flickr-free-ic3d pan white

6 crossing hexa-tori / 交差する6つの六芒星

SetOptions[Manipulate, {SaveDefinitions -> True, ContinuousAction -> False}];

 

Manipulate[

SetOptions[ParametricPlot3D, PlotRange -> Full, Mesh -> None,

Boxed -> False, Axes -> None, PlotPoints -> 400, ImageSize -> 1000,

Background -> Darker[Blue, 0.8],

PlotStyle -> Directive[Specularity[White, 30], Texture[Import["D:/tmp/863.jpg"]]],

TextureCoordinateFunction -> ({#4 + #5, #5/Pi} &), Lighting -> "Neutral"];

 

b = 6;(* hexa-torus *)

d = 6;(* number of torus *)

f[v_] := Sin[2 Sin[Sin[Sin[v]]]];

g[v_] := Sum[Cos[(2 k - 1) v]/(2 k - 1), {k, 4}];

x = (a - g[t] - f[b s]) Cos[s + Pi/(2 b)] + c;

y = f[t] + c;

z = (a - g[t] - f[b s]) Sin[s + Pi/(2 b)] + c;

rot = Table[{x, y, z}.RotationMatrix[2 i Pi/d, {0, 1, 0}], {i, d}];

 

ParametricPlot3D[rot, {t, 0, 2 Pi}, {s, 0, 2 Pi}]

, {a, 3, 10, 1}, {c, 1, 4, 1}

(* a:center hole size of a torus *)

(* c:distance from the center of rotation *)

]

 

(*---

The Texture is another color version of this:

www.flickr.com/photos/tanaka_juuyoh/5412528282

The g[] is a 4-partial sum of the Fourier series for Square wave.

g[]は矩形波のフーリエ展開の最初の4項

*)

  

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Uploaded on May 6, 2011