  Coherent vortical motion has been reported in a wide variety of populations
including living organisms (bacteria, fishes, human crowds) and synthetic
active matter (shaken grains, mixtures of biopolymers), yet a unified
description of the formation and structure of this pattern remains lacking.
Here we report the self-organization of motile colloids into a macroscopic
steadily rotating vortex. Combining physical experiments and numerical
simulations, we elucidate this collective behavior. We demonstrate that the
emergent-vortex structure lives on the verge of a phase separation, and single
out the very constituents responsible for this state of polar active matter.
Building on this observation, we establish a continuum theory and lay out a
strong foundation for the description of vortical collective motion in a broad
class of motile populations constrained by geometrical boundaries.
