Math 307, Fall 2005
Illustrations for Problem 2 of the Final Exam
Below are some animations illustrating the behavior of the map
in Problem 2 of the Final Exam:
In each example, the forward or backward iterations of a
region of the square (colored green)
are shown in sequence.
Only the first seven iterations of F or F-1
are shown, and then the sequence repeats.
These are animated GIFs, with a delay of about two seconds between
| xn+1 =
|| 2xn mod 1
| yn+1 =
|| yn/2 if 0 ≤ xn < 1/2
(yn+1)/2 if 1/2 ≤ xn < 1