Cross Section of the Quintic Calabi-Yau Manifold

The left picture shows a 3D cross section of the quintic 6D Calabi-Yau Manifold proposed for String Theory. The right picture shows various degrees of complexity.

Click here to download some POV-Ray code for this image.

Here is some Mathematica code:
(* runtime: 54 seconds, change n for other degrees of complexity *)
n = 5; CalabiYau[z_, k1_, k2_] := Module[{z1 = Exp[2Pi I k1/n]Cosh[z]^(2/n), z2 = Exp[2Pi I k2/n]Sinh[z]^(2/n)}, {Re[z1], Re[z2], Cos[alpha]Im[z1] + Sin[alpha]Im[z2]}];
Do[alpha = (0.25 + t)Pi; Show[Graphics3D[Table[ParametricPlot3D[CalabiYau[x + I y, k1, k2], {x, -1, 1}, {y, 0, Pi/2}, DisplayFunction -> Identity, Compiled ->False][[1]], {k1, 0, n - 1}, {k2, 0, n - 1}], PlotRange -> 1.5{{-1, 1}, {-1, 1}, {-1, 1}}, ViewPoint -> {1, 1, 0}]], {t, 0, 1, 0.1}];

Links

• The Elegant Universe – 3 hour online mini-series on String Theory by NOVA
• Calabi-Yau etched in Crystal – by Bathsheba Grossman
• Calabi-Yau Cross Sections – by Andrew Hanson
• Equations – Stewart Dickson
• Math