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 loosing the pure point diffraction property.
Categories: math.MG