  We demonstrate that the complex spatiotemporal structure in active fluids can
feature characteristics of hyperuniformity. Using a hydrodynamic model, we show
that the transition from hyperuniformity to non-hyperuniformity and
anti-hyperuniformity depends on the strength of active forcing and can be
related to features of active turbulence without and with scaling
characteristics of inertial turbulence. Combined with identified signatures of
Levy walks and non-universal diffusion in these systems, this allows for a
biological interpretation and the speculation of non-equilibrium hyperuniform
states in active fluids as optimal states with respect to robustness and
strategies of evasion and foraging.
