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Iterated Functions

What does it do? This display is used to plot points representing the iterates tex2html_wrap_inline215 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. tex2html_wrap_inline187. In this case, we understand t=n.

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