Laura Seaberg, Boston College
2022 AWM Research Symposium
Poster Presentation

Consider the question of expanding a real number in a non-integer base with a set of specified digits as coefficients. For some cases, there exist expansions with desirable properties--in particular, using a Pisot number $\beta$ (a real algebraic integer greater than 1 with all Galois conjugates inside the open unit disk) as a base and all nonnegative integers less than $\beta$ as digits permits dynamically interesting expansions. We survey work by Thurston, Akiyama, and others, which constructs a self-similar tiling of the plane using such information. To do this, a projection of the Minkowski embedding of the number field $\mathbb{Q}(\beta)$ encodes the information of a tiling through digit expansions. These tilings have prototiles with fractal boundary and are easily understood as substitution tilings, in addition to being visually striking.

Back to Search Research Symposium Abstracts