Video: A Bit of Chaos

Here's a quickie, showing some of the basics of nonlinear dynamics, which I think is one of the most interesting fields in physics.  You've probably heard of an aspect of it, sensationally named chaos theory.

(Image Credit: Bugman123: http://www.bugman123.com/Fractals/index.html)




A good deal of nonlinear systems arise as a combination of forcing terms and dissipation terms.  Say, for instance, you throw a handful of feathers - there is the initial force of the momentum you give them in the throw, and the force of gravity pulling them downwards.  And in a place with no atmosphere, it would be a very simple bit of behavior.  But with air, a dissipation term comes into play, sapping the momentum and impeding the gravity.

Or, say, you had a pendulum, released from some height (forcing), above some magnets (dissipation).

Sensitivity to initial conditions really means sensitive.

If you notice towards the end of the clip there, you'll see what amounts to random fuzz in the map.  This, specifically, is where the chaos is.  Much like the shaded part in this bifurcation diagram (think of the x-axis as the distance the pendulum is pulled from the center).