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Self-similar binary one-dimensional (1D) quasilattices (QLs) are classifiedinto mutual local-derivability (MLD) classes. It is shown that the MLDclassification is closely related to the number-theoretical classification ofparameters which specify the self-similar binary 1D QLs. An algorithm to derivean explicit substitution rule, which prescribes the transformation of a QL intoanother QL in the same MLD class, is presented. An explicit inflation rule,which prescribes the transformation of the self-similar 1D QL into itself, isobtained as a composition of the explicit substitution rules. Symmetricsubstitution rules and symmetric inflation rules are extensively discussed.Comment: 24 pages, 4 figures, submitted to PR

Binary Self-Similar One-Dimensional Quasilattices: Mutual Local-Derivability Classification and Substitution Rules