  We analyse the effect of the Basset history force on the sedimentation or
rising of inertial particles in a two-dimensional convection flow. When memory
effects are neglected, the system exhibits rich dynamics, including periodic,
quasi-periodic and chaotic attractors. Here we show that when the full
advection dynamics is considered, including the history force, both the nature
and the number of attractors change, and a fractalization of their basins of
attraction appears. In particular, we show that the history force significantly
weakens the horizontal diffusion and changes the speed of sedimentation or
rising. The influence of the history force is dependent on the size of the
advected particles, being stronger for larger particles.
