A Markov Partition For The Penrose Wang Shift

Harper Hults, Hikaru Jitsukawa, Casey Mann, Justin Zhang

Published 2023-02-27Version 1

It was recently shown in the Ph.D. thesis of H. Jang that any tiling by the Penrose rhombs is equivalent to a Wang tiling by a protoset of 24 Wang tiles. All such Wang tilings admited by these 24 Wang tiles we call the Penrose Wang shift. In this article, we demonstrate the existence of a Markov partition for the Penrose Wang shift that encodes the entire Penrose Wang shift via a Z2-action. Further, using the Markov partition, we demonstrate that the Penrose Wang shift exhibits 5 nonexpansive directions.