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This applet is designed to show you three interrelated concepts:

- The orbit of a seed under iteration of the linear function
**Ax + B**. - The corresponding time-series graph.
- The web diagram or graphical iteration of this function.

See the book Chaos for details about what these terms mean.

When you open this applet, you see four "windows". In the upper left
you will view the graph of **Ax + B** together with its graphical
iteration or web diagram. You will click in this window to choose the
appropriate seed **x _{0}**.
In the upper right are two sliders to control the values of

To use the applet, first select a value of **A** and **B** using
the sliders. Note how you see the graph of **y = Ax + B** moving
as you vary these "parameters." Be sure to change these values of
**A** and/or **B**, for otherwise you will be viewing the default
function **y = x**, which,to put it mildly, is not very
interesting!
You
also see the diagonal line ** y = x**. Now click on a point in the
window that contains the graph. The **x**-coordinate of this point
yields the seed for the orbit **x _{0}**. Click the

Now change the parameters **A** or **B** with the sliders. Note
how the orbit of your original seed changes.

**Questions:**

- For which values of
**A**do you see an attracting fixed point? - For which values of
**A**do you see a repelling fixed point? - For which values of
**A**do you see neither an attracting nor a repelling fixed point? - For which values of
**A**do you see a cycle of period 2? - How does changing the value of
**B**alter the answers to the above questions?

Go to Linear Web Applet.

Created by Adrian Vajiac and Robert L. Devaney.

For comments and suggestions write to Robert L. Devaney at bob@bu.edu