Aperiodic Tilings on the Computer

TL;DR

This paper reviews methods for constructing quasiperiodic tilings, including projection, inflation, and grid techniques, with sample Mathematica programs demonstrating these approaches in one and two dimensions.

Contribution

It provides a comparative overview of standard quasiperiodic tiling construction methods and shares sample code implementations for educational purposes.

Findings

Different methods produce equivalent tilings

Sample Mathematica programs illustrate each approach

Programs are available electronically for further use

Abstract

We briefly review the standard methods used to construct quasiperiodic tilings, such as the projection, the inflation, and the grid method. A number of sample Mathematica programs, implementing the different approaches for one- and two-dimensional examples, are discussed. Apart from small examples, the corresponding programs are not contained in the text, but will be made available in electronic form.