Julia Sets and the Mandelbrot Set

Basins of Attraction of Mechanical Systems

Here we have assembled the phase plane data for thousands of initial positions and speeds.

From the position and speed represented by each black point, the pendulum eventually comes to rest over the right magnet.

Taken together, the black points constitute the basin of attraction of the right magnet.

From the position and speed represented by each white point, the pendulum eventually comes to rest over the leftt magnet.

The white points form the basin of attraction of the left magnet.

The left picture shows the situation for high damping, the right for lower damping.

Return to Mechanical Basin Boundaries.