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arXiv · 2102.02497

A Rauzy fractal unbounded in all directions of the plane

Mélodie Andrieu
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Abstract

We construct an Arnoux-Rauzy word for which the set of all differences of two abelianized factors is equal to $\mathbb{Z}^3$. In particular, the imbalance of this word is infinite - and its Rauzy fractal is unbounded in all directions of the plane.

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Mélodie Andrieu. 2021-02-04. A Rauzy fractal unbounded in all directions of the plane. https://arxiv.org/abs/2102.02497

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