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I initially wanted to recreate the little dancing dots android lollipop's boot animation in javascript: enter image description here

For that, I've implemented a 3d $n$-body simulation (with css and js): http://codepen.io/abernier/pen/QyNzxY

Everything works pretty well actually, I can add planets (fixed or not), a mass for each and initial velocities.

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My problem is I really don't know what initial conditions to be set in order to reecreate that movement...

After some research on the web, it seems to be called a $n$-body choreography: http://gminton.org/#choreo

I also saw this interestings 3d choreographies: http://www.matapp.unimib.it/~ferrario/mov/index.html which look close to what I'm looking for... particularly this one (except it has only 3 bodies): enter image description here

Does anyone would know the one Google has used to make this animation?

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  • $\begingroup$ This kind of thing has been explored quite a bit in the mathematical physics literature. It's not actual physics (as in the natural science), since most of these orbits would be completely unstable in nature. The good news for you is that the website gives you the citations to the math papers. I would use those as starting point... but don't expect an easy read. The exploration of these orbits requires some serious mathematics and there is (provably) no recipe that can come up with these, the search space is chaotic. $\endgroup$
    – CuriousOne
    Commented Dec 30, 2015 at 0:39
  • $\begingroup$ @CuriousOne yeah unfortunately I haven't enough maths knowledges for that, only some code ones... That's also the reason why I'm posting in here :) $\endgroup$
    – abernier
    Commented Dec 30, 2015 at 0:42
  • $\begingroup$ @DanielGriscom a spiral path? Are you talking about the end of the animation where it scales to 0 to disappear? I only want to recreate the perpetual movement of the 4 particules when they perpetually loop around $\endgroup$
    – abernier
    Commented Dec 30, 2015 at 0:45
  • $\begingroup$ Like I said, there is no simple way of doing this. Basically you would have to write a non-linear search algorithm that scans a chaotic n-dimensional parameter space for (small!) islands of stability if you want to use an actual dynamic like this. As Daniel points out, most animations don't. They use formulas that look good instead of trying to solve dynamic models. I certainly would go that way, but that's more art than science. $\endgroup$
    – CuriousOne
    Commented Dec 30, 2015 at 0:47
  • $\begingroup$ Sorry; I moved my comment to an answer. I'll elucidate there. $\endgroup$
    – Daniel Griscom
    Commented Dec 30, 2015 at 0:47

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The Android boot animation is not an orbital simulation, but is instead a hand-drawn animation showing the animator's vision.

If you watch any of the dots (before the shrinking effect at the end), you'll find that it does seem to be orbiting a central point, getting closer and further away. However, each dot's motion also has a twisting action to it, as if all the orbiting dots had an added clockwise motion. A simple orbit around a single central mass would never do that; the orbiting object would confine itself to a plane. No real orbit would include that twisting action unless (and perhaps even if) there were a whole lot of attractors.

You've now changed your goal to emulate a different model, one of the "choreographies" on David Ferrario's video page. Those orbits are real orbits, which in theory could happen given standard Keplerian laws. However, note that they are all artificially tuned to specific, pretty, repeating patterns. Probably none of them would be stable in real life, nor would they be if you attempted a realistic simulation, due to the non-infinite precision of computers. The best way to generate a visual pattern such as these would be to generate the individual dot positions algorithmically (e.g. a circular path at a given orientation, phase and period).

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  • $\begingroup$ When you talk about a spiral path, can you confirm you are not talking about the end of the animation, where it scales to 0? I've just edit my post with another link to 3d choreographies: for me it's quite close from the result I want matapp.unimib.it/~ferrario/mov/index.html but the author does not gives the initial conditions (positions and velocities) to reproduce them... $\endgroup$
    – abernier
    Commented Dec 30, 2015 at 0:51
  • $\begingroup$ Especially this one: matapp.unimib.it/~ferrario/mov/orbite/doppiarifl3_1.avi $\endgroup$
    – abernier
    Commented Dec 30, 2015 at 0:56
  • $\begingroup$ oh I think I get what you mean by spiral! But it's not, it's just an exagerated perspective set to the camera on the animation. I've set a perspective like this on my WIP animation so you can refer to: codepen.io/abernier/pen/QyNzxY $\endgroup$
    – abernier
    Commented Dec 30, 2015 at 8:03

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