25
Feb
09

Chen-Gackstatter Minimal Surface

The Chen-Gackstatter Minimal Surface is a modified Enneper surface with holes in it. The following Mathematica code uses some functions that were adapted from Matthias Weber’sMathematica notebook:
(* runtime: 0.4 second *)
<< Graphics`Shapes`; k = 5; n = (k - 1)/k; rho = 1.0/Sqrt[4^n Gamma[(3 - n)/2] Gamma[1 + n/2]/(Gamma[(3 +n)/2]Gamma[1 - n/2])];
phi[n_, z_] := z^(1 + n)Hypergeometric2F1[(1 + n)/2, n, (3 + n)/2, z^2]/(1 + n); f[z_] := {0.5(phi[n, z]/rho - rho phi[-n, z]), 0.5I(rho phi[-n, z] + phi[n, z]/rho), z};
surface = ParametricPlot3D[Re[f[r Exp[I theta]]], {r, 0, 2}, {theta, 1*^-6, 2Pi}, PlotPoints -> {9, 33}, Compiled -> False, DisplayFunction -> Identity][[1]];
Show[Graphics3D[Table[RotateShape[surface, 0, 0, 2Pi i/k], {i, 0, k - 1}]]]

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3 Responses to “Chen-Gackstatter Minimal Surface”


  1. 1 Johanan Rakkav
    May 16, 2009 at 1:34 pm

    I barely understand what you’re talking about mathematically (if at all in many cases), but as an artist I find your work most impressive. Keep it up!

  2. May 24, 2009 at 6:45 pm

    Отличная статья.Респект автору.

  3. January 5, 2011 at 10:42 am

    I think yours is one of the most interesting website I’ve ever seen. Thank you


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