Matthias Kawski
Department of Mathematics 
Arizona State University 		  
JAVA-Projects in Mathematics
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If you have NETSCAPE 6 (or a JAVA 2 appletviewer) take a look at this newest, still somewhat unstable, "essential"applet that allows one to ZOOM in on essential singularities -- the color-code is supposed to be close to the PhotoShop LAB model, but I still have to work on it....
This is a preview of the kind of imagery that we plan do do in a fully interactive way in my JAVA project. See z-squared for an interactive complex analysis JAVA demo.
Rings of lights
The series shows the error terms in Laurent approximations of a function z -> a/(z-z1)+b/(z-z2).
For the color-coding scheme see the excellent explanation by Frank Farris at http://www-acc.scu.edu/~ffarris/complex.html. The basic idea is to use the relative magnitudes of RGB to code the argument of a complex number, and use the brightness to code its magnitude. In terms of the Riemann sphere, color 0 at the North pole white and infinity at the South pole black, and use a rainbow along the equator -- e.g. representing the unit-circle...

These images were created using MATLAB, numerically calculating the coefficients of the Laurent series via Cauchy's integral formula and using elaborate mappings of a (Riemann) sphere onto a surface close to the faces of a (color) cube.... Using the new JAVA Foundation-classes in JAVA 2 we are working on a fully interactive version -- the above images shall serve as inspiration and guidepost for the desired quality...

For more recent related work see the JOMA article by Andrew Bennett on a Complex Function Grapher.