A mechanical alarm clock going off on a hard surface is a typical example of a system in which fast oscillations drive a secondary, slower dynamics.

The rapid vibrations of the clock's arm are not precisely symmetric.

Together with the heavy, inhomogeneous internal structure and the interaction with the surface these oscillations can cause the clock to drift slowly in a complicated trajectory that is difficult to calculate or predict. Moreover, the drift is deterministic and does not resemble a random walk.

.mp4 format (1M+0.9M)

 

The following movies show the top view of an alarm clock drifting slowly as its mechanical arm vibrates. The image is projected on a blackboard with the initial position marked down.

The two trajectories are practically the same.

1st try

repeated