Domain Coloring of Complex Functions: An Implementation-Oriented Introduction

This article gives a short overview of domain coloring for complex functions that have four-dimensional function graphs and therefore can't be visualized traditionally. The authors discuss several color schemes, focus on various aspects of complex functions, and provide Java-like pseudocode examples explaining the crucial ideas of the coloring algorithms to allow for easy reproduction.

What is a Function?

Let's briefly recap the definition of a function to fix terminology. A function consists of three parts: first, a set of input values, which is called the domain of the function; second, a set called the range of and third, for every input value , a unique value , called the function value of at , denoted . The set of all pairs , is a subset of the product set and called the function graph of .