The most known Kolakoski sequence is defined on the alphabet set $\{1,2\}$. It is used as a fixed point of the run-length encoding operator. But what about the sequence constructed on $\{1,3\}$. Are there any applications of this sequence ?.
2026-03-29 18:32:17.1774809137
Are there any practical applications of the Kolakoski sequence $(1,3)$.
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Unlike the classical Kolakoski sequence on the alphabet $\{1,2\}$, it's analogue on $\{1,3\}$ can be related to a primitive substitution rule. Using this connection, it has been proven that the corresponding bi-infinite fixed point is a regular generic model set and thus having a pure point diffraction spectrum. The Kolakoski-$(3,1)$ sequence is then obtained as a deformation, without losing the pure point diffraction property.
I hope you can get the required information in this paper by Baake and Sing. Hope it helps.