1and driven systems [2][3][4][5] . It is commonly held that potential interactions 6 , depletion forces 7 , or sensing 8 are the only mechanisms which can create long-lived compact structures. Here we show that persistent motile structures can form spontaneously from hydrodynamic interactions alone, with no sensing or potential interactions. We study this structure formation in a system of colloidal rollers suspended and translating above a floor, using both experiments and large-scale three-dimensional simulations. In this system, clusters originate from a previously unreported fingering instability, where fingers pinch o from an unstable front to form autonomous 'critters', whose size is selected by the height of the particles above the floor. These critters are a stable state of the system, move much faster than individual particles, and quickly respond to a changing drive. With speed and direction set by a rotating magnetic field, these active structures o er interesting possibilities for guided transport, flow generation, and mixing at the microscale.We have identified a new instability in one of the most basic systems of low-Reynolds-number (steady Stokes or overdamped) flow, a collection of spheres rotating near a wall. This system has been well studied analytically and numerically 9,10 , since it is considered a base model for understanding many microbial and colloidal flows. The instability visually resembles wet paint dripping down a wall or individual droplets sliding down a windshield 11 -examples of Rayleigh-Taylor instabilities 12 . However, in those and other clustering phenomena, what holds things together is surface tension or other forces deriving from an interaction potential.Here we use a model system to explore whether hydrodynamic interactions alone, without particle collisions, attractions or sense/response redirection, can lead to stable finite clusters.The experimental system consists of polymer colloids with radius a = 0.66 µm which have a small permanent magnetic moment (|m| ∼ 5 × 10 −16 A m −2 ) from an embedded haematite cube 13 (see schematic in Fig. 1a). Inter-particle magnetic interactions are small compared to thermal energy (< 0.1k B T ). A rotating magnetic field (B = B 0 cos(ωt)x + sin(ωt)ẑ ) with magnitude B 0 and frequency f = ω/2π is applied, causing all the particles to rotate about the y-axis at the same rate ω. The particles rotate synchronously with the field for ω < ω c , where ω c is the critical frequency above which the applied magnetic torque is not enough to balance the viscous torque on the particle (see Supplementary Section I for details of the rotation mechanism). In all of our experiments, ω < ω c . In contrast with recent experiments on Quincke rollers 14 , the rotation direction is prescribed and does not arise from the system dynamics.Hydrodynamics is the dominant inter-particle interaction in this system, which is distinctly different from many other systems of rotating magnetic particles, where dynamics is found to be a strong function of inter-particle ...