Check out how a double pendulum displays sensitivity to initial conditions in this narrated ram video.
This six-and-a-half minute narrated ram video shows how chaotic dynamical systems like severe storms can be numerically modeled.
The von Koch snowflake is a
self-similar curve with a dimension of (ln 4)/(ln 3) -- yes, that is a
fractional dimension which is a little over 1.26. This MPEG video
demonstrates its self-similarity. Set your player to loop and you will see
what we mean.
The dynamical systems and technology project at Boston University has developed a number of quicktime movies featuring fractal patterns. Check out the one-eyed starfish , a dancing sierpinksi , and this one called spiral mania.
The math department at the University of East
Anglia developed two MPEG videos of zooms on the Mandelbrot set:
animation the first and
animation the second.
If you want to
generate more images of the Mandelbrot Set and Julia Sets, take a look at
David Joyce's Geometric Pix Gallery, which not
only lets you generate images, it explains what they are.