CHAOTIC WATERWHEEL

This experiment illustrates what is popularly known as chaos. The study of chaos is part of the modern theory of dynamical systems, which is the area of Mathematics dedicated to systems that evolve over time.

It is in this area that Artur Ávila works, recently awarded the Fields Medal at the International Congress of Mathematicians.

Observing chaos is not always easy. This system, for example, is controlled by a parameter, which is the water flow. Depending on the value of this parameter, the system can adopt a periodic behavior or, alternatively, a non-periodic behavior.

In general, non-periodic behavior is associated with sensitivity to initial conditions, which makes accurate predictions of long-term movement difficult (see the double pendulums exhibit to learn more).

USEFUL LINKS

This Wikipedia page talks about the chaotic water wheel, also called Malkus waterwheel or Lorenz waterwheel. Its function as a pedagogical tool and its use for the study of dynamic systems are explained, in addition to presenting a two-wheel computer simulation starting from different initial situations.

This Harvard University's article talks about the chaotic waterwheel, showing how it works and how it should be assembled. It also brings some comments about this type of experiment and a video that comparatively presents waterwheels in operation.                                                           

This Laboratory of Analysis, Computing and Experimentation's article from the Georgia Institute of Technology aims to build a chaotic waterwheel to confirm its chaotic nature and explore the parameters of the wheel. With this, it will be possible to solve the system of equations using Matlab.

Finally, we saw that the chaotic water wheel illustrates chaos. In this Fiocruz' article, we have a general notion of what chaos is, from a scientific point of view, while this Wikipedia page complements the study by talking about Chaos Theory, a very broad field that addresses studies in several areas.