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I was wondering if anyone could suggest software/packages to create nice knot diagrams (hopefully with a link to images they have made in the past).

I have used xy-pic recently but am mainly interested in hearing about other options.

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See also syzygy module of Asymptote for some specific sorts of knots. katlas.math.toronto.edu/drorbn/index.php?title=06-1350/… – Leo Liu May 2 '11 at 14:03
    
If you're interested in only a few knots, you might want to take a look at the blue knot gallery of Jim Belk. – Martin Thoma Nov 8 '13 at 18:47

I have a prototype package for this using TikZ/PGF. At the moment, it is a bit basic as it was originally designed to draw very specific link diagrams and only afterwards did I start to extract the more general bits. Nonetheless, it can produce quite nice knot diagrams (I think) and I'd be happy to hear ideas on how it could be improved. You can get it from my homepage (when it is a little more polished then I'll put it on CTAN).

Here are some samples to whet your appetite. First, the preamble for all these examples:

\documentclass{article}
\usepackage{brunnian}

\usetikzlibrary{%
  arrows%
}

\tikzset{every path/.style={red,line width=2pt},every node/.style={transform shape,knot crossing,inner sep=1.5pt},>=triangle 60,text node/.style={rectangle,transform shape=false,black}}

Next, a trefoil

\begin{tikzpicture}
\foreach \brk in {0,1,2} {
\begin{scope}[rotate=\brk * 120]
\node (k\brk) at (0,-1) {};
\end{scope}
}
\draw (0,0) \foreach \brk in {0,1,2} {let \n0=\brk, \n1={int(Mod(\brk+1,3))}, \n2={int(Mod(\brk+2,3))} in (k\n0) .. controls (k\n0.16 south east) and (k\n1.16 south west) .. (k\n1.center) .. controls (k\n1.4 north east) and (k\n2.4 north west) .. (k\n2)} (k2);
\end{tikzpicture}

trefoil

This extends very easily to, for example, a cinquefoil:

\begin{tikzpicture}
\foreach \brk in {0,...,4} {
\begin{scope}[rotate=\brk * 72]
\node (k\brk) at (0,-1.5) {};
\end{scope}
}
\draw (0,0) \foreach \brk in {0,...,4} {let \n0=\brk, \n1={int(Mod(\brk+1,5))}, \n2={int(Mod(\brk+2,5))} in (k\n0) .. controls (k\n0.16 south east) and (k\n1.16 south west) .. (k\n1.center) .. controls (k\n1.4 north east) and (k\n2.4 north west) .. (k\n2)} (k2);
\end{tikzpicture}

cinquefoil

\begin{tikzpicture}
\foreach \brk in {0,...,4} {
\begin{scope}[rotate=-\brk * 72]
\node (k\brk) at (0,-1.5) {};
\pgfmathtruncatemacro{\brl}{\brk+97}
\node[text node] at (0,2) {\(\char\brl\)};
\end{scope}
}
\node[text node] at (0,0) {\(f\)};
\node[text node] at (126:2.5) {\(g\)};
\draw (0,0) \foreach \brk in {0,...,4} {let \n0=\brk, \n1={int(Mod(\brk-1,5))}, \n2={int(Mod(\brk-2,5))} in (k\n0) .. controls (k\n0.16 south east) and (k\n1.16 south west) .. (k\n1.center) .. controls (k\n1.4 north east) and (k\n2.4 north west) .. (k\n2)} (k2);

\end{tikzpicture}

(K)not sure what this one is called, it's an obvious extension of the figure 8 knot:

sort of figure 8ish

\begin{tikzpicture}
\node[rotate=45] (tl) at (-1,1) {};
\node[rotate=-45] (tr) at (1,1) {};
\edef\twists{10}
\foreach \brk in {0,...,\twists} {
\node (m\brk) at (0,-1 - \brk) {};
}
\foreach \brk in {1,...,\twists} {
\pgfmathparse{int(\brk - 1)}
\edef\brl{\pgfmathresult}
\draw (m\brk) .. controls (m\brk.4 north west) and (m\brl.4 south west) .. (m\brl.center);
\draw (m\brk.center) .. controls (m\brk.4 north east) and (m\brl.4 south east) .. (m\brl);
}
\draw (m0) .. controls (m0.8 north west) and (tl.3 south west) .. (tl.center);
\draw (m0.center) .. controls (m0.8 north east) and (tr.3 south east) .. (tr);
\draw (tl.center) .. controls (tl.16 north east) and (tr.16 north west) .. (tr);
\draw (m\twists) .. controls (m\twists.32 south east) and (tr.32 north east) .. (tr.center);
\draw (m\twists.center) .. controls (m\twists.32 south west) and (tl.32 north west) .. (tl);
\draw (tl) -- (tr.center);
\end{tikzpicture}

Also have examples of the Reidemeister moves and likewise. Most of the images listed at this nLab page were done using this package and then exported to SVG via tex4ht. All of the images at this page were done using this package. In particular, the following monstrosity!

iterated Brunnian link with inscription

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thanks for the links and nice examples! I think I'll have some fun fiddling around with this – confusedmath May 2 '11 at 15:10
    
The link is broken. – chaosflaws Jul 2 at 20:57
    
@chaosflaws This answer is hopelessly out of date. My newer answer below supersedes this one. – Loop Space Jul 2 at 23:14

Run with xelatex or use package auto-pst-pdf or run latex->dvips->ps2pdf

\documentclass{article}
\usepackage{pst-knot}
\begin{document}

\begin{pspicture}(-2,-2)(5,2)
 \psKnot[linewidth=3pt,linecolor=red](0,0){3-1}
 \psKnot[linewidth=3pt,linecolor=blue](4,0){4-1}
\end{pspicture}

\end{document}

enter image description here

The documentation explains the meaning of 3-1 and 4-1

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(This question, although old, keeps coming up when I search for tikz knots - yes, I know I'm searching for my own package but it's how I find the documentation when I'm on a foreign machine - so I thought I'd add an answer about the tikz knots library which was developed some time after this question was asked.)

There's a TikZ library, knots, which is available on CTAN (as part of a package called spath3) and github. There are quite a few questions on this site with examples using this package, here are just a few:

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