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When a small particle is transported in an incompressible flow, which is steady in some frame of reference, the particle can be attracted to a periodic orbit or to a more complex attractor. Usually, such an attractor is caused by inertia forces on the particle, which rely on the density mismatch between particle and fluid. However, attractors can also be caused by repulsive forces from a boundary acting on the particle due to its finite size. The mechanism leading to particle-motion attractors by particle-boundary interaction is discussed and typical examples are presented. While the mechanism acts on a single particle, many or even all particles of a dilute suspension can cluster on or near the single-particle attractor. If the attractor is periodic or quasi-periodic the resulting particulate structure is called finite-size Lagrangian coherent structure. In systems with tangentially moving boundaries finite-size coherent structures can form very rapidly, because their creation relies on repeated particle-boundary interactions, the period of which scales with the characteristic time of the flow. The effect leading to finite-size coherent structures may find application in sorting particles by their size in microsystems when other methods cannot be applied.