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Kolakoski-$(3,1)$ Is a (Deformed) Model Set

Published:2004-06-01
Printed: Jun 2004
• Michael Baake
• Bernd Sing
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Abstract

Unlike the (classical) Kolakoski sequence on the alphabet $\{1,2\}$, its analogue on $\{1,3\}$ can be related to a primitive substitution rule. Using this connection, we prove that the corresponding bi-infinite fixed point is a regular generic model set and thus has a pure point diffraction spectrum. The Kolakoski-$(3,1)$ sequence is then obtained as a deformation, without losing the pure point diffraction property.
 MSC Classifications: 52C23 - Quasicrystals, aperiodic tilings 37B10 - Symbolic dynamics [See also 37Cxx, 37Dxx] 28A80 - Fractals [See also 37Fxx] 43A25 - Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups

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