  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.
