Orbit Diagram

• The logistic function Cx(1 - x)

• The quadratic function x² + C

• Cubic functions C(x - x³/3)

• 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