Looks like I'm into animation this week. I found this site that shows animations of fractals:
There are dozens of sites like these, but this one has nice, clear graphics. Animations like these can surprise a kid who thinks math is boring!
I dabbled a little in fractal animation myself. The movie below comes from one of the models detailed in my book: Star Fractals (part of the GeomeTricks series). You start with two stars, one "fat" and one "skinny," and create a few levels of fractals for both. Eventually the stars look the same, except for the tiny points at the ends.