Complex but not chaotic

This occurred to me ages ago, but only now, given the choice between writing and tidying the house, am I bothering to write it up!

As a child growing up in the '80s, I have a natural tendency to look at anything non-linear, and go "Ooooh! Chaos!". For example, water flow, when the water breaks up into little funny-shaped droplets and goes all over the place, that's got to be chaotic. No way could I write a program on a computer and believe that the simulation will match what happens in reality.

But then I see something like this Hackaday link, effectively stroboscoping such falling water. Being able to stroboscope the water is basically saying that the configuration is reproducable at each sample point. There's clearly going to be small perturbations of the input each time, yet the output is still pretty much the same. You can see water breaking up into droplets at the same place several feet down. Highly sensitive to initial conditions? Yeah, right.

So, complicated behaviour? Well, surface tension acting on water being waved falling through the air, so I'd say, "yes". Chaotic behaviour? Clearly "no". There go my 80s retro preconceptions.

Posted 2014-12-23.