  In cellular vortical flows, namely arrays of counter-rotating vortices, short
but flexible filaments can show simple random walks through their stretch-coil
interactions with flow stagnation points. Here, we study the dynamics of
semi-rigid filaments long enough to broadly sample the vortical field. Using
simulation, we find a surprising variety of long-time transport behavior --
random walks, ballistic transport, and trapping -- depending upon the
filament's relative length and effective flexibility. Moreover, we find that
filaments execute L\'evy walks whose diffusion exponents generally decrease
with increasing filament length, until transitioning to Brownian walks.
Lyapunov exponents likewise increase with length. Even completely rigid
filaments, whose dynamics is finite-dimensional, show a surprising variety of
transport states and chaos. Fast filament dispersal is related to an underlying
geometry of ``conveyor belts''. Evidence for these various transport states are
found in experiments using arrays of counter-rotating rollers, immersed in a
fluid and transporting a flexible ribbon.
