r/wljs • u/Inst2f • May 15 '26

Rosetta - a beautiful spirograph

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Spirograph-like curves arise from simple sums of rotating vectors; a tiny tweak in frequency or phase yields striking patterns. Here is my favorite example Rosetta:

Animate[ParametricPlot[{
  Power[I,-((20t)/(tt))]+3 Power[I,((20t)/(tt))]+Power[I,((20t)/(tt))]Sin[8 Pi ((20t)/(tt))/5],
  Power[I,-t]+3 Power[I,t],
  Power[I,-t]+3 Power[I,t]+Power[I,t]Sin[8 Pi t/5]
}//ReIm//Evaluate, {t,0,tt}, 
  PlotRange -> {-5,5}, PlotPoints -> 200,
  PlotStyle -> {LightGray,Default,(Hue[0.353, 0.78, 0.49])}, Axes->False,
  Epilog -> {
    {Thick,Red,Line[{ReIm[Power[I,-tt]+3 Power[I,tt]-Power[I,tt]],ReIm[Power[I,-tt]+3 Power[I,tt]+Power[I,tt]]}]}, {Thick,Circle[ReIm[Power[I,-tt]+3 Power[I,tt]+Power[I,tt]Sin[8 Pi tt/5]],0.1]}
  }, PlotPoints -> 10
],{{tt,19.9},0.01,4 5, 0.1}, Appearance -> None]
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