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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, 37B10, 28A80, 43A25 show english descriptions Quasicrystals, aperiodic tilings
Symbolic dynamics [See also 37Cxx, 37Dxx]
Fractals [See also 37Fxx]
Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
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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