So, what I am thinking about here is a cooking mixer placed into a bowl which is turned on and left moving on its own. The bowl is such that it does not topple nor the mixer falls out of it.
Once the mixer is turned on the bowl starts vibrating. Like phones sometimes do, during the vibration the bowl slowly moves around the plane it lays on.
Now I swear I saw the bowl first going one direction and few seconds later coming back in the opposite direction. Unfortunately I was not able to study more precisely the system (my mother needed to be left cooking without too much science around).
My question is of course: how could such a thing happen?
I have some hypotheses:
-the mixer was connected to a cable and the cable was sort of tangled so it could have behaved slightly like a spring, calling back the bowl once it was too distant. But in my opinion the motion due to the vibration is too slow to stretch a spring-like constraint: before getting too distant, the system would naturally stop in the point of equilibrium between the forces created by spring and slope.
-maybe the motion I saw was an elliptic trajectory of the bowl around a (very flat) well in the plane and the system did not fell straight in the center of the well because of a conserved sort of angular momentum, due to either the details of the plane (which appears to be "very" flat to my eyes) or some initial conditions (like my mom accidentally gave it some momentum at the beginning of the process).
-maybe the motion caused by vibration in the case of a sufficiently flat and equipotential surface is a random walk.
Of course there is the possibility that I was mistaken and the change of pattern did not happen, but I am pretty sure I have seen that happening.