16
Jan
09

Jorge-Meeks K-Noids


The following Mathematica code uses some functions that were adapted from Matthias Weber’sMathematica notebook:
(* runtime: 0.4 second *)
<< Graphics`Shapes`;
k = 5; phi1[z_] := z^(k - 1) (k/(1 - z^k) - (k - 1) LerchPhi[z^k, 1, 1 - 1/k])/k^2; phi2[z_] := z(1/(1 - z^k) + (k - 1)LerchPhi[z^k, 1, 1/k]/k)/k;
f[z_] := {0.5 (phi2[z] - phi1[z]), 0.5 I (phi1[z] + phi2[z]), 1/(k - k z^k)};
surface = ParametricPlot3D[Re[f[(1 + 2/(I Exp[x + I y] - 1))^(2/k)]], {x,0, Pi/2}, {y, -Pi/2, Pi/2}, PlotPoints -> {8, 16}, Compiled -> False, DisplayFunction -> Identity][[1]];
surface = {surface, AffineShape[surface, {1, -1, 1}]};
Show[Graphics3D[Table[RotateShape[surface, 0, 0, 2Pi i/k], {i, 0, k - 1}]]];

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