Fractals

[Slavakion]

I was trying to learn what fractals were and figured I'd ask TFP. What I know so far...

There is a function that contains the terms z and c. Z is a variable point while c is a constant including a real and nonreal component.
ex. f(z)=z^2 + c
z=5
c=1 + 2.3i

Something about how the output value only belongs to the set if it doesn't rapidly approach infinity (?). Fractals have the property that if you magnify a small part it's the same as the original view (or something a bit more elegantly stated).

Please, correct me. I don't think I know what I'm talking about.

[shakran]

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