I believe in keeping it simple. Fractals are objects that are similar at different magnifications.
Here's a good example. The left hand image is a Mandelbrot set. Click anywhere on the image to zoom in. As you zoom you'll notice that at high levels of magnification, it looks quite a bit like it does zoomed all the way out.
http://aleph0.clarku.edu/~djoyce/julia/explorer.html