Do experiment 8.3, page 92. You should perform this experiment
for both the quadratic family (x2 + c)
and the logistic family (kx(1-x)).
Use the
Orbit Diagram applets on the web
to examine the window structure of both
of these orbit diagrams.
Perform the Procedure part of the Experiment, and then
answer Questions 2-4 briefly. You should turn in your charts for
both families. Look at Note 1 if you are having difficulty
determining which windows are the largest. Here is a sample of the
chart that you should hand in for each family of functions.
Use the quadratic
or logistic map applets to display the corresponding orbit diagrams.
The program initially computes
200 points on the orbit of the critical point for your function, but
then displays only the last 100. You may change each of these numbers
manually. As you zoom, you will generally need to increase the number
of iterations.
The orbit diagram is always displayed using the orbit of the critical
point: you cannot change this with this software. We'll see why we
do this later.
Think about Question 5, but do not hand anything in on
this topic (yet).
For an overview about what is expected in your lab reports, click here