Chaos in Motion

Zenzicubic
Zenzicubic
249
0
Published 2022-10-01
This is a compilation of some chaotic systems I made animations of. I used Heun's method to integrate the equations, and plotted everything on JS canvas.
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Attractors:
0:00 The Duffing oscillator
1:24 The Van der Pol oscillator
2:09 The Ueda attractor
3:51 Poincare section of the Duffing oscillator
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The first and third clips are of trajectories evolving. The second and fourth clips depict plots of points evolving superimposed on their vector fields. In case you want to make one of your own, here are the parameters.

For Duffing: δ = 0.25, β = 0.3, ω = 1, timestep = 0.01
For Ueda: μ = 1.01, γ = 8, β = 0.35, ν = 0.25, timestep = 0.01
For van der Pol: μ = 1, timestep = 0.01
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Music is Debussy's Arabesque, performed by Ad van Nederpelt.

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All Comments (3)
  • @negativebudgetproductions4908
    The last animation on the Duffing attractor shows the chaotic nature very well, you can see how sections get stretched and folded over: Classic mixing dynamic, a staple of chaos. It looks like a piece of dough being kneaded. I think this video would be a bit better if it lingered less on each attractor - maybe speeding up the drawing after the first bits are drawn would be a good idea for some of these. But overall clean and nice animation, well done!
  • @isaacm1929
    It's a beautiful animation. Have a great day.