The spectacle of animals moving en masse is arguably one of the most fascinating phenomena in biology. For example, schools of fish can move in an orderly manner, and then change direction abruptly or, if under pressure from a nearby predator, swirl like a vigorously stirred fluid. The non-living world also has examples of collective motion, in systems that consist of units ranging from macromolecules to metallic rods, or even robots. On page 448 of this issue, Sumino et al. describe another, until now unobserved, example of such behaviour: the coordinated motion of hundreds of thousands of subcellular structures known as microtubules, which spontaneously self-organize into a lattice-like structure of vortices. When considered in the context of about half a dozen known universal classes of collective-motion pattern, this new structure poses challenges in terms of explaining how it can arise and its relevance to applications.