A characterization of Thurston's Master Teapot

TL;DR

This paper provides an explicit, algorithmically implementable characterization of Thurston's Master Teapot, enabling the determination of whether points belong to its complement, and explores its geometric symmetry properties.

Contribution

It offers the first explicit description of the Master Teapot points and demonstrates a specific asymmetry in its intersection with the unit cylinder.

Findings

Explicit characterization of the Master Teapot

Algorithm for testing point membership

Asymmetry in the intersection with the unit cylinder

Abstract

We prove an explicit characterization of the points in Thurston's Master Teapot. This description can be implemented algorithmically to test whether a point in $\mathbb{C} \times \mathbb{R}$ belongs to the complement of the Master Teapot. As an application, we show that the intersection of the Master Teapot with the unit cylinder is not symmetrical under reflection through the plane that is the product of the imaginary axis of $\mathbb{C}$ and $\mathbb{R}$.