I read a book "Visual Complex Functions" by Elias Wegert. In it autor argues for so called phase portraits as a good way to visualize complex function of one complex variable. Each function value is represented by a pixel with a hue (which is an angular quantity) equal to function value's phase angle. He argues that the result provides a lot of information about function and even allows to restore analytic functions (up to a constant).
The other 2 components of the colorspace, saturation and light, can be used to show lines of equal phase and equal magnitude. Author calls it "enhanced phase portrait". Interesting, that there is no level tracing. Lines appear as a byproduct of using a modified hue palette. I put up a script and couple of sample images on wiki. 'sq' utility generates unit square of complex numbers. Evaluate your choice of function on it and color each pixel with ccEnhPh and you have yourself a phase portrait to view with viewmat or save with writebmp. http://code.jsoftware.com/wiki/User:Andrew_Nikitin/Phase_portraits I think that if you like pretty pictures (and want to get some insight on complex function behavior), this technique provides a lot of bang for a very little buck. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
