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In cellular vortical flows, namely arrays of counter-rotating vortices, shortbut flexible filaments can show simple random walks through their stretch-coilinteractions with flow stagnation points. Here, we study the dynamics ofsemi-rigid filaments long enough to broadly sample the vortical field. Usingsimulation, we find a surprising variety of long-time transport behavior --random walks, ballistic transport, and trapping -- depending upon thefilament's relative length and effective flexibility. Moreover, we find thatfilaments execute L\'evy walks whose diffusion exponents generally decreasewith increasing filament length, until transitioning to Brownian walks.Lyapunov exponents likewise increase with length. Even completely rigidfilaments, whose dynamics is finite-dimensional, show a surprising variety oftransport states and chaos. Fast filament dispersal is related to an underlyinggeometry of ``conveyor belts''. Evidence for these various transport states arefound in experiments using arrays of counter-rotating rollers, immersed in afluid and transporting a flexible ribbon.

L\'evy Walks and Path Chaos in the Dispersal of Elongated Structures Moving across Cellular Vortical Flows