Tileset As: 3 squares with local rules for non-periodic tiling

This paper presents a tileset of 3 squares with local constraints on their borders and corners that enforce non-periodic tiling. We start with a description of the tileset and we demonstrate that it can tile the entire plane non-periodically creating interesting patterns. Rules are also proposed to generate the tiling. They make use of 9 supertiles with border color constraints only.

Publication Details

Journal
ArXiv.org
Published
2025-03-03
Primary Topic
Quasicrystal Structures and Properties
Type
article
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article

Tileset As: 3 squares with local rules for non-periodic tiling

ArXiv.org
Quasicrystal Structures and Properties
article

Tileset As: 3 squares with local rules for non-periodic tiling

article en

Abstract

This paper presents a tileset of 3 squares with local constraints on their borders and corners that enforce non-periodic tiling. We start with a description of the tileset and we demonstrate that it can tile the entire plane non-periodically creating interesting patterns. Rules are also proposed to generate the tiling. They make use of 9 supertiles with border color constraints only.

ArXiv.org
Openalex Percentile: Top 60%
Quasicrystal Structures and Properties
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Tileset As: 3 squares with local rules for non-periodic tiling · ArXiv.org (2025) | TGRS Research Map | TGRS