The following pictures show the movement of the mass-point of the ball at the pendulum for different initial conditions. There are certain values for the forces and the mass of the ball assumed. As the initial condition we consider the velocity as zero. The pictures show a view from the top. This system reacts very sensitive of changes in the initial condition.
If we now would calculate for each initial position of the pendulum on which magnet it will end and would colourise these point with the colour of this magnet we would obtain a fractal.