A new simple family of non-periodic tilings with square tiles

TL;DR

This paper introduces a new family of non-periodic tilings using square tiles, which are simple to generate and relate to triangle tilings, providing an accessible proof of their non-periodicity.

Contribution

It presents a novel, simple family of non-periodic square tile tilings that are mutually locally derivable with triangle tilings, with straightforward non-periodicity proofs.

Findings

New non-periodic tiling family with square tiles

Mutually locally derivable with triangle tilings

Simple proof of non-periodicity

Abstract

We define a new family of non-periodic tilings with square tiles that is mutually locally derivable with some family of tilings with isosceles right triangles. Both families are defined by simple local rules, and the proof of their non-periodicity is as simple as that of the non-periodicity of Robinson's tilings.