**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
*x*_{0}
on top of the plot. (*x*_{0} 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
*x*_{0}.

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