2020/07/21 by Nikolay Vereshchagin, Vereshchagin, Nikolay
Computer Science · Materials Science · Mathematics · #Cellular Automata and Applications #Combinatorics (math.CO) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2007.10658
openalex publication_date 2020/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a family of substitution tilings with similar right triangles of two sizes which is obtained using the substitution rule introduced in [Danzer, L. and van Ophuysen, G. A species of planar triangular tilings with inflation factor √(-τ). Res. Bull. Panjab Univ. Sci. 2000, 50, 1-4, pp. 137--175 (2001)]. In that paper, it is proved this family of tilings can be obtained from a local rule using decorated tiles. That is, that this family is sofic. In the present paper, we provide an alternative proof of this fact. We use more decorated tiles than Danzer and van Ophuysen (22 in place of 10). However, our decoration of supertiles is more intuitive and our local rule is simpler.