Kolakoski-(2m, 2n) Are Limit-periodic Model Sets

We consider (generalized) Kolakoski sequences on an alphabet with two even numbers. They can be related to a primitive substitution rule of constant length l. Using this connection, we prove that they have pure point dynamical and pure point diffractive spectrum, where we make use of the strong interplay between these two concepts. Since these sequences can then be described as model sets with l-adic internal space, we add an approach to “visualize” such internal spaces.