Consider the following two-dimensional mapping [6], 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.