Painting patterns of light with two connected pendulums

In Short

A double pendulum is a very simple way to illustrate a chaotic system. Even though it is composed of two pendulums, whose respective motions are easily predictable, the double pendulum will never swing the same way twice.

In our installation its surprising movements are visualised, leading to glowing patterns – each one you create will be completely individual.

Details and Theory

The line describing the motion of a pendulum’s centre of mass is called its trajectory. The theoretical description of the trajectory of a double pendulum leads to coupled nonlinear equations. Nonlinear systems generally have the property that a small change in initial conditions causes a large change in its dynamics.

Therefore, if you release the pendulum several times from almost the same position, you will get a completely different pattern each time. If all initial parameters were exactly adjustable (which is impossible in reality), the ‘chaos’ of the double pendulum could be controlled – hence we specifically call it ‘deterministic chaos’.

In our installation, an ultraviolet laser mounted on the tip of the pendulum creates an afterglow on a phosphorescent film that illuminates the path of the pendulum.