On the self-similarities of the Penrose tiling

TL;DR

This paper demonstrates that the Penrose tiling possesses infinitely many independent scaling factors and inflation centers, revealing complex self-similarity properties.

Contribution

It uncovers the existence of infinite independent scaling factors and inflation centers in Penrose tilings, advancing understanding of their self-similar structure.

Findings

Penrose tiling has infinitely many scaling factors.

Penrose tiling admits infinitely many inflation centers.

Reveals complex self-similarity in Penrose tilings.

Abstract

We show that the well known two-dimensional Penrose tiling admits an infinite number of independent scaling factors and an infinite number of inflation centers.