Go to the Orbit Diagram Applet . PLAY around with it for ten minutes or so to get an idea of what it does. The label in the upper left corner tells you what orbit diagram you're seeing (the function also appears in red below). Doesn't the orbit diagram for the tent map look weird? I find it really cool that all the others look pretty much the same!
Change the label in the upper left corner to Quadratic.
READ Section 8.1. For each of Observations 1, 2, 3, 4, and 5, ZOOM in until you can see the behavior described. Figures 8.1-6 also illustrate these observations.
DO Experiment 8.3. For the quadratic function, fill in
the values of the letters in this table for Generations 1-4 as described
in the text. See the comment on the top of p. 94.
| Generation 1 | 3 | 1 | ||||||||||||
| Generation 2 | 3 | 5 | 6 | 1 | ||||||||||
| Generation 3 | 3 | E | 5 | D | C | 6 | B | A | 1 | |||||
| Generation 4 | 6 | e | B | d | g | A | b | a | 1 | |||||
| Generation 5????? |
PERFORM the same experiment for the Logistic function (this time, the table goes in the opposite direction).
ANSWER questions 2-4 under the section ``Notes and Questions'' on p. 94.
ANSWER question 14 in the Exercises on p. 95.
PRINT this orbit diagram for the quadratic map. On it, GRAPH the following functions (remembering that c is the horizontal axis and x is the vertical axis!) What do the cyan lines on the diagram correspond to? This is related to question 18 in the Exercises.