  Particles occupying sites of a random lattice present density fluctuations at
all length scales. It has been proposed that increasing interparticle
interactions reduces long range density fluctuations, deviating from random
behaviour. This leads to power laws in the structure factor and the number
variance that can be used to characterize deviations from randomness which
eventually lead to disordered hyperuniformity. It is not yet fully clear how to
link density fluctuations with interactions in a disordered hyperuniform
system. Interactions between superconducting vortices are very sensitive to
vortex pinning, to the crystal structure of the superconductor and to the value
of the magnetic field. This creates lattices with different degrees of
disorder. Here we study disordered vortex lattices in several superconducting
compounds (Co-doped NbSe$_2$, LiFeAs and CaKFe$_4$As$_4$) and in two amorphous
W-based thin films, one with strong nanostructured pinning (W-film-1) and
another one with weak or nearly absent pinning (W-film-2). We calculate for
each case the structure factor and number variance and compare to calculations
on an interacting set of partially pinned particles. We find that random
density fluctuations appear when pinning overcomes interactions and show that
the suppression of density fluctuations is indeed correlated to the presence of
interactions. Furthermore, we find that we can describe all studied vortex
lattices within a single framework consisting of a continous deviation from
hyperuniformity towards random distributions when increasing the strength of
pinning with respect to the intervortex interaction.
