A Rauzy fractal unbounded in all directions of the plane

DOI10.5802/CRMATH.162arXiv2102.02497MaRDI QIDQ6359805

Mélodie Andrieu

Publication date: 4 February 2021

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.

Mathematics Subject Classification ID

Combinatorics on words (68R15) Fractals (28A80) Irregularities of distribution, discrepancy (11K38) Irrationality; linear independence over a field (11J72) Tiling dynamics (37B52)

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