Domain Coloring of Complex Functions

Visualizing functions is an omnipresent task in many sciences and almost every day we are confronted with diagrams in newspapers and magazines showing functions of all possible flavours. Usually such functions are visualized by plotting their function graph inside an appropriate coordinate system, with the probably most prominent choice being the cartesian coordinate system. This allows us to get an overall impression of the function’s behaviour as well as to detect certain distinctive features such as minimal or maximal points or points where the direction of curvature changes. In particular, we can “see” the dependence between input and output. However, this technique is limited to three dimensions, simply because we do not know how to draw higher-dimensional cartesian coordinate systems.