Markov partitions for toral ℤ 2 -rotations featuring Jeandel–Rao Wang shift and model sets

We define a partition $\mathcal{P}_0$ and $\mathbb{Z}^2$-rotation ($\mathbb{Z}^2$-action defined by rotations) on 2-dimensional torus whose associated symbolic dynamical system is minimal proper subshift of the Jeandel-Rao aperiodic Wang shift 11 tiles. another $\mathcal{P}_\mathcal{U}$ $\mathbb{T}^2$ equal to 19 This proves that Markov for $\mathbb{T}^2$. prove in both cases toral maximal equicontinuous factor subshifts set fiber cardinalities map $\{1,2,8\}$. The two are uniquely ergodic isomorphic as measure-preserving systems $\mathbb{Z}^2$-rotations. It provides construction these shifts model sets 4-to-2 cut project schemes. A do-it-yourself puzzle available appendix illustrate results.