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Bouncing balls in a circle gives one of the simplest systems to exhibit chaos, as was pointed out in a comment by Andrew Moylan.  The animation above shows two balls which start off with almost exactly the same speed and location, but before long they are travelling along completely different trajectories. Such high sensitivity to the initial conditions defines chaos. 

In this visualisation, each point in the circle is given a colour in a rainbow pattern. The animation shows at each time where a ball dropped at each point within the circle has ended up, by colouring that point appropriately. For example at the first frame, all the balls are stationary, and we see the rainbow pattern. Then as time progresses, the balls drop down and the pattern correspondingly goes up. A black band appears and moves up, which shows which balls are doing their first bounce. Soon the order disappears- it looks random like the divergence of the two balls above. [more] [code]

Bouncing balls in a circle gives one of the simplest systems to exhibit chaos, as was pointed out in a comment by Andrew Moylan.  The animation above shows two balls which start off with almost exactly the same speed and location, but before long they are travelling along completely different trajectories. Such high sensitivity to the initial conditions defines chaos

Chaos Visualisation

In this visualisation, each point in the circle is given a colour in a rainbow pattern. The animation shows at each time where a ball dropped at each point within the circle has ended up, by colouring that point appropriately. For example at the first frame, all the balls are stationary, and we see the rainbow pattern. Then as time progresses, the balls drop down and the pattern correspondingly goes up. A black band appears and moves up, which shows which balls are doing their first bounce. Soon the order disappears- it looks random like the divergence of the two balls above. [more] [code]

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    Actually, it’s not all that chaotic, there is an appropriately measurable cause and effect to it. The potential for...
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Matt Henderson

I post original stuff about maths, space, computational linguistics and other things that I like. This blog is meant to be accessible and interesting to people of all backgrounds. My undergrad was maths in Cambridge, and I'm now starting research in Speech and Language technology. Email me at If you're new, check out this overview of my posts. All code posted is in Mathematica.

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