Department of Mathematics

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:

xn+1 = 2xn mod 1
yn+1 = yn/2          if 0 ≤ xn < 1/2
(yn+1)/2   if 1/2 ≤ xn < 1
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 frames.