If you still do not know what Fractals are, you should read, a Fractal Awakening.

Julia Set:



Dragon Curve:



Sierpinskis Gasket:



Read about Serpinskis Magic Triangle.

Fractal Tree:



Lathe:

This is not really a fractal generator, but is really nice to play around with.



Resources:

Fractal Flash Source

A List of Fractal Generators

Java Based Fractal Generator

Wacker Art Fractal Generator