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

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 Rise UpContinuing 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}] ]