1997/07/30 by C. L. Henley, Christopher L. Henley, Henley, C. L.
Computer Science · Materials Science · Physics and Astronomy · #Cellular Automata and Applications #Condensed Matter (cond-mat) #FOS: Physical sciences #Quasicrystal Structures and Properties #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9707326
4 pages, LaTeX; two eps figures; to appear, Proceedings of the 6th International Conference on Quasicrystals (Tokyo, 1997)
arxiv created 1997/07/30 · openalex publication_date 1997/07/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Jeong and Steinhardt (JS) implement local rules by selecting the sub-ensemble of tilings which have the maximum occurrences of a chosen pattern (``cluster'') C It is unknown how to prove that a given C implies a given sub-ensemble; counterexamples given here demonstrate this problem is nonlocal, and show the JS results depend on periodic boundary conditions. Sub-ensembles which are tilings of supertiles are at least as interesting, mathematically and physically, as the ideal cases emphasized by JS; the case C = star-decagon is explored here. Finally, I suggest minimizing the frequency of chosen intersite distances as a more physical alternative to the cluster approach.