When studying real functions of one or two variables, an intuitive grasp of some properties one acquires looking at their graphs. Unlike real functions of one or two variables, whose graphs are curves in $\mathbb{R}^2$, respectively surfaces in $\mathbb{R}^3$, the graph of a complex function, $f:\mathbb{C}\to\mathbb{C}$, lies in $\mathbb{R}^4$. Visualization in four dimensions is a difficult task and the method employed depends on the "geometry" of the object to be visualized.

Fortunately, the development of cylindrical color models, such as HSL and HSV, and the possibility to express the values $f(z)$ of a complex function in polar coordinates, $f(z)=|f(z)|\exp(i \arg(f(z))$, led to the design of a fruitful technique of visualization of the values of a complex function through a color-coding method. This method is called domain coloring.

A list of references dedicated to visualization of complex functions, as well as of the software implementations of different methods of visualization can be found in Notices of AMS and on Hans Lundmark's complex analysis pages.