  We simulate the nonlocal Stokesian hydrodynamics of an elastic filament which
is active due a permanent distribution of stresslets along its contour. A
bending instability of an initially straight filament spontaneously breaks flow
symmetry and leads to autonomous filament motion which, depending on
conformational symmetry, can be translational or rotational. At high ratios of
activity to elasticity, the linear instability develops into nonlinear
fluctuating states with large amplitude deformations. The dynamics of these
states can be qualitatively understood as a superposition of translational and
rotational motion associated with filament conformational modes of opposite
symmetry. Our results can be tested in molecular-motor filament mixtures,
synthetic chains of autocatalytic particles, or other linearly connected
systems where chemical energy is converted to mechanical energy in a fluid
environment.
