Hans Lundmark has an interesting page on visualizing complex functions. The idea is to map functions from f : C → C using position, hue, and saturation. The domain values of the function provide the (x, y) position. The function output value provides the hue and saturation; the hue is determined by the complex argument (angle), and the saturation is determined by the absolute value.
The output struck me as a nice example of algorithmic art. I whipped up my own version in Java to experiment, and to be able to produce high-resolution images for printing. Here's a couple of my images:
An example function from the paper ( f ( z ) = ( z − 2 )2 ( z + 1 − 2i ) ( z + 2 + 2i ) / z3 )