Physics – Mathematical Physics
Scientific paper
2006-01-12
IRMA - Lectures in Mathematical & Theoretical Physics 10 (2006) 79-131
Physics
Mathematical Physics
Scientific paper
One-dimensional cut-and-project point sets obtained from the square lattice in the plane are considered from a unifying point of view and in the perspective of aperiodic wavelet constructions. We successively examine their geometrical aspects, combinatorial properties from the point of view of the theory of languages, and self-similarity with algebraic scaling factor $\theta$. We explain the relation of the cut-and-project sets to non-standard numeration systems based on $\theta$. We finally examine the substitutivity, a weakened version of substitution invariance, which provides us with an algorithm for symbolic generation of cut-and-project sequences.
Gazeau Jean Pierre
Masáková Zuzana
Pelantová Edita
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