Kolakoski sequences – an example of aperiodic order

Abstract (Generalized) Kolakoski sequences are built of two symbols – similar to the Fibonacci-chain – and can be constructed by a very simple rule. They are general enough to allow a richness of structures: e.g., some show pure point diffraction spectrum, others diffuse scattering. We will illustrate the methods to classify these sequences and to calculate their diffraction spectra. But we will also indicate that there are still open questions in the theory of diffraction of one-dimensional aperiodic sequences.