We combine technical, experimental, and theoretical efforts to investigate the collective dynamics of artificial microcilia in a viscous fluid. We take advantage of soft lithography and colloidal self-assembly to devise microcarpets made of hundreds of slender magnetic rods. This novel experimental setup is used to investigate the dynamics of extended cilia arrays driven by a precessing magnetic field. Whereas the dynamics of an isolated cilium is a rigid body rotation, collective beating results in a symmetry breaking of the precession patterns. The trajectories of the cilia are anisotropic and experience a significant structural evolution as the actuation frequency increases. We present a minimal model to account for our experimental findings and demonstrate how the global geometry of the array imposes the shape of the trajectories via long-range hydrodynamic interactions.