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## Iterated Functions

What does it do? This display is used to plot points representing the iterates of a function. The function is not necessarily one-dimensional. You are free to start plotting at any time during the iteration. In particular, if you seek periodic orbits, you may run a large number of iterations first, and only then plot the points.

How do I use it? This plot differs significantly from differential equation plots. In particular, in this case the independent variable t becomes discrete, representing the index of the iteration. To begin, you should enter the function to be iterated in the form x=f(x), with the meaning that the new value for x is to be computed as a function f of the old value: i.e. . In this case, we understand t=n.

• To plot iterates of a one-dimensional function, you will probably want to set t on the horizontal axis, and have the dependent variable on the vertical axis. To plot iterates of two (or higher) dimensional function, you will probably want to put different dependent variables on the axes.
• In the plot dialog box, there is a checkbox that allows you to choose the size of the points that are drawn to represent the iterates.
• By selecting the Algorithm Controls item from the Numerics menu, you may choose the iterate at which you want to start plotting. For example, you could choose to compute 100 iterates before you actually start plotting any.

What are the defaults? The default window is (-10,10)x(-10,10). The points are initially drawn "small".

Kevin Cooper
Wed Sep 30 15:21:52 PDT 1998