Volvox barberi flocks actively, forming near-optimal, two-dimensional, polydisperse lattice packings

Volvox barberi are multicellular protists forming spherical colonies of 10000-50000 differentiated somatic and germ cells. Here, I show that these colonies actively self-organize over minutes into “flocks” that can contain more than 100 colonies moving and rotating collectively for hours. The colonies in flocks form two-dimensional, irregular, “active crystals”, with lattice angles and colony diameters both following log-normal distributions. Comparison with a molecular dynamics simulation of soft spheres with diameters matched to the Volvox, and a weak long-range attractive force, show that the Volvox flocks achieve optimal random close-packing. A dye tracer in the Volvox medium reveals large hydrodynamic vortices generated by colony and flock rotations, providing a likely source of the forces leading to flocking and optimal packing.