Visualizing modular forms

Abstract

We examine several currently used techniques for visualizing complex-valued functions applied to modular forms. We plot several examples and study the benefits and limitations of each technique. We then introduce a method of visualization that can take advantage of colormaps in Python's matplotlib library, describe an implementation, and give more examples. Much of this discussion applies to general visualizations of complex-valued functions in the plane.

20 pages, many figures, after first major set of revisions

References in corpus (3)

• Optimizing colormaps with consideration for color vision deficiency to enable accurate interpretation of scientific data
• Good Colour Maps: How to Design Them
• Phase Plots of Complex Functions: a Journey in Illustration

Cited by in corpus (1)

• Computing classical modular forms