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[GIF] Inevitability ((7, 3)-torus knot)

Clayton Shonkwiler

Clayton Shonkwiler, Colorado State University

Posted 8 years ago

Inevitability Same basic code as To Infinity, but this time with a $(7,3)$ torus knot and simpler lighting. Also, viewed from above rather than from the front. Stereo3D[{x1_, y1_, x2_, y2_}] := {x1/(1 - y2), y1/(1 - y2), x2/(1 - y2)}; pqtorus[t_, p_, q_] := 1/Sqrt[2] {E^(p I t), E^(q I t)}; With[{viewpoint = {0, 0, 10}, cols = RGBColor /@ {"#EDF2F6", "#494953"}}, Manipulate[ Graphics3D[{Sphere[#, .1] & /@ Table[Stereo3D[Flatten[ReIm /@ pqtorus[t + θ, 7, -3]]], {t, 0, 2 Pi, 2 Pi/200}]}, PlotRange -> 3, ViewPoint -> viewpoint, ViewVertical -> {0, 1, 0}, Boxed -> False, Background -> cols[[-1]], ImageSize -> 540, Lighting -> {{"Point", cols[[1]], {0, 0, 1/2}}, {"Ambient", cols[[-1]], viewpoint}}], {θ, 0, Pi/100}] ]

(7, 3)-torus knot

Inevitability

Same basic code as To Infinity, but this time with a $(7,3)$ torus knot and simpler lighting. Also, viewed from above rather than from the front.

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

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

With[{viewpoint = {0, 0, 10}, 
  cols = RGBColor /@ {"#EDF2F6", "#494953"}},
 Manipulate[
  Graphics3D[{Sphere[#, .1] & /@ 
     Table[Stereo3D[Flatten[ReIm /@ pqtorus[t + θ, 7, -3]]], {t, 0, 2 Pi, 2 Pi/200}]}, 
   PlotRange -> 3, ViewPoint -> viewpoint, 
   ViewVertical -> {0, 1, 0}, Boxed -> False, 
   Background -> cols[[-1]], ImageSize -> 540,
   Lighting -> {{"Point", cols[[1]], {0, 0, 1/2}}, {"Ambient", cols[[-1]], viewpoint}}],
  {θ, 0, Pi/100}]
 ]

POSTED BY: Clayton Shonkwiler

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J. M.

Posted 8 years ago

Some slight shortening: With[{viewpoint = {0, 0, 10}, cols = RGBColor /@ {"#EDF2F6", "#494953"}}, Manipulate[Graphics3D[{Sphere[Table[(Most[#]/(1 - Last[#])) & [ Flatten[ReIm[Exp[{7, -3} I (t + θ)]/Sqrt[2]]]], {t, 0, 2 Pi, 2 Pi/200}], 0.1]}, Background -> cols[[-1]], Boxed -> False, ImageSize -> 540, Lighting -> {{"Point", cols[[1]], {0, 0, 1/2}}, {"Ambient", cols[[-1]], viewpoint}}, PlotRange -> 3, ViewPoint -> viewpoint, ViewVertical -> {0, 1, 0}], {θ, 0, Pi/100}]]

Some slight shortening:

With[{viewpoint = {0, 0, 10}, cols = RGBColor /@ {"#EDF2F6", "#494953"}}, 
        Manipulate[Graphics3D[{Sphere[Table[(Most[#]/(1 - Last[#])) & [
                                            Flatten[ReIm[Exp[{7, -3} I (t + θ)]/Sqrt[2]]]],
                                            {t, 0, 2 Pi, 2 Pi/200}], 0.1]}, Background -> cols[[-1]],
                               Boxed -> False, ImageSize -> 540, 
                               Lighting -> {{"Point", cols[[1]], {0, 0, 1/2}},
                                            {"Ambient", cols[[-1]], viewpoint}}, PlotRange -> 3, 
                               ViewPoint -> viewpoint, ViewVertical -> {0, 1, 0}], {θ, 0, Pi/100}]]

POSTED BY: J. M.