Abstract

Symmetry: Culture and Science
Volume 33, Number 1, pages 005-024 (2022)
https://doi.org/10.26830/symmetry_2022_1_005

ADDITIONS TO PENROSE NONPERIODIC TILING: A SIMPLE METHODOLOGICAL APPROACH

Robert Earl Dewar^*

^* Independent artist, 11600 Bonanza Dr., Tehachapi, CA 93561, USA.
E-mail: robertearldewar1@gmail.com

Abstract: A simple method is described that makes it easy to create new Penrose class tile patterns or artistic designs for use in the fields of art, architecture, and industrial design. The author describes how he first discovered a new tile pattern from the classic kites and darts pattern using a novel local transformation method and then shows how from using hindsight it would have been much easier to derive it using the simple method presented here. There are an unlimited number of tile patterns in the class of Penrose nonperiodic tilings, which are hypothetically derivable from those that are already known. This simple method makes it possible to create new patterns and designs without having to invent corresponding aperiodic tile sets with matching marks.

Keywords: aperiodic tiles, nonperiodic tiling, Penrose tiling, HBS tiling, DKL tiling, KDk tiling, einstein tiling

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