2021/10/15 by Theo P. Schaad, Schaad, Theo P.
Biochemistry, Genetics and Molecular Biology · Materials Science · #DNA and Biological Computing #FOS: Mathematics #General Mathematics (math.GM) #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2112.00625
openalex publication_date 2021/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A quasiperiodic 7-fold rhombic tiling is constructed with an iterative substitution scheme. The inflation factor is 5.04892..., the square of the longer diagonal of a regular heptagon. There are many substitutions possible that fill larger similar tiles with three base shapes but finding the matching rules (how the larger tiles fit together to make even larger tiles) turns into a challenging puzzle. At the end, a new solution is found with seven substitution rules. The relationship to a higher-order Fibonacci series is explored. The tiling is presented with a celestial theme reminiscent of a starry night.