Binary self-similar one-dimensional quasilattices: Mutual local-derivability classification and substitution rules

Details Binary self-similar one-dimensional quasilattices: Mutual local-derivability classification and substitution rules Binary self-similar one-dimensional quasilattices: Mutual local-derivability classification and substitution rules

2001-05-02

arxiv.org/abs/cond-mat/0105023v1

J. Phys. Soc. Jpn., Vol.70, pp.2918-2933 (2001)

Physics

Condensed Matter

24 pages, 4 figures, submitted to PRB

Scientific paper

10.1143/JPSJ.70.2918

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.

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