A Family of Non-Periodic Tilings, Describable Using Elementary Tools and Exhibiting a New Kind of Structural Regularity
2025/06/09 by Miki Imura, Imura, Miki · 9 voices
Computer Science · Engineering · Materials Science · Mathematics · #Advanced Materials and Mechanics #Algebra over a field #Cellular Automata and Applications #Class (philosophy) #Modular design #Orthogonality #Quasicrystal Structures and Properties #Term (time) #Type (biology) #math.CO
paper · pdf · doi:10.48550/arxiv.2506.07638
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract
We present a construction of a family of non-periodic tilings using elementary tools such as modular arithmetic and vector geometry. These tilings exhibit a distinct type of structural regularity, which we term modulo-staggered rotational symmetry. The construction is self-contained and does not rely on previous tiling theories or systems.
Citations
Discussions
- A Family of Non-Periodic Tilings, Describable Using Elementary Tools [hn, 80 points, 10 comments]
- Whoah! More aperiodic monotiles! https://arxiv.org/abs/2506.07638 [bsky, 4 points, 1 comments]
- arxiv.org/pdf/2506.07638 arxiv.org/pdf/2506.07638 [bsky, 2 points, 0 comments]
- A Family of Non-Periodic Tilings, Describable Using Elementary Tools https://arxiv.org/abs/2506.07638 [bsky, 0 points, 0 comments]
- A Family of Non-Periodic Tilings, Describable Using Elementary Tools https://arxiv.org/abs/2506.07638 [comments] [38 points] [bsky, 0 points, 0 comments]
- https://arxiv.org/abs/2506.07638 この論文では、非周期的なタイリングの新しいファミリーを紹介しています。 初等的なツールで記述可能で、新しい構造規則性を示しています。 詳細はarXivのリンクを参照してください。 [bsky, 0 points, 0 comments]
- A Family of Non-Periodic Tilings, Describable Using Elementary Tools [bsky, 0 points, 0 comments]
- A Family of Non-Periodic Tilings, Describable Using Elementary Tools https://arxiv.org/abs/2506.07638 (https://news.ycombinator.com/item?id=44240691) [bsky, 0 points, 0 comments]
- A Family of Non-Periodic Tilings, Describable Using Elementary Tools https://arxiv.org/abs/2506.07638 (https://news.ycombinator.com/item?id=44240691) [bsky, 0 points, 0 comments]
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