Here’s the most bizarre video I’ve seen recently. (Patience is required; it takes forever to load.)
There are more sponges and other three-dimensional fractals here, here and here.
Addendum: For sheer trippiness, nothing beats the Mandelbrot set. Here’s the classic fractal video, “Nothing but Zooms,” presented in four parts. Unfortunately, the image quality is low, even for YouTube.
Part one
Part two
Part three
Part four
Here are some more videos of varying degrees of gimmickiness featuring the ultimate paisley.
This one
That one
This other one
What’s the Mandelbrot set? Let Jonathan Coulton explain. (N.B.: naughty words.)