Visualizing Complex Functions

From the paper (PDF) “Lifted Domain Coloring” by Konstantin Poelke and Dr. Konrad Polthier:

Domain coloring, as the name suggests, makes use of a color spectrum to compensate the missing dimension. More precisely, we discard the approach of plotting the function somehow on an independent axis (as we would do when we plot the modulus over the domain, for instance), but plot it right onto the domain, i.e. we color the domain in a particular way. Now, the effectiveness and flexibility of domain coloring lies in the choice
of an adequate reference color scheme…The new color schemes specifically enhance the display of singularities, symmetries and path integrals…

Those color schemes also make killer desktop backgrounds.