Figure 7. Structural properties.

(A) Density plots of packing fraction and average individual speed (averaged per frame) as functions of rotation O_p and polarization O_r for 150 fish. (B) The plot illustrates the correlation between individual speed and local polarization estimated in two ways from the underlying density maps (the example shown in the background is for 150 fish). The stapled curves are produced by averaging across individual speeds for each value of the order parameter; the solid curves from averaging across the order parameter values for each individual speed. The local polarization of an individual fish is defined as the polarization Op restricted to the area inside a circle with radius 15.6 cm (approximately 3 body lengths) centered at the individual fish. (C) Average individual speed at different radial positions in the milling state. (D) Average rotational order parameter at the same positions. The radial division of the milling state in (C) and (D) is constructed by centering six shells outside each other, where the outermost shell has a radius defined by the distance from the group's center of mass to the median distance of the five most peripheral fish (see illustration in Fig. S11). The width of each shell is the radius of the outer shell divided by six. The averages are calculated for each shell, where the outer shell even includes peripheral fish.