Using this applet you can display the web diagram (graphical iteration) for a variety of functions, including

- The logistic function
**Cx(1 - x)** - The quadratic function
**x**^{2}+ C - Cubic functions
**C(x - x**^{3}/3) - Quartic functions
**Cx(1 - x)(1 - 2x)** - Sine functions
**C sin(x)** - Cosine functions
**C cos(x)** - Tent functions
**Cx**if**0 <= x <= 0.5**;**C(1 - x)**if**0.5 < x <= 1**. - The Doubling function
**2x mod 1**

After opening nonlinear web, you will see the graph of the logistic
function
**F(x) = 3x(1 - x)** displayed. You may change this graph to that
of **F(x) = Cx(1 - x)** for ** 0 < C < 4** by using the scroll
bar on the right.

You may select other functions from the list above using the menu in
the upper left hand corner. You may also view the graph of the
**n**th iterate (**1 <= n<= 6**) of the function using the lower
left menu.
Remember to click **Clear** in order to remove the old graph from
the window.

Moving the cursor over the graph window, you will see displayed in the
lower left hand corner the current **x**-value. Click on a point
in the window to display the web diagram corresponding to the chosen
**x**-value. The first twenty five iterations are displayed in
black; the subsequent 175
iterations are displayed in red. This allows you to
see the "fate of the orbit" without viewing the transient behavior.
Click on **Delete Transients** to remove the first part of the
orbit. Click on **Add Transients**. to restore the transient behavior.

You may see the orbit one step at a time by using the **Iterate**
button. Be sure that the **Del Tans** button is showing (otherwise
you will not see the first few iterates). Each click of this the
**Iterate** button gives a successive point on the orbit. Clicking
a new **x**-value changes to the orbit of that point. The seed
corresponding to the chosen orbit is displayed in the lower left.

Go to Nonlinear Web Applet.

For more information about the web diagram, consult the book Chaos

Created by Rodin Enchev. Modified by Adrian Vajiac and Robert L. Devaney.

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