Up: Iteration
One-Dimensional Dynamical Systems
Part 3: Iteration
Instructions for the Macintosh: Iterations
The software Chaos and Dynamics can be found in the apple-menu, under
'Math Apps'. Go to 'Devaney's Chaos Lab' and load
'Lab 1-Function Iteration'. When you load the Lab, the current
function is automatically set to the Logistic map.
Function Iteration with
= 2.
Instructions to Iterate
- Push the Chart button to get a setup for plotting iterates
against (discrete) time.
- Change
to 2: Notice the number marked Parameter under the Current
Function box.
- You may wish to change the starting value x0
on top of the plot. (x0 should be chosen in the
closed interval [0,1].) Then push Iterate.
- If you push Chart again the picture clears and you can
compute another orbit. Experiment with different values for
and
x0.
Instructions for the Macintosh: Graphical Iteration
The software Chaos and Dynamics can be found in the apple-menu, under
'Math Apps'. Go to 'Devaney's Chaos Lab' and load
'Lab 2-Plot and Analyze'. For the Logistic map, pick a
value between
0 and 4, and iterate as follows:
Visualizing an orbit with graphical iteration for the Logistic
map.
Instructions to Iterate
- Push the Add Graph button, marked with a '+'. You should
see a graph of the Logistic family.
- Change the parameter
: Notice the
number under the column marked Parameter. This is the value of
. Edit this
number (and hit return).
- Double click on any point in the graph window; the iteration
will start with the x value of this point. This x
value also appears in the Analysis Start box.
Alternatively, edit the Analysis Start box to the desired
initial x value (and hit return). Then press Analysis.
- Press Analysis to stop the iteration, and try another
point.
Up: Iteration
The Geometry Center Home Page
Written by Hinke Osinga
Comments to:
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Created: Apr 3 1998 ---
Last modified: Wed Apr 8 19:01:17 1998