Chaos Pendulum

The difference between a normal pendulum and a chaos pendulum is the additional joint. It causes chaotical and unpredictable behaviour:

If you visualize it’s behaviour with a bifurcation diagram, fractal patterns become visible


To visualize the chaos of a physical system (ie. continuous in time), you have to determine a rendering criterion (“when m1 stops” in the above image), and plot the value of one or more property of the system when this criterion is fulfilled.
Here, only one property is plotted, so we at least one more dimension is needed to get a picture: this is a stepped parameter, the initial displacement of the lower pendulum, theta2. If you would choose a secound property instead of the stepped parameter, you would get a so-called Poincare section of the phase space of the system.


2000px-Magnetic_pendulumTheres other types of chaos pendulums – for example a 3-point magnetic pendulum.

Below is a video that shows the different final positions, depending on the different starting positions.



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