First, in a vibrating container they put a liquid like silicon oil, vibrations are just bellow the Faraday instability threshold. Then a drop of the same liquid is dropped on the surface, but it does not coalesce, it bounces. And further bounces make a static wave pattern on the liquid surface just bellow the drop and its immediate neighborhood. As the spike grows, instability increases and the drop slides down the spike, and start moving horizontally.
Then they have a combo object drop+wave pattern moving at 1/10th the speed of wave in this liquid, straight. They call it a walker.
What is really amazing is that the wave pattern below the drop has some kind of memory: it has accumulated energy from several drop bounces. It can also make the drop see "forward", as the small wave pattern bounces back from nearby obstacles. So the drop is "aware" of its environment and "recall" the path it has followed.
Diffraction is observed and explained by the multiple reflexions the wave makes when the drop passes through a small hole, randomizing the wave pattern and the angle of the path afterward. Interference patterns observed are explained a la de Broglie: as the drop passes through one of the two holes, its associated wave passes through both, carrying forward the message of the second hole to the drop and changing the statistical repartition of the drop's path direction. One more stunning result: they are circling the drop by moving the container (Coriolis), then the associated wave adopts a discrete series of pattern, depending on the speed and radius. Very much like the energy quantization of electrons.
English (and French) abstract
A short article (French but it has photos and formulas)
Full thesis (French,10Mb)