Graphs can be tremendously important in understanding mathematical functions, but issues arise when graphing complex functions. This is because complex functions have 2 dimensional inputs and 2 dimensional outputs, resulting in the need of 4 total dimensions.
To get around this, we can use colour wheel graphs (or domain colouring). This is a trick that uses colour to fill in the extra dimensions. The 2 dimensions required by the inputs are represented in the space of a picture. The 2 dimensions of our outputs are represented in colour. The argument of the output value gives us a pixel's hue, and its magnitude gives us its lightness. The saturation of all points is 100%. More information can be found in the references.
This program uses the Python Imaging Library, as well as a few libraries available in standard Python:
mathto make certain constants and functions easily available.cmathfor dealing with complex numbers.colorsysfor converting between different colour models.
This example was inspired by Wikipedia.
Converting the magnitude of the output vector to a saturation requires an extra parameter. Currently, this values needs to be determined through trial and error for each function. In future, it would hopefully be calculated somehow - likely in a way to create as much contrast as possible in the output image.