To start up Mathematica in a Unix window, type 'math', or 'mathematica' if your prefer the notebook version. On a PC, use the start button and find Mathematica in the Program directory. The Package written for this course is called 'Chaos.m'. Inside Mathematica, load this Package by typing

- Pick a value for
and type
*lambda*= .

- Type
*PlotGraphical*to get the graph of the corresponding function. If you do not want to see the graphical iteration, you can also type

*ShowGraph[1, color]*

where*color*is the color of the graph. You can choose:*red, blue, green, yellow, pink,*and*purple*, or*RGBColor[a, b, c]*, with*a, b, c*in [0,1].

- To add a graph of the second iterate to this picture, type

*AddGraph[2, other-color]*

You get a new picture that contains both graphs.

- You may wish to zoom in to this picture. For this, type

*Show[%, PlotRange -> {{0.6, 0.8}, {0.6, 0.8}}]*

A new figure appears of only the box [0.6, 0.8] X [0.6, 0.8]. You can type something similar to zoom in more, but also to zoom out, even though the last picture does not show all points.

To start up Mathematica in a Unix window, type 'math', or 'mathematica' if your prefer the notebook version. On a PC, use the start button and find Mathematica in the Program directory. The Package written for this course is called 'Chaos.m'. Inside Mathematica, load this Package by typing

*An enlargement of the orbit diagram for the Logistic family.*

- To start the computation, type

*OrbitDiagram[first-its, total-its]*

The program begins by computing*total-its*iterates of an arbitrary point*x*. However, iterates are displayed only after_{0}*first-its*iterates. Therefore, the*transients*are not shown in the picture. In Mathematica it is not possible to have the picture being partially drawn already while computing. Therefore, it may take quite a while. In total 200 orbits are computed for each picture, and a count-down is being printed so that you can guess how long it takes.

- To get a picture that reflects the eventual attracting behavior
more accurately, increase
*first-its*and*total-its*.

- You can zoom in with

*Show[%, PlotRange -> {{3.1, 3.8}, {0.6, 0.8}}]*

However, when you zoom in, you probably want to increase*first-its*and*total-its*even more. Therefore, you may want to type

*OrbitDiagram[first-its, total-its, {{3.1, 3.8}, {0.6, 0.8}}]*

The computations are done now only for the ranges specified. (So you cannot zoom out on this picture!)

Written by Hinke Osinga

Comments to:
webmaster@geom.umn.edu

Created: Apr 3 1998 ---
Last modified: Mon May 11 16:35:21 1998