Converting non-periodic tilings with Tile(1, 1) into tilings with three types of pentagons, I

2023/07/17 by Teruhisa Sugimoto, Sugimoto, Teruhisa
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · #05B45 #52C20 #Cellular Automata and Applications #DNA and Biological Computing #F.2.2 #FOS: Mathematics #Metric Geometry (math.MG) #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2307.08184

openalex publication_date 2023/07/17 · openalex created_date 2023/07/19 · openalex updated_date 2026/07/28

Abstract

Non-periodic tilings with Tile(1, 1) using the substitution method, as presented by Smith et al. in [2] and [3], can be converted into non-periodic tilings with three types of pentagons. When arbitrary replacements are excluded, the resulting non-periodic tilings with three types of pentagons exhibit two patterns. Note that, during the conversion process in this manuscript, the rhombus is not subdivided into smaller similar rhombuses.

Related

• Converting tilings with multiple types of rhombuses to pentagonal tilings
• A new simple family of non-periodic tilings with square tiles
• Generalization of Non-periodic Rhomb Substitution Tilings
• A non FLC regular pentagonal tiling of the plane
• Nonperiodic tilings related to Stern's diatomic series and based on tiles decorated with elements of \mathbbF_p