Swimming in circles can lead to exotic hyperuniform states of active living matter

Fig. 1. Schematics indicating circular sampling windows in two dimensions for three different particle systems: garden-variety disordered nonhyperuniform (Left), disordered hyperuniform (Middle), and crystal (Right) configurations, as adapted from ref. 2. In each of these examples, the number of particles within a window will fluctuate as the window position varies, which specifies the local number variance sigma 2(R). In the case of a garden-variety disordered nonhyperuniform configuration, the variance sigma 2(R) grows like R2 (area of the window). By contrast, the disordered hyperuniform system, shown in the Middle, has a variance sigma 2(R) that grows like R (circumference of the window), which has the same growth rate