Binary self-similar one-dimensional quasilattices: Mutual local-derivability classification and substitution rules
arXiv:cond-mat/0105023 · doi:10.1143/JPSJ.70.2918
Abstract
Self-similar binary one-dimensional (1D) quasilattices (QLs) are classified into mutual local-derivability (MLD) classes. It is shown that the MLD classification is closely related to the number-theoretical classification of parameters which specify the self-similar binary 1D QLs. An algorithm to derive an explicit substitution rule, which prescribes the transformation of a QL into another QL in the same MLD class, is presented. An explicit inflation rule, which prescribes the transformation of the self-similar 1D QL into itself, is obtained as a composition of the explicit substitution rules. Symmetric substitution rules and symmetric inflation rules are extensively discussed.
24 pages, 4 figures, submitted to PRB