  The scaling behaviour of the diffraction intensity near the origin is
investigated for (partially) ordered systems, with an emphasis on illustrative,
rigorous results. This is an established method to detect and quantify the
fluctuation behaviour known under the term hyperuniformity. Here, we consider
one-dimensional systems with pure point, singular continuous and absolutely
continuous diffraction spectra, which include perfectly ordered cut and project
and inflation point sets as well as systems with stochastic disorder.
