Saturn's narrow F ring exhibits several unusual features that vary on timescales of hours to years. These include transient clumps, a central core surrounded by a multistranded structure and a regular series of longitudinal channels associated with Prometheus, one of the ring's two `shepherding' satellites. Several smaller moonlets and clumps have been detected in the ring's immediate vicinity, and a population of embedded objects has been inferred. Here we report direct evidence of moonlets embedded in the ring's bright core, and show that most of the F ring's morphology results from the continual gravitational and collisional effects of small satellites, often combined with the perturbing effect of Prometheus. The F-ring region is perhaps the only location in the Solar System where large-scale collisional processes are occurring on an almost daily basis.