A pendulum tends to have very predictable behaviour, hence the old fashioned grandfather clock, but not so the MAGNETIC  PENDULUM! Swing a magnet over a metal plate containing two or more attractive magnets and you find that it is almost impossible to predict which magnet the pendulum will ultimately be attracted to. However in theory the mathematical equations governing the system allow us to determine the precise behaviour of the pendulum. If you start relatively near to a magnet the pendulum will simply be attracted to that magnet, but further away the motion is difficult to predict.

In the experiment shown, the position of the swinging magnet is shown for three different (white, yellow and blue), but close, starting positions (picture with yellow border). Yet each are attracted to a specific magnet, say the one on the right (yellow).


The result (picture with blue border), as shown in the computer simulation, is obviously fractal and immediately the unpredictable behaviour makes sense.
Since the domain of attraction is fractal it has infinite structure so that points which are arbitrarily close may be in the domains of attraction of different magnets.
Make your own pendulum