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

http://dx.doi.org/10.4153/CMB-2004-018-6
Canad. Math. Bull. 47(2004), 168-190

  Published:2004-06-01
 Printed: Jun 2004

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.