  In periodically sheared suspensions there is a dynamical phase transition
characterized by a critical strain amplitude $\gamma_c$ between an absorbing
state where particle trajectories are reversible and an active state where
trajectories are chaotic and diffusive. Repulsive non-hydrodynamic interactions
between "colliding" particles' surfaces have been proposed as a source of this
broken time reversal symmetry. A simple toy model called Random Organization
qualitatively reproduces the dynamical features of this transition. Random
Organization and other absorbing state models exhibit hyperuniformity, a strong
suppression of density fluctuations on long length-scales quantified by a
structure factor $S(q \rightarrow 0) \sim q^\alpha$ with $\alpha > 0$, at
criticality. Here we show experimentally that the particles in periodically
sheared suspensions organize into structures with anisotropic short-range order
but isotropic, long-range hyperuniform order when oscillatory shear amplitudes
approach $\gamma_c$.
