*"The knot is structurally independent of the substrate that carries it.*

All information in the knot occurs in its relationship with the ambient space.”

- Louis Kauffman

Mathematica code:

r[t_] := {Sin[t] + 2 Sin[2*t], Cos[t] - 2 Cos[2*t], -Sin[3*t]};

T[t_] := 1/Norm[r'[t]]*r'[t];

U[t_] := 1/Norm[r''[t]]*r''[t];

V[t_] := Cross[T[t], U[t]];

W[a_, d_, t_] := r[t] + d*Cos[a]*U[t] + d*Sin[a]*V[t]

Manipulate[With[{d = .5, M = 124, Q = 124},

Graphics3D[

Table[

GraphicsComplex[

Flatten[Table[

W[(a + s)*2 Pi/3, d, t + s*8*Pi/M],

{t, {j*2 Pi/M, (j + 1) 2 Pi/M}}, {a, 0, 2, 1}], 1],

Polygon[{{1, 2, 5, 4}, {2, 3, 6, 5}, {3, 1, 4, 6}}]],

{j, 0, Q, 1}],

Lighting -> "Neutral", Boxed -> False, ViewPoint -> Above,

ImageSize -> 600, PlotRange -> 3.5]],

{s, 0, 1}]