For a more thorough explanation of the fractal creation process used here, a good place to start is with the "Koch Curve," about which there is plenty of information on-line. The following good sites for further reading were available as of July 2007:
"Fractals: An Introductory Lesson" at http://www.arcytech.org/java/fractals/
"Classic Iterated Function Systems" at http://ecademy.agnesscott.edu/~lriddle/ifs/ifs.html
"Koch curve" at http://planetmath.org/encyclopedia/KochCurve.html
"Koch curve" at http://ccl.northwestern.edu/netlogo/models/KochCurve
Acknowledgment: I got started with Flash development at the Flash at the Beach MAA PREP workshop held at the University of Rhode Island in June 2007, which was directed by Doug Ensley and Barbara Kaskosz. I thank Doug and Barbara for their wonderful workshop and continued support!