The difference between a normal pendulum and a chaos pendulum is the additional joint. The behaviour of a regular pendulum is easy to predict if you know the two basic variables like lenght and starting height.
But if you add another joint, the tiniest difference in starting conditions will result in a drastically different path. The behaviour becomes chaotic and unpredictable.
If you visualize the behaviour of a chaos pendulum with a bifurcation diagram fractal patterns in that chaos become visible:
Theres other types of chaos pendulums – for example the magnetic pendulum. A piece of iron is attached to a string which is hung above three magnets, arranged in a triangle. The polarity of all magnets is the same.
If you let the piece of iron swing it will follow a chaotic path. The higher the starting velocity the more unpredictable the final position becomes.
Below is a video that shows the different final positions, depending on the different starting positions.