Ok here we go (fractal set of Mandelbrot/Julia):

first you have to know what a complex number is, a complex number is composed of 2 numbers, the real and imaginery parts (this is used to described two dimensions, you can picture the real part as X and the imaginery part as Y). Such a number is written:

Z = X + iY (i is a special number such that i**2=-1 (**2 means squared).

A serie is defined as a recursive function: Z_n = f(Z_(n-1)), so in the case of the fractal set, it's the following equation:

Z_n = (Z_(n-1))**2 + C (where Z and C are complex numbers).

We start with Z_0 = C

Z_1 = Z_0**2 + C

and so on.

If the serie diverge (its modulus becomes superior to 2), we plot it in black. If after n iteration the serie hasn't diverged, we color it with a color representing its value.

So the fractal aspect here is that a finite equation cannot computes if the Z_infinite diverges or converges (and if so to what value).

You can see the display of computation I just described at:

http://mathforum.org/alejandre/applet.mandlebrot.htmlBut you see the problem is pretty simple, and the definition of chaos in this context is crystal clear. It's chaotic in the sense that it cannot be predicted by other means that actually computing it infinitely (which is not feasible apparently).

TheLight