Can a Lorenz Attractor Graph Be Produced in a Lab Experiment?

[djmike]

hi people, I've been looking into Chaos theory and would like to build an experiment to produce a Lorenz attractor graph. is this possible? does the water wheel produce the butterfly wings graph? a lot of the articles on the net say the same thing so i have given up there.

im reading through nonlinear dynamics and Chaos-Strogatz and Chaos-Gleick. they say the graphs are produced from Lorenz convection current equations on a computer simulation. this is why I am wondering how to produce them in a lab experiment.

many thanks

 

[Sirus]

Producing the Lorenz attractor itself is quite complicated I believe, because of the complexity of systems such as the weather/convection currents and the extremely large number of parameters to control. However, many simple electric circuits exist which exhibit nonlinear dynamical behavior.

The simplest one I have found is here: http://documents.wolfram.com/v4-de/GettingStarted/ChaoticCircuit.html

You can play with voltage here to see the resulting attractor: http://library.wolfram.com/webMathematica/Engineering/Circuit.jsp

Here is an article detailing other more complex circuits: http://sprott.physics.wisc.edu/pubs/paper249/paper249.htm

Despite their apparent simplicity, these are still quite difficult to replicate.

 

[djmike]

thanks very much. looking at your links an electronic experiment is probably going to give the best results. I've got to make an experiment for my MPhys final year project. I am going to start looking at the electric circuits for Chaos. i wanted to make something that's not electrical as it is planned(hopefully) to go into the lab as an undergrad experiment or alternatively in a display case. there are plenty of circuit based exeriments i had to do, so something else would have been nice. on the other hand there is the grade of my project to consider and an electric circuit would probably give me more options

 

[Sirus]

A pendulum can also be driven into chaotic motion, but it can only be graphed using a computer interface and appropriate software, so it's not easy.

 

[djmike]

i was thinking of that...also I've seen a magnetic resonator exp using flash photography, something the dept uses.

What has caught my attention is the gelotin turbulence exp for chemical mixing applications. they use coloured needles with a turbine to generate and map chaotic flow. the needles are dye injected and illuminated with a laser(dept speciallity) plane through a half cylinder lense. i think this must also be mapped with a computer...but would make a nice demostration. ill speak to my supervisor as this sounds good

ill add the link in a bit when i find it