Fractals appear most conspicuously in plants such as ferns, cauliflower etc.
Here's something about fractals in erosion:
http://www.forester.net/ecm_0205_fractal.html
The article also explains fractals in general, Martinus.
A fractal is essentially anything that shows self-similarity at different levels of magnification.
It's not an American thing, even though images of Mandelbrot sets tend to have very loud colours.