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<p><strong>Abstract.</strong> It is argued that the complexity of fluid particle trajectories provides the basis for a new method, referred to as the Complexity Method (CM), for estimation of Lagrangian coherent structures in aperiodic flows that are measured over finite time intervals. The basic principles of the CM are explained and the CM is tested in a variety of examples, both idealized and realistic, and in different reference frames. Two measures of complexity are explored in detail: thedoi:10.5194/npg-18-977-2011 fatcat:qor53d3plvemzgpzrro23lztkq