Courtesy of Konrad Polthier and Konstantin Poelke, Free University of Berlin
"Complex functions are important in many areas of mathematics, physics and engineering. A complex function is one in which both variables are complex numbers. The picture shows the visualization of a complex function using a specifically designed color scheme.
Following a technique called 'domain coloring,' the color scheme assigns a certain color to every complex number, inducing a coloring of the function domain according to its values at every point. So using this picture, you can explore properties of the function by easily spotting zeroes (black spots) or singularities (white spots). Contour lines indicate how the function deforms the complex plan."