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.

中文翻译：

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斐波那契式王移位的计数系统

通过研究类似斐波那契的王氏移位，我们基于二进制字母$ \ {0,1 \} $为$ \ mathbb {Z} $和$ \ mathbb {Z} ^ 2 $定义了一个计数系统。我们引入了一组16个Wang瓦片，它们接受由确定性有限自动机描述的平面的有效平铺，并以位置$（m，n）\ in \ mathbb {Z} ^ 2 $的表示作为输入并输出Wang瓦。