Julia Sets and the Mandelbrot Set

Magnetic Basin Boundaries

Here is a general description of the problem, togeher with an initial position map:

Because the magnets do not lie along a line, the initial position of the pendulum occupies two coordinates.

So instead of the phase plane, here points represent only the initial position of the pendulum. For this experiment, we start the pendulum from rest.

Here is a more detailed description of the experimental set-up.

First, use an overhead transparency to immobilize the magnets Next, the pendulum can be made of string, or of balsa wood

Make sure the pendulum and the stationary magnets are arranged so they attract one another.

Place the stationary magnets on the overhead projector surface and attach the pendulum to the projector head. Turn on the projector. Depending on where the pendulum is released, it can undergo complicated motion before settling over one of the magnets.

Projected image of the pendulum and stationary magnets