Julia Sets and the Mandelbrot Set

Magnetic Basin Boundaries

Arrange three magnets on the vertices of an equilateral triangle on a horizontal surface.
Paint one magnet red, one yellow, and one blue.
Suspend an iron pendulum above the magnets.
Wherever the pendulum is released, it will eventually come to rest over one of the three magnets.
Paint the starting point with the color of the magnet over which the pendulum eventually comes to rest.
Here is an example of such a plot. Magnifying any portion of the boundary reveals the Wada property: any point on the boundary between two regions is also on the boundary of the third.
The videotape Fractals: an Animated Discussion by H-O Peitgen contains an instructive animation of this problem.