Unique Indexing of Penrose Tiles and Its Application to Information-Bearing Markers

Abstract

We propose a method of uniquely indexing tiles in a geometric pattern composed of kites and darts, known as Penrose tilings. This indexing is based on inflation, which is a property to generate larger tiles hierarchically, and independent of rotation and scaling of the pattern. By the indices of specific tiles in a pattern we can communicate information, as we do with Quick Response (QR) codes and Augmented Reality (AR) markers. We present a decoding method with these applications in mind, in which inflation is applied to identified tiles retrieving embedded code using pattern matching based on the geometric hashing. We also present a technique to identify specific tiles in an invisible way. We generated a pattern composed of 6251 tiles in which we can potentially embed 69813 bits of information using our method.