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

Self-similar binary one-dimensional (1D) quasilattices (QLs) arc, classifie d into mutual local-derivability (MLD) classes. It is shown that the MLD cl assification is closely related to the number-theoretical classification of parameters which specify the self-similar binary 1D QLs. An algorithm to d erive an explicit substitution rule, which prescribes the transformation of a QL into another QL in the same MLD class, is presented. An explicit infl ation rule, which prescribes the transformation of the self-similar 1D QL i nto itself, is obtained as a composition of the explicit substitution rules . Symmetric substitution rules and symmetric inflation rules are extensivel y discussed.