50 double pendulums, whose initial velocities differ only by 1 part in 1000pic.twitter.com/3b75BDkwF1
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50 double pendulums whose initial velocities differ by only 1 part in 1 Million
#WaitForItpic.twitter.com/sHZUaFPzSC
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So satisfying. Do you think it's possible to take the end state of this simulation, reverse the velocities, and watch the 50 pendulums (pendula?) come together again, or do chaotic dynamics + floating point rounding errors make that impossible?
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sure.. or i can just reverse the gif lol
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Numerical errors can play an importan role here. Not sure how to distinguish between real physics and errors due to floating point. Probably you can use double precision and compare with single precision ...
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Yea you can use a number to things to help like energy conservation
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This is awesome²! What did you use to create the animation?
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That would interest me, too.
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If you simulate to identical pendulums, how long until the two diverge due to numerical noise?
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There is only a few operations in a single time step of a single pendulum, so they are most likely implemented in a deterministic way, meaning that two runs cannot deverge. If not, the answer depends on the implementation.
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this is really one of your best visualizations yet
Thanks. Twitter will use this to make your timeline better. UndoUndo
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Is there any relation between the size of the velocity differences (1/1e6 vs 1/1e3) and the time it would take for these 50 to diverges into chaos above some arbitrary threshold?
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