A novel variant of rhombic Penrose tiling

TL;DR

This paper introduces a new variant of rhombic Penrose tiling with unique visual features, increased complexity, and enhanced hyperuniform order, expanding the understanding of quasiperiodic tilings with tenfold symmetry.

Contribution

It presents a novel quasiperiodic tiling variant with additional prototiles and complex patterns, maintaining key properties of Penrose tilings while introducing new structural features.

Findings

Shares key features with Penrose tiling, including vertex environments and inflation symmetry.

Displays a high density of decagonal motifs forming flower patterns.

Shows a slightly higher degree of hyperuniform order than standard Penrose tiling.

Abstract

We present a novel variant of a planar quasiperiodic tiling with tenfold symmetry, employing the same thick and thin rhombuses as the celebrated rhombic Penrose tiling. Despite its distinct visual appearance, this new tiling shares several key features with its predecessor, including similar vertex environments, polygonal acceptance domains based on regular pentagons, and an inflation/deflation symmetry associated with the golden mean as its fundamental scaling ratio. Additional complexities arise from an increased number of prototiles and a dual grid pattern that incorporates folded lines alongside ordinary straight lines. This tiling exhibits a high density of a compact decagonal motif forming a two-tiered, five-petaled flower pattern, which spans a substantial portion of the tiling. We identify a slightly enhanced degree of hyperuniform order compared to the standard rhombic Penrose tiling.