A Markov partition for Jeandel-Rao aperiodic Wang tilings
Sebastien Labbé · arXiv (Cornell University) · 2019
We define a Markov partition for a $\mathbb{Z}^2$-rotation on the 2-dimensional torus whose associated symbolic dynamical system is a minimal and aperiodic Wang shift defined by 19 Wang tiles. We define another partition for another $\mathbb{Z}^2$-rotation on a 2-dimensional torus whose associated symbolic dynamical system is a minimal proper subshift of the Jeandel-Rao aperiodic Wang shift defined by 11 Wang tiles. As a result, we prove in both cases that the $\mathbb{Z}^2$-rotation on the torus is the maximal equicontinuous factor of the minimal subshifts. It provides a construction of these Wang tilings as model sets of 4-to-2 cut and project schemes. A do-it-yourself puzzle is available in the appendix to illustrate the results.