Chaos Theory - the Butterfly Effect

[mike_j]

Mathematician's Explanation
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

Engineer's explanation.

The light traces are from an led on the tip of a freely jointed double compound pendulum which exhibits chaotic (unpredictable) behaviour when swung.

This is a possible entry into a 'creative' image competition. Any comments? Just as a matter of interest the Photoshop file is 12000 x 9000 pixels and 368MB

[Graham_of_Rainham]

Re: Chaos Theory - the Butterfly Effect

Back in the 60s when at school we built an Harmonogram with a two pendulums. One had a table attached the other an arm with a pen that drew these type of pictures on paper attached to the table.

I've often thought of doing something like this with LEDs and my camera that has live view Bulb/Time that would allow for easy start / stop of the composition.

Thanks for the inspiration.

Former MIMechE

[mike_j]

Re: Chaos Theory - the Butterfly Effect

Hi Graham

I expect that your harmonographs were Lissajous figures which provide most attractive patterns. The difference between them and these traces are that the Lissajous figures are mathematically predictable and describable whereas these chaos figures can branch into so many variants that mathematical prediction is not practical (I think).

It's quite entertaining watching the pendulum, it will be swinging reasonably sensibly when suddenly the top section almost stops and the bottom jointed section starts swinging full circles for a short time. I may try video sometime. The exposures on my examples are 15 seconds. I start the camera on 10s delay and go to the pendulum, wait for the shutter then swing the pendulum A longer exposure results in a lot of rather boring swinging at the bottom of the arc.

Thans for the comment.

Michael (ex IEE)

[Graham_of_Rainham]

Re: Chaos Theory - the Butterfly Effect

You are correct, and they did get a bit repetitively similar...

Do you have a picture of your setup ?