Complex domain coloring (also sometimes called "reverse mapping") is a method of visualizing complex function of complex variable. It is a natural generalization of density plots and contour plots of real functions of two variables. You can find a very good introduction into the topic at Hans Lundmark's complex analysis pages. There is also this Wikipedia page.
Originally, when I started experimenting with this method, I used the Gnu Image Manipulation Program a.k.a. GIMP, together with MathMap Plugin. Lately I have been using couple of simple python scripts with the help of numpy module and Python Imaging Library.
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