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[GIF] Rise Up ((29, 5)-torus knot)

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(29,5)-torus knot

Rise Up

Continuing the torus knot theme (1, 2, 3). This is just a simple rotation of a $(29,5)$-torus knot. It's entirely three-dimensional, but because it's much simpler to parametrize torus knots on the Clifford torus in 4D, I am as usual parametrizing there and then stereographically projecting to 3D.

Here's the code:

Stereo3D[{x1_, y1_, x2_, y2_}] := {x1/(1 - y2), y1/(1 - y2), x2/(1 - y2)};

pqtorus[t_, θ_, p_, q_] := 1/Sqrt[2] {E^(p I (t + θ/p)), E^(q I t)};

With[{viewpoint = {0, 3, 0}, n = 450*29, p = 29, q = 5, 
  cols = RGBColor /@ {"#F21368", "#22C7A9", "#474655"}},
 Manipulate[
  Graphics3D[
   {Tube[Table[Stereo3D[Flatten[ReIm /@ pqtorus[t, -θ, p, -q]]], {t, 0., 2 π, 2 π/n}], .07]},
   PlotRange -> 2.7, ViewPoint -> viewpoint, ViewAngle -> π/9, 
   ViewVertical -> {0, 0, -1}, Boxed -> False, 
   Background -> cols[[-1]], ImageSize -> 540,
   Lighting -> {{"Point", cols[[1]], {3/4, 0, 0}}, {"Point",  cols[[2]], {-3/4, 0, 0}}, 
     {"Ambient", cols[[-1]], viewpoint}, {"Point", Darker[cols[[-1]], .87], viewpoint}}],
  {θ, 0, 2 π/q}]
 ]
POSTED BY: Clayton Shonkwiler
Answer
10 days ago

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