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I wonder whether it is possible to draw the "logo" of string theory with LaTeX. I think it is doable, but not sure how to do it. Any guru wants to give it a shot?

3-D projection of a Calbi-Yau manifold

Source: https://commons.wikimedia.org/wiki/File:Calabi-Yau-alternate.png and (in better quality) https://commons.wikimedia.org/wiki/File:Calabi-Yau.png (both own work by Lunch; CC BY-SA 2.5)

Speravir
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Sibbs Gambling
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    In TeX?!! I don't believe it is possible. – Sigur Nov 09 '13 at 14:59
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    As long as you can provide us with its function to plot, PSTricks can happily do it, IMHO. – kiss my armpit Nov 09 '13 at 15:21
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    @Marienplatz, here is it: http://en.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold – Sigur Nov 09 '13 at 16:34
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    The problem is on the borders of TeX & Co., but it is interesting, so let our PSTricks ot TikZ/PGF specialists find a solution. I am voting for reopening. – Przemysław Scherwentke Nov 09 '13 at 18:29
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    I'm not sure it's practical as an application of PGF/PSTricks; the manifold is a 3D projection of higher-dimensional object. It would be far more efficient to find a PDF or other vector representation of the manifold already created and customize it with a vector editor such as Inkscape. In either case, this specific problem is a manifestation of the more general class of problems here on TeX.SX. – Sean Allred Nov 09 '13 at 20:24
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    I would second @Marienplatz : if you manage to provide a "suitable" description of the involved surface(s) along with the color information, we can think about it. "Suitable" means either a parameterized surface x(u,v), y(u,v), z(y,v) with color data C or a huge data table X Y Z C where C can be RGB or scalar color values. But a task like "do research on string theory to understand suitable representations of the object given as rendition" is unrelated to tex.sx . Unfortunately, the mentioned wikipedia link does not appear to answer that question. – Christian Feuersänger Nov 10 '13 at 11:55

1 Answers1

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I searched a bit on the net and found a parametrization for cross-sections of the quintic 6D Calabi-Yau, so here's the Asympote implementation:

\documentclass{standalone}
\usepackage{asymptote}

\begin{document}

\begin{asy}[width=10cm,height=10cm]
import graph3;

size3(200);
currentprojection=orthographic(3,3,2);
currentlight=light(8,10,2);

int k1, k2, n = 5;
real alpha = 0.3*pi;

// cross section of the quintic 6D Calabi-Yau manifold
triple cy(pair z) {  

  pair z1, z2;

  if(z==(0,0)) {
    z1 = exp(2*pi*I*k1/n);
    z2 = 0;
  } else {
    z1 = exp(2*pi*I*k1/n)*exp(log(cos(I*z))*2/n);
    z2 = exp(2*pi*I*k2/n)*exp(log(-I*sin(I*z))*2/n);
  }

  return (z2.x, cos(alpha)*z1.y + sin(alpha)*z2.y, z1.x);

}

for(k1=0; k1<n; ++k1) {
  for(k2=0; k2<n; ++k2) {
    surface s = surface(cy,(-1,0),(1,0.5*pi),20,20);
    draw(s,yellow+orange);
  }
}

\end{asy}

\end{document}

enter image description here

Don't know which one is shown in your "logo", but that's at least a Calabi-Yau manifold. If you view the resulting PDF with acroread, you can rotate the beast.

Alex
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    This is better than the original! You can also use the opacity option draw(s,red+opacity(0.6)); and modify currentlight to give part of the red/blue appearance. – alfC Feb 01 '14 at 03:56
  • I was not able to compile this latex code in Overleaf or on my Mac with a full latex installation. I don't see any errors in the log file only warnings such as: No file c3f935e53c8b4367b319754137b94ccc.aux. \openout1 = c3f935e53c8b4367b319754137b94ccc.aux'. ... Package asymptote Warning: filec3f935e53c8b4367b319754137b94ccc-1.eps' not fo und on input line 40. Any idea? – itart Jan 30 '20 at 12:28