matthen

Things of interest in Maths & Science

Photo

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]

  1. risvoi reblogged this from 14-billion-years-later
  2. grnephrite reblogged this from matthen
  3. youngspecialist reblogged this from likeaphysicist
  4. fokinel reblogged this from matthen
  5. cuttinheadz reblogged this from unusual-entities
  6. unusual-entities reblogged this from s-cientia
  7. reality-was-never-real reblogged this from likeaphysicist
  8. bartlmiller reblogged this from likeaphysicist
  9. themagnificentunknown reblogged this from elusivemusings
  10. fantasycal reblogged this from quantumblreasoning
  11. true-stories-never-end reblogged this from iamtherkyeet
  12. iamtherkyeet reblogged this from matthen
  13. empathy-vs-apathy-nyc reblogged this from elusivemusings
  14. deadmanshining reblogged this from elusivemusings and added:
    Actually, it’s not all that chaotic, there is an appropriately measurable cause and effect to it. The potential for...
  15. heterosaxophones reblogged this from my-life-in-disarray
  16. my-life-in-disarray reblogged this from elusivemusings
  17. likea-jigsaw reblogged this from earthboundmisfitt
  18. overcomeinsanity reblogged this from elusivemusings
  19. earthboundmisfitt reblogged this from elusivemusings
  20. sunnyolives reblogged this from elusivemusings
  21. knowledgeistreasure reblogged this from elusivemusings
  22. thisblankpage reblogged this from elusivemusings
  23. elusivemusings reblogged this from opulentjoy
  24. tobreakfastattiffanyswego reblogged this from the-entropic-agenda
  25. mariestephanii reblogged this from msladyluck
blog comments powered by Disqus
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.

Topics

Share

I will pay you handsomely if you share my blog with your friends.

Tweets

Youtube

Recent Comments

Get Updates

Subscribe by email, to get the latest updates in your inbox automatically. Or use RSS if you have a news reader.