ComplexToys.jl: Didactical Tools for Complex Analysis

Welcome to the documentation of the ComplexToys.jl package, a collection of useful plotting routines for teaching and learning complex analysis, based on DomainColoring.jl and Makie, often taking inspiration in the work of Wegert.^[1]

This online documentation is under construction. Take a look at the Guide to get started, or use the built-in help functionality of the Julia REPL.

To install run:

using Pkg; pkg"add ComplexToys"

The package includes interactive versions of the plots included in DomainColoring.jl:

• domaincolor(z->f(z)) plots various domain colorings of $f$;
• checkerplot(z->f(z)) and sawplot(z->f(z) plot various properties of $f$ in gray scale; and
• pdphaseplot(z->f(z) and tphaseplot(z->f(z) provide phase plots of $f$ readable to people with color vision deficiency.

A more comprehensive overview of these functions is given in the DomainColoring.jl documentation.

Additionally, a collection of three dimensional plots is provided:

• modularsurface(z->f(z)) plots a modular surface of $f$, i.e. a surface plot of the magnitude;
• riemannsphere(z->f(z)) plots a domain coloring of $f$ on the Riemann sphere;
• riemannpow(k) plots a projection of the Riemann surface of $z^k$; and
• riemannlog() plots a projection of the Riemann surface of $\log(z)$.