  We study the dynamics and patterning of polar contractile filaments on the
surface of a cylindrical cell using active hydrodynamic equations that
incorporate couplings between curvature and filament orientation. Cables and
rings spontaneously emerge as steady state configurations on the cylinder, and
can be stationary or moving, helical or segments moving along helical
trajectories. Contractility induces coalescence of proximal rings. We observe
phase transitions in the steady state patterns upon changing cell diameter and
make several testable predictions. Our results are relevant to the dynamics and
patterning of a variety of active biopolymers in cylindrical cells.
