A Numeration System for Fibonacci-Like Wang Shifts

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Sébastien Labbé, Jana Lepsová

Published: 01 Jan 2021, Last Modified: 15 May 2025WORDS 2021EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Motivated by the study of Fibonacci-like Wang shifts, we define a numeration system for \(\mathbb {Z}\) and \(\mathbb {Z}^2\) based on the binary alphabet \(\{0,1\}\). We introduce a set of 16 Wang tiles that admits a valid tiling of the plane described by a deterministic finite automaton taking as input the representation of a position \((m,n)\in \mathbb {Z}^2\) and outputting a Wang tile.