283 Photos - Oct 3, 2011
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"Because, because, because, because
Because of the wonderful things TikZ does!"

If I get round to releasing the package on CTAN, the code for this will be:

\begin{tikzpicture}[
every Penrose tile/.style={draw},
every kite/.style={fill=reverseGoldenTriangle},
every dart/.style={fill=goldenTriangle},
Penrose tile/.code={
\pgfmathsetmacro\tint{int((183-#1)/3)}
\pgfkeysalso{tint fill colour=\tint}
}
]
\foreach[evaluate=\k as \mk using {\k+Mod(\k,2)},evaluate=\k as \ax
using {Mod(\k,2) == 0 ? "T" : "t"}] \k in {0,...,9} {
\begin{scope}[rotate=\mk*36]
\PenroseDecomposition[Penrose step=8cm]{kite}{6}{\ax}
\end{scope}
}
\end{tikzpicture}Photo: Hard at work avoiding grading ...

Someone asked me about using my knots package to draw Celtic knots.  In the words of a Great Man[1], "Yes, we can!".

Only, it's a bit tedious so the next question was as to a way to automate it.  At the risk of repeating myself, "Klart det kan!".

Here's the user code.  The "package" code is not yet available.  I'm not really sure it's worth a CTAN package all by itself, it could work as a part of my knots package but that won't get updated for a bit.  So if anyone would like it to be available, the best solution would be for that someone to ask a question on TeX-SX along the lines of "I'd like to automatically draw Celtic knots.  In my ideal world, one would just have to type <the code below> and produce <the attached image>.  Does anyone have any idea how to do this?".

\begin{tikzpicture}[
scale=.5,
celtic/.style={
double=white,
red,
double distance=5pt,
line width=1pt
},
celtic bar/.style={
ultra thick,
black,
draw
},
]
\CelticSetSize{20}{12}
\CelticSetSymmetricCrossing{10}{1}{|}
\CelticSetSymmetricCrossing{3}{2}{|}
\CelticSetSymmetricCrossing{3}{4}{|}
\CelticSetSymmetricCrossing{6}{3}{|}
\CelticSetSymmetricCrossing{10}{5}{|}
\CelticSetSymmetricCrossing{10}{3}{-}
\CelticSetSymmetricCrossing{9}{6}{-}
\CelticSetSymmetricCrossing{6}{5}{-}
\CelticSetSymmetricCrossing{3}{6}{-}
\CelticSetSymmetricCrossing{1}{4}{-}
\draw[gray!30,ultra thin] (0,0) grid (20,12);
\draw[ultra thick] (0,0) rectangle (20,12);
\CelticDrawCrossings[celtic bar]
\CelticDrawPath[celtic]
\begin{scope}[yshift=-12cm]
\draw[gray!30,ultra thin] (0,0) grid (20,12);
\draw[ultra thick] (0,0) rectangle (20,12);
\CelticDrawCrossings[celtic bar]
\CelticDrawPath*[celtic]
\end{scope}
\end{tikzpicture}


[1] Oops!  Nearly forgot the footnote.  In case anyone is worried I've gone all political, remember that I am *British* and I have kids of a certain age.  My cultural icons are not necessarily the same as yours.[2]

[2] Also, for those who don't know the chronology of British and American minor celebrities, as with so many great ideas, we had it first and you stole it.Photo: Got about half my grading done, so celebrated by working on the interface.

Here's what you'd write in the document to produce the attached picture:

\begin{tikzpicture}[
scale=.5,
celtic path/.style={
draw,
double=gray!40,
red,
double distance=4mm,
line width=1pt
},
celtic surround/.style={
ultra thick,
black,
draw
},
]
\CelticDrawPath[
size={12,12},
symmetric crossings={
2:10,3:9,-
},
at={(1,1)}
]
\end{tikzpicture}

(I notice no-one has posted a question about this on TeX-SX.  Looks like I might have to ask-and-answer it myself.)Photo: Last one for the day.Photo: I just couldn't let it lie ...

Much as I like +Mike Stay 's Borromean rings, I feel that they lack a certain Celtic something.  So I've reworked them to make them a bit more like something one might meet on an island off Northumberland.  They're no longer the Borromean rings (at least, I'm pretty sure that the individual components are knotted) but they do share the "no two are linked but all three are" property.

If one works in Milnor's Link Group setting, then they are equivalent to the Borromean Rings.

(I'd like to add that I worked out the pattern using the javascript program that Mike linked to, and then transferred it to my TikZ code.  Looking at the colours, some might think that the latter stage was a step too far.)Photo: I think this is the one that should really be called a "Penrose Rose".  In case the detail is not clear, each tile is a single block colour.

And I'd like to note, to record that I did think of this, that the picture that I really ought to apply this effect to would be one of a certain time traveller's companion (think about it ...).  However, whilst such images are easy to find, I'd prefer not to run afoul of copyright.

So if any passing #TimeLord (for example, +Doctor Who  ), or companion thereof, happens to own the copyright on a suitable image and would be willing to allow me to apply this effect (and distribute the result), please get in touch!  The result is really quite striking.

Oh, and it is rendered using TeX.  But it was designed using Codea.

#DoctorWho #DoctorWhoArt