I agree, fractals are beautiful and fascinating. I tried to get my kids interested in them a while back and did a little research. From what I understand, it has to do with fracturing and moving parts of an original whole.
Here is the best not-so-mathematical definition I could find: "A rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole."

So it is a math thing, but there are programs for creating fractals and they make you think you don't have to understand the mathematics of it. Go to google.com and search for fractal programs free. Maybe you'll give it a go!
Here are the two best sites I could find illustrating what happens in fractals:
http://www.go2net.com/internet/deep/1996/12/11/
and
http://hobbe.lub.lu.se/~hakan/papers/fract/fract/node5.html

BTW, I read your profile and I admire your basket-weaving ability. That takes as much talent as, if not more than, creating fractals!

Lia, Thanks for your response and the info. I think I'll give it a try. dar

hi dar, you're welcome.
I thought I remembered a site where you could save and print examples of fractal artwork. Can't find the one I had in mind, but here's another: http://kitara.org/ I assume they are for personal use only; you'd have to read the guidelines there.
This site: http://www.aartika.co.uk/uf/index.html has a nice gallery, and allows saving images to use in your artwork if you get their permission first.
Thanks for reminding me about this art form!

Hi,

I would like to kindly suggest our site to check where you can find free fractal art software and public gallery as well.
Bests,
Esthefan