform at least 3000 iterations. It is important to watch the pattern of the points when they fill in on the graph as the iterations proceed.