Using this applet you can display the orbit diagram (bifurcation diagram) 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**.

For more details on what the orbit diagram is, consult the booklet Chaos, especially pages 172-191.

To display the orbit diagram for any of the families mentioned above, first
choose the family from the menu in the upper left corner of the
window. Click the **Iterate** button.
You then see the orbit diagram displayed with the parameter
**C** plotted horizontally and the critical orbit for each
**C**-value
plotted on the vertical
line directly over **C**.

Actually, what you see is the fate of the orbit, for we display only a
certain number of iterations (displayed in the **Iterations**
window) but remove the first few iterations (the number removed is
displayed in the **First show** window.)

You may magnify portions of the orbit diagram as follows. You need to
select a rectangle to be magnified. To do this click and drag to form
the appropriate rectangle.
You should see the
rectangle displayed. Click magnify to compute the portion of the
orbit diagram inside this rectangle. Note
that you need not adjust the number of iterations computed and
displayed; this is done automatically. If you wish to see a darker
picture, you can increase the number of iterations by erasing the
number in the Iterations window and then entering a larger number.
**You Need to hit Return after doing this**. You may also
increase this number by clicking the + button over and over.

Click **Demagnify** to
return to the previous image. You may perform successive
magnifications, but remember that each picture is saved in memory when
you do this. You may magnify at most 10 times.
Click **Home** to return to the original orbit
diagram.

Go to Orbit Diagram Applet.

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

Created by Clara Bodelon and Robert L. Devaney.

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