  We show how to achieve both fast and hyperuniform dispersions of particles in
viscous fluids. To do so, we first extend the concept of critical random
organization to chaotic drives. We show how palindromic sequences of chaotic
advection cause microscopic particles to effectively interact at long range
thereby inhibiting critical self-organization. Based on this understanding we
go around this limitation and design sequences of stirring and unstirring which
simultaneously optimize the speed of particle spreading and the homogeneity of
the resulting dispersions.
