penrose (12jul18)

git-svn-id: svn://tug.org/texlive/trunk@48202 c570f23f-e606-0410-a88d-b1316a301751

2 files changed, 2801 insertions, 0 deletions

diff --git a/Master/texmf-dist/source/latex/penrose/penrose.ins b/Master/texmf-dist/source/latex/penrose/penrose.ins
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+%%
+%% This is file `penrose.ins',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% penrose.dtx  (with options: `install')
+%% ----------------------------------------------------------------
+%% penrose --- TikZ library for producing Penrose tilings
+%% E-mail: loopspace@mathforge.org
+%% Released under the LaTeX Project Public License v1.3c or later
+%% See http://www.latex-project.org/lppl.txt
+%% ----------------------------------------------------------------
+%% 
+\input docstrip.tex
+\keepsilent
+\askforoverwritefalse
+\preamble
+----------------------------------------------------------------
+penrose --- TikZ library for producing Penrose tilings
+E-mail: loopspace@mathforge.org
+Released under the LaTeX Project Public License v1.3c or later
+See http://www.latex-project.org/lppl.txt
+----------------------------------------------------------------
+
+\endpreamble
+\postamble
+
+Copyright (C) 2014-2016 by Andrew Stacey <loopspace@mathforge.org>
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License (LPPL), either
+version 1.3c of this license or (at your option) any later
+version.  The latest version of this license is in the file:
+
+http://www.latex-project.org/lppl.txt
+
+This work is "maintained" (as per LPPL maintenance status) by
+Andrew Stacey.
+
+This work consists of the files  penrose.dtx
+                                 penrose_doc.tex
+and the derived files            penrose.ins
+                                 penrose_code.pdf
+                                 tikzlibrarypenrose.code.tex
+                                 penrose.pdf
+                                 README
+
+\endpostamble
+\usedir{tex/latex/penrose}
+\generate{
+  \file{tikzlibrarypenrose.code.tex}{\from{\jobname.dtx}{library}}
+}
+\endbatchfile
+%% 
+%% Copyright (C) 2014-2016 by Andrew Stacey <loopspace@mathforge.org>
+%% 
+%% This work may be distributed and/or modified under the
+%% conditions of the LaTeX Project Public License (LPPL), either
+%% version 1.3c of this license or (at your option) any later
+%% version.  The latest version of this license is in the file:
+%% 
+%% http://www.latex-project.org/lppl.txt
+%% 
+%% This work is "maintained" (as per LPPL maintenance status) by
+%% Andrew Stacey.
+%% 
+%% This work consists of the files  penrose.dtx
+%%                                  penrose_doc.tex
+%% and the derived files            penrose.ins
+%%                                  penrose_code.pdf
+%%                                  tikzlibrarypenrose.code.tex
+%%                                  penrose.pdf
+%%                                  README
+%% 
+%%
+%% End of file `penrose.ins'.
diff --git a/Master/texmf-dist/source/latex/penrose/penrose_code.dtx b/Master/texmf-dist/source/latex/penrose/penrose_code.dtx
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index 00000000000..be7030312fe
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+++ b/Master/texmf-dist/source/latex/penrose/penrose_code.dtx
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+% \iffalse meta-comment
+%<*internal>
+\iffalse
+%</internal>
+%<*readme>
+----------------------------------------------------------------
+penrose --- TikZ library for producing Penrose tilings
+E-mail: loopspace@mathforge.org
+Released under the LaTeX Project Public License v1.3c or later
+See http://www.latex-project.org/lppl.txt
+----------------------------------------------------------------
+
+This package is for the creation of Penrose tilings using either kite-and-dart or rhombuses, and either by manual placement or automatic generation.
+%</readme>
+%<*internal>
+\fi
+\def\nameofplainTeX{plain}
+\ifx\fmtname\nameofplainTeX\else
+  \expandafter\begingroup
+\fi
+%</internal>
+%<*install>
+\input l3docstrip.tex
+\keepsilent
+\askforoverwritefalse
+\preamble
+----------------------------------------------------------------
+penrose --- TikZ library for producing Penrose tilings
+E-mail: loopspace@mathforge.org
+Released under the LaTeX Project Public License v1.3c or later
+See http://www.latex-project.org/lppl.txt
+----------------------------------------------------------------
+
+\endpreamble
+\postamble
+
+Copyright (C) 2014-2018 by Andrew Stacey <loopspace@mathforge.org>
+
+This work may be distributed and/or modified under the
+conditions of the LaTeX Project Public License (LPPL), either
+version 1.3c of this license or (at your option) any later
+version.  The latest version of this license is in the file:
+
+http://www.latex-project.org/lppl.txt
+
+This work is "maintained" (as per LPPL maintenance status) by
+Andrew Stacey.
+
+This work consists of the files  penrose3.dtx
+                                 penrose.tex
+and the derived files            penrose.ins
+                                 penrose3.pdf
+                                 penrose.pdf
+                                 tikzlibrarypenrose.code.tex
+                                 README
+
+\endpostamble
+\usedir{tex/latex/penrose}
+\generate{
+  \file{tikzlibrarypenrose.code.tex}{\from{\jobname.dtx}{library}}
+}
+%</install>
+%<install>\endbatchfile
+%<*internal>
+\usedir{source/latex/penrose}
+\generate{
+  \file{\jobname.ins}{\from{\jobname.dtx}{install}}
+}
+\nopreamble\nopostamble
+\usedir{doc/latex/penrose}
+\generate{
+  \file{README.txt}{\from{\jobname.dtx}{readme}}
+}
+\ifx\fmtname\nameofplainTeX
+  \expandafter\endbatchfile
+\else
+  \expandafter\endgroup
+\fi
+%</internal>
+%<*driver>
+\documentclass[full]{l3doc}
+\usepackage[T1]{fontenc}
+\usepackage{lmodern}
+\usepackage{tikz}
+\usepackage{trace}
+\usetikzlibrary{penrose}
+%\traceoff
+%\usepackage[numbered]{hypdoc}
+\definecolor{lstbgcolor}{rgb}{0.9,0.9,0.9} 
+ 
+\usepackage{listings}
+\lstloadlanguages{[LaTeX]TeX}
+\lstset{breakatwhitespace=true,breaklines=true,language=TeX}
+ 
+\usepackage{fancyvrb}
+
+\newenvironment{example}
+  {\VerbatimEnvironment
+   \begin{VerbatimOut}[gobble=2]{example.out}}
+  {\end{VerbatimOut}
+   \begin{center}
+%   \setlength{\parindent}{0pt}
+   \fbox{\begin{minipage}{.9\linewidth}
+     \lstset{breakatwhitespace=true,breaklines=true,language=TeX,basicstyle=\small}
+     \lstinputlisting[]{example.out}
+   \end{minipage}}
+
+   \fbox{\begin{minipage}{.9\linewidth}
+     \input{example.out}
+   \end{minipage}}
+\end{center}
+}
+\EnableCrossrefs
+\CodelineIndex
+\RecordChanges
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \CheckSum{2944}
+%
+% \CharacterTable
+%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%   Digits        \0\1\2\3\4\5\6\7\8\9
+%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%   Dollar        \$     Percent       \%     Ampersand     \&
+%   Acute accent  \'     Left paren    \(     Right paren   \)
+%   Asterisk      \*     Plus          \+     Comma         \,
+%   Minus         \-     Point         \.     Solidus       \/
+%   Colon         \:     Semicolon     \;     Less than     \<
+%   Equals        \=     Greater than  \>     Question mark \?
+%   Commercial at \@     Left bracket  \[     Backslash     \\
+%   Right bracket \]     Circumflex    \^     Underscore    \_
+%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%   Right brace   \}     Tilde         \~}
+%
+%
+% \changes{1.0}{2014/05/07}{Converted to DTX file}
+%
+% \DoNotIndex
+%   {
+%     \begingroup,
+%     \catcode,
+%     \active,
+%     \csname,
+%     \endcsname,
+%   }%
+%
+% \providecommand*{\url}{\texttt}
+% \title{The \textsf{Penrose} package}
+% \author{Andrew Stacey\texorpdfstring{\\ \url{loopspace@mathforge.org}}{}}
+% \date{1.0 from 2018/07/10}
+%
+%
+% \maketitle
+%
+% 
+% \section{Introduction}
+%
+% This is a TikZ library for drawing Penrose tiles (kite/dart, rhombus, and pentagon versions).
+% It provides two methods of drawing: one in which an automatic pattern is built, and one where the tiles can be placed ``by hand''.
+% The tiles can be shaped and (hopefully!) still fit together.
+% For user documentation, see the \Verb+penrose.pdf+ file.
+%
+% \StopEventually{}
+%
+% \section{Implementation}
+%
+% \iffalse
+%<*library>
+% \fi
+% \subsection{Initialisation}
+%
+%
+%    \begin{macrocode}
+%<@@=penrose>
+%    \end{macrocode}
+% We use the \Verb+spath3+ library for manipulating the paths that will make up the tiles.
+%
+%    \begin{macrocode}
+\RequirePackage{spath3}
+%    \end{macrocode}
+% Now we move in to the realm of \LaTeX3.
+%    \begin{macrocode}
+\ExplSyntaxOn
+%    \end{macrocode}
+%
+% Start with some basic paths (lines) for the sides of the tiles so that we know that we have well-defined tiles at the outset.
+%
+%    \begin{macrocode}
+\MakeSPath{Penrose path a}
+      {
+        \pgfsyssoftpath@movetotoken{0pt}{0pt}
+        \pgfsyssoftpath@linetotoken{1pt}{0pt}
+      }
+\SPathPrepare{Penrose path a}
+\CloneSPath {Penrose path a}{Penrose path b}
+\CloneSPath {Penrose path a}{Penrose path c}
+\CloneSPath {Penrose path a}{Penrose path d}
+\CloneSPath {Penrose path a}{Penrose path A}
+\CloneSPath {Penrose path a}{Penrose path B}
+\CloneSPath {Penrose path a}{Penrose path C}
+\CloneSPath {Penrose path a}{Penrose path D}
+%    \end{macrocode}
+%
+% \begin{variable}{\l__penrose_tmpa_fp, \l__penrose_tmpb_fp, \l__penrose_tmpc_fp, \l__penrose_tmpa_tl, \l__penrose_tmpb_tl, \l__penrose_tmpc_tl}
+% We need a few temporary variables to hold intermediate calculations.
+%
+%    \begin{macrocode}
+\fp_new:N \l__penrose_tmpa_fp
+\fp_new:N \l__penrose_tmpb_fp
+\fp_new:N \l__penrose_tmpc_fp
+\tl_new:N \l__penrose_tmpa_tl
+\tl_new:N \l__penrose_tmpb_tl
+\tl_new:N \l__penrose_tmpc_tl
+%    \end{macrocode}
+% \end{variable}
+%
+% \subsection{Creating the Tiles}
+%
+% \begin{macro}[internal]{\penrose_normalise_path:n}
+% When defining the path for a side, we normalise so that it starts at the origin and ends at \Verb+(1pt,0pt)+.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \penrose_normalise_path:n #1
+{
+%    \end{macrocode}
+% Get the initial point of the path and convert to floating point.
+%    \begin{macrocode}
+  \spath_get:nnN {#1} {initial point} \l__penrose_tmpa_tl
+  \fp_set:Nn \l__penrose_tmpa_fp {\tl_head:N \l__penrose_tmpa_tl}
+  \tl_set:Nx \l__penrose_tmpa_tl {\tl_tail:N \l__penrose_tmpa_tl}
+  \fp_set:Nn \l__penrose_tmpb_fp {\tl_head:N \l__penrose_tmpa_tl}
+%    \end{macrocode}
+% Get the final point of the path, and compute the difference of the final and initial points.
+%
+% The resulting numbers, say \(a\) and \(b\), will be put into a matrix to rotate and scale the path.
+% The formula for the matrix is:
+%^^A
+% \[
+% \frac{1}{a^2 + b^2}
+% \begin{bmatrix} a & b \\ -b & a \end{bmatrix}
+% \]
+%
+%    \begin{macrocode}
+  \spath_get:nnN {#1} {final point} \l__penrose_tmpa_tl
+  \fp_set:Nn \l__penrose_tmpa_fp
+  {\tl_head:N \l__penrose_tmpa_tl - \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpa_tl {\tl_tail:N \l__penrose_tmpa_tl}
+  \fp_set:Nn \l__penrose_tmpb_fp
+  {\tl_head:N \l__penrose_tmpa_tl - \l__penrose_tmpb_fp}
+%    \end{macrocode}
+% Now compute the square of the length of the path for scaling.
+%    \begin{macrocode}
+  \fp_set:Nn \l__penrose_tmpc_fp
+  {\l__penrose_tmpa_fp^2 + \l__penrose_tmpb_fp^2}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_tmpa_fp/\l__penrose_tmpc_fp}
+  \fp_set:Nn \l__penrose_tmpb_fp {\l__penrose_tmpb_fp/\l__penrose_tmpc_fp}
+  \fp_set:Nn \l__penrose_tmpc_fp {-\l__penrose_tmpb_fp}
+%    \end{macrocode}
+% Now construct the matrix.
+%    \begin{macrocode}
+  \tl_set:Nx \l__penrose_tmpb_tl
+  {
+    {\fp_use:N \l__penrose_tmpa_fp}
+    {\fp_use:N \l__penrose_tmpb_fp}
+    {\fp_use:N \l__penrose_tmpc_fp}
+    {\fp_use:N \l__penrose_tmpa_fp}
+  }
+%    \end{macrocode}
+% Get the initial point back again for the translation part.
+%    \begin{macrocode}
+  \spath_get:nnN {#1} {initial point} \l__penrose_tmpa_tl
+%    \end{macrocode}
+% But we need to premultiply by the matrix because of how the transformations are applied.
+%    \begin{macrocode}
+  \fp_set:Nn \l__penrose_tmpa_fp
+  {
+    (-1) * \l__penrose_tmpa_fp * \tl_head:N \l__penrose_tmpa_tl
+    + (-1) * \l__penrose_tmpb_fp * \tl_tail:N \l__penrose_tmpa_tl
+  }
+  \fp_set:Nn \l__penrose_tmpb_fp
+  {
+    (-1) * \l__penrose_tmpa_fp * \tl_tail:N \l__penrose_tmpa_tl
+    +  \l__penrose_tmpb_fp * \tl_head:N \l__penrose_tmpa_tl
+  }
+%    \end{macrocode}
+% Finally, we apply the transformation to the path.
+%    \begin{macrocode}
+  \tl_put_right:Nx \l__penrose_tmpb_tl {
+    {\fp_to_dim:N \l__penrose_tmpa_fp}
+    {\fp_to_dim:N \l__penrose_tmpb_fp}
+  }
+  \spath_transform:nV {#1} \l__penrose_tmpb_tl
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\SetPenrosePath}
+% This sets the path corresponding to a particular side to the current path, and normalises it.
+%    \begin{macrocode}
+\NewDocumentCommand \SetPenrosePath { m }
+{
+  \pgfsyssoftpath@getcurrentpath\l__penrose_tmpa_tl
+  \spath_clear_new:n {Penrose path #1}
+  \spath_put:nnV {Penrose path #1} {path} \l__penrose_tmpa_tl
+  \penrose_normalise_path:n {Penrose path #1}
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\tikz_scan_point:n}
+% This is a wrapper around \Verb+\tikz@scan@one@point+ to make it easier to use with \LaTeX3 variables.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \tikz_scan_point:n #1
+{
+  \tikz@scan@one@point\pgfutil@firstofone#1\relax
+}
+\cs_generate_variant:Nn \tikz_scan_point:n {V}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\penrose_make_tile:nnn}
+% This builds the tile path from its pieces.
+% The arguments are the name of the tile, the descriptions of the sides, and a token list of the coordinates.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \penrose_make_tile:nnn #1#2#3
+{
+%    \end{macrocode}
+% Get the first coordinate and initialise the path with a move to this point.
+%    \begin{macrocode}
+  \tl_set:Nn \l__penrose_tmpa_tl {#3}
+  \tl_set:Nx \l__penrose_tmpb_tl {\tl_head:N \l__penrose_tmpa_tl}
+  \tl_set:Nn \l__penrose_tmpa_tl {\pgfsyssoftpath@movetotoken}
+  \tikz_scan_point:V \l__penrose_tmpb_tl
+  \tl_put_right:Nx \l__penrose_tmpa_tl
+  {
+    {\dim_use:N \pgf@x}{\dim_use:N \pgf@y}
+  }
+  \spath_clear_new:n {Penrose path tile #1}
+  \spath_put:nnV {Penrose path tile #1} {path} \l__penrose_tmpa_tl
+%    \end{macrocode}
+% Now we have our path initialised, we can start appending the side paths according to the specification in the second argument.
+%
+% We append the initial coordinate to the end of the list to make a closed cycle.
+%    \begin{macrocode}
+  \tl_set:Nn \l__penrose_tmpa_tl {#3}
+  \tl_put_right:Nx \l__penrose_tmpa_tl {{\tl_head:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+% Now we walk through the description of the sides, adding the specified paths to our tile path.
+%    \begin{macrocode}
+  \tl_map_inline:nn {#2} {
+%    \end{macrocode}
+% Clone the path for this side.
+%    \begin{macrocode}
+    \spath_clone:nn {Penrose path ##1} {Penrose path tmpa}
+%    \end{macrocode}
+% Strip off the next coordinate, and convert it to a point.
+%    \begin{macrocode}
+    \tl_set:Nx \l__penrose_tmpb_tl {\tl_head:N \l__penrose_tmpa_tl}
+    \tl_set:Nx \l__penrose_tmpa_tl {\tl_tail:N \l__penrose_tmpa_tl}
+    \tikz_scan_point:V \l__penrose_tmpb_tl
+%    \end{macrocode}
+% Store the resulting coordinate.
+%    \begin{macrocode}
+    \fp_set:Nn \l__penrose_tmpa_fp { \pgf@x }
+    \fp_set:Nn \l__penrose_tmpb_fp { \pgf@y }
+%    \end{macrocode}
+% Now get the next coordinate.
+%    \begin{macrocode}
+    \tl_set:Nx \l__penrose_tmpb_tl {\tl_head:N \l__penrose_tmpa_tl}
+    \tikz_scan_point:V \l__penrose_tmpb_tl
+%    \end{macrocode}
+% We want the difference between the two coordinates.
+%    \begin{macrocode}
+    \fp_set:Nn \l__penrose_tmpa_fp {\pgf@x - \l__penrose_tmpa_fp}
+    \fp_set:Nn \l__penrose_tmpb_fp {\pgf@y - \l__penrose_tmpb_fp}
+%    \end{macrocode}
+% This is converted into a transformation matrix.
+%    \begin{macrocode}
+    \fp_set:Nn \l__penrose_tmpc_fp {-\l__penrose_tmpb_fp}
+    \tl_set:Nx \l__penrose_tmpb_tl
+    {
+      {\fp_use:N \l__penrose_tmpa_fp}
+      {\fp_use:N \l__penrose_tmpc_fp}
+      {\fp_use:N \l__penrose_tmpb_fp}
+      {\fp_use:N \l__penrose_tmpa_fp}
+      {0}
+      {0}
+    }
+%    \end{macrocode}
+% The transformation is applied to the cloned path.
+%    \begin{macrocode}
+    \spath_transform:nV {Penrose path tmpa} \l__penrose_tmpb_tl
+%    \end{macrocode}
+% And this is welded to the tile path.
+%    \begin{macrocode}
+    \spath_weld:nn {Penrose path tile #1} {Penrose path tmpa}
+  }
+%    \end{macrocode}
+% At the end we close the path.
+%    \begin{macrocode}
+  \spath_close_path:n {Penrose path tile #1}
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\penrose_make_tile:nn}
+% A wrapper around the above which allows us to specify the second two arguments as two items in a token list.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \penrose_make_tile:nn #1#2
+{
+  \penrose_make_tile:nnn {#1} #2
+}
+\cs_generate_variant:Nn \penrose_make_tile:nn {nV}
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Specifying the Tiles}
+%
+% The tile specifications are contained in a \Verb+prop+.
+%    \begin{macrocode}
+\prop_new:N \g__penrose_tiles_prop
+%    \end{macrocode}
+%
+% \begin{macro}[internal]{\tl_add_coordinate:Nnn}
+% Process a coordinate through \Verb+fp+ and adds it to a token list.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \tl_add_coordinate:Nnn #1#2#3 {
+  \fp_set:Nn \l__penrose_tmpa_fp{#2}
+  \fp_set:Nn \l__penrose_tmpb_fp{#3}
+  \tl_put_right:Nx #1
+  {
+    {(\fp_use:N \l__penrose_tmpa_fp, \fp_use:N \l__penrose_tmpb_fp)}
+  }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% Now we specify the tiles.
+% The specification is a clockwise list of the vertices together with the labels of the corresponding sides.
+% There are three basic paths, \Verb+a+, \Verb+b+, \Verb+c+, and their complements (which are capitalised).
+%
+% \begin{itemize}
+% \item Thin Rhombus.
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(18)}{sind(18)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {2*cosd(18)}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(18)}{-sind(18)}
+
+\prop_gput:Nnx \g__penrose_tiles_prop {thin~ rhombus}
+{{a A B b} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Thick Rhombus.
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(36)}{sind(36)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {2*cosd(36)}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(36)}{-sind(36)}
+
+\prop_gput:Nnx \g__penrose_tiles_prop {thick~ rhombus}
+{{B a A b} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Dart.
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl
+{2*sind(18)*cosd(108)}{2*sind(18)*sind(108)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {2*sind(18)}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl
+{2*sind(18)*cosd(108)}{-2*sind(18)*sind(108)}
+
+\prop_gput:Nnx \g__penrose_tiles_prop {dart}
+{{c a A C} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Kite.
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(36)}{sind(36)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {1}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(36)}{-sind(36)}
+
+\prop_gput:Nnx \g__penrose_tiles_prop {kite}
+{{a c C A} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Golden Triangle.
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(18)}{sind(18)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(18)}{-sind(18)}
+
+\prop_gput:Nnx \g__penrose_tiles_prop {golden~ triangle}
+{{a c b} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Reverse Golden Triangle.
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(18)}{sind(18)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(18)}{-sind(18)}
+
+\prop_gput:Nnx \g__penrose_tiles_prop {reverse~ golden~ triangle}
+{{B C A} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Golden Gnomon
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(36)}{sind(36)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {2*cosd(36)}{0}
+
+\prop_gput:Nnx \g__penrose_tiles_prop {golden~ gnomon}
+{{C b A} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Reverse Golden Gnomon
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {2*cosd(36)}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(36)}{-sind(36)}
+\prop_gput:Nnx \g__penrose_tiles_prop {reverse~ golden~ gnomon}
+{{a B c} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Primary Pentagon (pentagon 5)
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(108)}{sind(108)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl
+{1+cosd(72)+cosd(144)}{sind(72)+sind(144)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {1+cosd(72)}{sind(72)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {1}{0}
+\prop_gput:Nnx \g__penrose_tiles_prop {pentagon~ 5}
+{{a a a a a} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Secondary Pentagon (pentagon 3)
+%    \begin{macrocode}
+\prop_gput:Nnx \g__penrose_tiles_prop {pentagon~ 3}
+{{A b a a b} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Tertiary Pentagon (pentagon 2)
+%    \begin{macrocode}
+\prop_gput:Nnx \g__penrose_tiles_prop {pentagon~ 2}
+{{d A c c A} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Pentagram
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {1}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {1-cosd(36)}{-sind(36)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl
+{1-cosd(36)-cosd(108)}{-sind(36)-sind(108)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(108)}{-sind(108)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl
+{-1+3*cosd(108)+cosd(36)}{-sind(36)-sind(108)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl
+{-1+2*cosd(108)+cosd(36)}{-sind(36)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {-1+2*cosd(108)}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {2*cosd(108)}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(108)}{sind(108)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\prop_gput:Nnx \g__penrose_tiles_prop {pentagram}
+{{C C C C C C C C C C} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Boat
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {-1+2*cosd(108)}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {2*cosd(108)}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(108)}{sind(108)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {1}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {1-cosd(36)}{-sind(36)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl
+{-1+2*cosd(108)+cosd(36)}{-sind(36)}
+\prop_gput:Nnx \g__penrose_tiles_prop {boat}
+{{C C C C B D B} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \item Diamond.
+%    \begin{macrocode}
+\tl_clear:N \l__penrose_tmpa_tl
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {0}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(18)}{sind(18)}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {2*cosd(18)}{0}
+\tl_add_coordinate:Nnn \l__penrose_tmpa_tl {cosd(18)}{-sind(18)}
+\prop_gput:Nnx \g__penrose_tiles_prop {diamond}
+{{D B B D} {\tl_use:N \l__penrose_tmpa_tl}}
+%    \end{macrocode}
+%
+% \end{itemize}
+%
+% \begin{macro}[internal]{\MakePenroseTile}
+% This is the user wrapper around the tile creation macros.
+%    \begin{macrocode}
+\NewDocumentCommand \MakePenroseTile {m}
+{
+  \prop_get:NnN \g__penrose_tiles_prop {#1} \l__penrose_tmpa_tl
+  \penrose_make_tile:nV {#1} \l__penrose_tmpa_tl
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\UsePenroseTile}
+% This is the command that actually places a tile on the page.
+% The first argument is optional and is for styling.
+%    \begin{macrocode}
+\NewDocumentCommand \UsePenroseTile {O{} m} 
+{
+%    \end{macrocode}
+% We need to transform the tile to correspond to the current transformation matrix.
+% To ensure that we only transform the current tile, we clone it first.
+%    \begin{macrocode}
+  \spath_clone:nn {Penrose path tile #2} {Penrose path tmpa}
+%    \end{macrocode}
+% The transformation matrix returned by PGF appears to be transposed from what it should be.
+% (This needs a little more investigation, it might be that I've implemented the multiplication incorrectly here.)
+%    \begin{macrocode}
+  \pgfgettransform \l__penrose_tmpa_tl
+  \tl_clear:N \l__penrose_tmpb_tl
+  \tl_set:Nx \l__penrose_tmpb_tl {{\tl_head:N \l__penrose_tmpa_tl}}
+  \tl_set:Nx \l__penrose_tmpa_tl {\tl_tail:N \l__penrose_tmpa_tl}
+  \tl_put_right:Nx \l__penrose_tmpb_tl
+  {
+    {\tl_item:Nn \l__penrose_tmpa_tl {2}}
+  }
+  \tl_put_right:Nx \l__penrose_tmpb_tl
+  {
+    {\tl_item:Nn \l__penrose_tmpa_tl {1}}
+  }
+  \tl_set:Nx \l__penrose_tmpa_tl {\tl_tail:N \l__penrose_tmpa_tl}
+  \tl_set:Nx \l__penrose_tmpa_tl {\tl_tail:N \l__penrose_tmpa_tl}
+  \tl_put_right:NV \l__penrose_tmpb_tl \l__penrose_tmpa_tl
+%    \end{macrocode}
+% Apply the transformation, protocol the path, and render it.
+%    \begin{macrocode}
+  \spath_transform:nV {Penrose path tmpa} \l__penrose_tmpb_tl
+  \spath_protocol_path:n {Penrose path tmpa}
+  \spath_tikz_path:nn {#1}{Penrose path tmpa}
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% This is a style for a user to take a path and make it into the path for one of the sides.
+% It needs to store both that side and the reverse.
+%    \begin{macrocode}
+\tikzset{
+  save~ Penrose~ path/.code={
+    \tikz@addmode{
+%    \end{macrocode}
+% Get the current path.
+%    \begin{macrocode}
+      \pgfsyssoftpath@getcurrentpath\l__penrose_tmpa_tl
+%    \end{macrocode}
+% Clear the receiving path, and store the current path in it.
+%    \begin{macrocode}
+      \spath_clear_new:n {Penrose path #1}
+      \spath_put:nnV {Penrose path #1} {path} \l__penrose_tmpa_tl
+%    \end{macrocode}
+% Normalise the path.
+%    \begin{macrocode}
+      \penrose_normalise_path:n {Penrose path #1}
+%    \end{macrocode}
+% Now create the reverse path.
+% The name is the upper case version.
+%    \begin{macrocode}
+      \tex_uppercase:D {\tl_set:Nx \l__penrose_tmpa_tl {#1}}
+%    \end{macrocode}
+% Clone the path.
+%    \begin{macrocode}
+      \spath_clone:nn {Penrose path #1}
+      {Penrose path \tl_use:N \l__penrose_tmpa_tl }
+%    \end{macrocode}
+% Reverse it.
+%    \begin{macrocode}
+      \spath_reverse:n {Penrose path \tl_use:N \l__penrose_tmpa_tl}
+%    \end{macrocode}
+% Swap the start and end.
+%    \begin{macrocode}
+      \spath_transform:nnnnnnn {Penrose path \tl_use:N \l__penrose_tmpa_tl}
+      {-1} {0} {0} {-1} {1} {0}
+    }
+  },
+  expand~ key/.code={
+    \exp_args:NV \pgfkeysalso #1
+  }
+}
+%    \end{macrocode}
+%
+% Create the basic tile shapes.
+%    \begin{macrocode}
+\MakePenroseTile {thin~ rhombus}
+\MakePenroseTile {thick~ rhombus} 
+\MakePenroseTile {dart}
+\MakePenroseTile {kite}
+\MakePenroseTile {golden~ triangle}
+\MakePenroseTile {reverse~ golden~ triangle}
+\MakePenroseTile {golden~ gnomon}
+\MakePenroseTile {reverse~ golden~ gnomon}
+\MakePenroseTile {pentagon~ 5}
+\MakePenroseTile {pentagon~ 3}
+\MakePenroseTile {pentagon~ 2}
+\MakePenroseTile {pentagram}
+\MakePenroseTile {boat}
+\MakePenroseTile {diamond}
+%    \end{macrocode}
+%
+% \subsection{Lindenmayer System}
+% 
+% This is an implementation of the Lindenmayer System description of Penrose tilings as a way of generating tilings from a specific starting seed.
+%
+% The implementation uses \Verb+prop+s to store \emph{rules} and \emph{actions}.
+% The rules are used to expand the starting seed to a certain level, after which the actions are carried out.
+% The syntax is based on the PGF library, but as we're already using \LaTeX3 it is reimplemented in that.
+%
+% These are the rules for generating rhombus tilings.
+%    \begin{macrocode}
+\prop_new:N \g__penrose_rhombus_lms_rule_prop
+\prop_put:Nnn \g__penrose_rhombus_lms_rule_prop {T} {[f*sT][f>g]}
+\prop_put:Nnn \g__penrose_rhombus_lms_rule_prop {t} {[f_st][f>G]}
+\prop_put:Nnn \g__penrose_rhombus_lms_rule_prop {G} {[f+sG][sf>g][sf*sT]}
+\prop_put:Nnn \g__penrose_rhombus_lms_rule_prop {g} {[f-sg][sf>G][sf_st]}
+%    \end{macrocode}
+%
+% These are the rules for generating kite and dart tilings.
+%    \begin{macrocode}
+\prop_new:N \g__penrose_kite_lms_rule_prop
+\prop_put:Nnn \g__penrose_kite_lms_rule_prop {T} {[f*sT][f>st][+sg]}
+\prop_put:Nnn \g__penrose_kite_lms_rule_prop {t} {[f_st][f>sT][-sG]}
+\prop_put:Nnn \g__penrose_kite_lms_rule_prop {G} {[f*+sG][sT]}
+\prop_put:Nnn \g__penrose_kite_lms_rule_prop {g} {[f-_sg][st]}
+%    \end{macrocode}
+%
+% These are the rules for generating pentagon tilings.
+%    \begin{macrocode}
+\prop_new:N \g__penrose_pentagon_lms_rule_prop
+\prop_put:Nnn \g__penrose_pentagon_lms_rule_prop {P}
+{[s>P][1sF+Q][1+sF+Q][1*sF+Q][1-sF+Q][1_sF+Q]} % pentagon 5
+\prop_put:Nnn \g__penrose_pentagon_lms_rule_prop {Q}
+{[s>P][1+sFR][1*sF*R][1-sF+Q][1_sF+Q][1sF+Q][->fsD]} % pentagon 3
+\prop_put:Nnn \g__penrose_pentagon_lms_rule_prop {R}
+{[s>P][1-sF+Q][1+sF*R][1*sFR][1_sF*R][1sFR][_>fsD][>fsD]} % pentagon 2
+\prop_put:Nnn \g__penrose_pentagon_lms_rule_prop {G}
+{
+  [s>G]
+  [se[>d+R][e1B]]
+  [+se[>d+R][e1B]]
+  [-se[>d+R][e1B]]
+  [*se[>d+R][e1B]]
+  [_se[>d+R][e1B]]
+} % pentagram
+\prop_put:Nnn \g__penrose_pentagon_lms_rule_prop {B}
+{
+  [s>G]
+  [se[>d+R][e1B]]
+  [+se[>d+R][e1B]]
+  [-se[>d+R][e1B]]
+} % boat
+\prop_put:Nnn \g__penrose_pentagon_lms_rule_prop {D}
+{[s>d+R][s>eG][se1B]} % diamond
+%    \end{macrocode}
+%
+% Each of the standard tilings can also be drawn using triangles using the same rules.
+%    \begin{macrocode}
+\prop_set_eq:NN \g__penrose_rtriangle_lms_rule_prop
+\g__penrose_rhombus_lms_rule_prop
+\prop_set_eq:NN \g__penrose_ktriangle_lms_rule_prop
+\g__penrose_kite_lms_rule_prop
+%    \end{macrocode}
+%
+% These hold the various actions.
+%    \begin{macrocode}
+\prop_new:N \g__penrose_default_lms_action_prop
+\prop_new:N \g__penrose_rhombus_lms_action_prop
+\prop_new:N \g__penrose_kite_lms_action_prop
+\prop_new:N \g__penrose_rtriangle_lms_action_prop
+\prop_new:N \g__penrose_ktriangle_lms_action_prop
+\prop_new:N \g__penrose_pentagon_lms_action_prop
+%    \end{macrocode}
+%
+% We need some parameters.
+%    \begin{macrocode}
+\dim_new:N \l__penrose_step_dim
+\dim_set:Nn \l__penrose_step_dim {1cm}
+%    \end{macrocode}
+%
+% These are the defaults, which will be used in all the rule sets.
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_default_lms_action_prop {[} {\group_begin:}
+\prop_put:Nnn \g__penrose_default_lms_action_prop {]} {\group_end:}
+\prop_put:Nnn \g__penrose_default_lms_action_prop {f}
+{\pgftransformxshift{\l__penrose_step_dim}}
+\prop_put:Nnn \g__penrose_default_lms_action_prop {s} {
+  \fp_set:Nn \l__penrose_tmpa_fp { 2 * sind(18) * \l__penrose_step_dim }
+  \dim_set:Nn \l__penrose_step_dim {\fp_to_dim:N \l__penrose_tmpa_fp}
+}
+%    \end{macrocode}
+%
+% The rhombus rules need a variety of turns.
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_rhombus_lms_action_prop {+}
+{\pgftransformrotate{144}}
+\prop_put:Nnn \g__penrose_rhombus_lms_action_prop {*}
+{\pgftransformrotate{108}}
+\prop_put:Nnn \g__penrose_rhombus_lms_action_prop {-}
+{\pgftransformrotate{216}}
+\prop_put:Nnn \g__penrose_rhombus_lms_action_prop {_}
+{\pgftransformrotate{252}}
+\prop_put:Nnn \g__penrose_rhombus_lms_action_prop {>}
+{\pgftransformrotate{180}}
+%    \end{macrocode}
+%
+% Up to now, the actions for the rhombus and its triangle replacement are the same.
+%    \begin{macrocode}
+\prop_set_eq:NN \g__penrose_rtriangle_lms_action_prop
+\g__penrose_rhombus_lms_action_prop
+%    \end{macrocode}
+%
+% Now we do the actions that actually draw something.
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_rhombus_lms_action_prop {T} {
+  \group_begin:
+%    \end{macrocode}
+% As we go through, we keep track of how many tiles we've drawn.
+%    \begin{macrocode}
+  \int_gincr:N \l__penrose_tile_int
+%    \end{macrocode}
+% Set up the position, size, and angle correctly.
+%    \begin{macrocode}
+  \pgftransformrotate{198}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim*2*cosd(18)}
+  \pgftransformxshift{-\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+%    \end{macrocode}
+% Now we draw the thin rhombus, applying every style we can possibly imagine.
+% The \Verb+Penrose tile+ style gets the current tile and total tile numbers passed to it.
+%    \begin{macrocode}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ thin~ rhombus/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{thin~rhombus}
+  \group_end:
+}
+%    \end{macrocode}
+%
+% Same for the thick rhombus.
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_rhombus_lms_action_prop {G} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)/(2*cosd(36))}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ thick~ rhombus/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{thick~rhombus}
+  \group_end:
+}
+%    \end{macrocode}
+%
+% Now we do the same for the kite and dart tiling.
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_kite_lms_action_prop {+} {\pgftransformrotate{36}}
+\prop_put:Nnn \g__penrose_kite_lms_action_prop {*} {\pgftransformrotate{108}}
+\prop_put:Nnn \g__penrose_kite_lms_action_prop {-} {\pgftransformrotate{-36}}
+\prop_put:Nnn \g__penrose_kite_lms_action_prop {_}
+{\pgftransformrotate{-108}}
+\prop_put:Nnn \g__penrose_kite_lms_action_prop {>} {\pgftransformrotate{180}}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_set_eq:NN \g__penrose_ktriangle_lms_action_prop
+\g__penrose_kite_lms_action_prop
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_kite_lms_action_prop {T} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \pgftransformrotate{36}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ kite/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{kite}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_kite_lms_action_prop {g} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \pgftransformrotate{144}
+  \pgftransformxshift{-\l__penrose_step_dim * 2 * sin(18)}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ dart/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{dart}
+  \group_end:
+}
+%    \end{macrocode}
+%
+% Now we set up the actions for the triangle variations.
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_rtriangle_lms_action_prop {T} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \pgftransformrotate{18}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ reverse~ golden~ triangle/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{reverse~ golden~ triangle}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_rtriangle_lms_action_prop {t} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \pgftransformrotate{-18}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ golden~ triangle/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{golden~ triangle}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_rtriangle_lms_action_prop {G} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \pgftransformrotate{180}
+  \pgftransformxshift{-\l__penrose_step_dim}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)/(2*cosd(36))}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ reverse~ golden~ gnomon/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{reverse~ golden~ gnomon}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_rtriangle_lms_action_prop {g} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \pgftransformrotate{180}
+  \pgftransformxshift{-\l__penrose_step_dim}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)/(2*cosd(36))}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ golden~ gnomon/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{golden~ gnomon}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_ktriangle_lms_action_prop {T} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \pgftransformrotate{18}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ reverse~ golden~ triangle/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{reverse~ golden~ triangle}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_ktriangle_lms_action_prop {t} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \pgftransformrotate{-18}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ golden~ triangle/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{golden~ triangle}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_ktriangle_lms_action_prop {G} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \pgftransformrotate{180}
+  \pgftransformxshift{-\l__penrose_step_dim}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)/(2*cosd(36))}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ reverse~ golden~ gnomon/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{reverse~ golden~ gnomon}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_ktriangle_lms_action_prop {g} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \pgftransformrotate{180}
+  \pgftransformxshift{-\l__penrose_step_dim}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)/(2*cosd(36))}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ golden~ gnomon/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{golden~ gnomon}
+  \group_end:
+}
+%    \end{macrocode}
+%
+% Now we do the same for the pentagonal tilings.
+%
+% The rules need a variety of turns.
+%    \begin{macrocode}
+\int_new:N \l__penrose_pentagon_parity_int
+\seq_new:N \l__penrose_pentagon_parity_seq
+\seq_set_from_clist:Nn \l__penrose_pentagon_parity_seq {odd,even}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {1} {
+  \int_set:Nn \l__penrose_pentagon_parity_int
+  {3 -  \l__penrose_pentagon_parity_int}
+  }
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {+}
+{\pgftransformrotate{72}}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {*}
+{\pgftransformrotate{144}}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {-}
+{\pgftransformrotate{288}}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {_}
+{\pgftransformrotate{216}}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {>}
+{\pgftransformrotate{180}}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {|}
+{\pgftransformxscale{-1}}
+%    \end{macrocode}
+% The scale factor is different.
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {s} {
+  \fp_set:Nn \l__penrose_tmpa_fp
+  {
+    1/(2 + 2 * cosd(72) ) * \l__penrose_step_dim
+  }
+  \dim_set:Nn \l__penrose_step_dim {\fp_to_dim:N \l__penrose_tmpa_fp}
+}
+%    \end{macrocode}
+% And we tend to work better vertically.
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {f} {
+  \fp_set:Nn \l__penrose_tmpa_fp {  tand(54)/2 * \l__penrose_step_dim }
+  \pgftransformyshift{\fp_to_dim:N \l__penrose_tmpa_fp}
+}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {F} {
+  \fp_set:Nn \l__penrose_tmpa_fp {  tand(54) * \l__penrose_step_dim }
+  \pgftransformyshift{\fp_to_dim:N \l__penrose_tmpa_fp}
+}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {d} {
+  \fp_set:Nn \l__penrose_tmpa_fp
+  {
+    (tand(54)/2 - tand(72)/2 + sind(36) ) * \l__penrose_step_dim
+  }
+  \pgftransformyshift{\fp_to_dim:N \l__penrose_tmpa_fp}
+}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {e} {
+  \fp_set:Nn \l__penrose_tmpa_fp
+  {
+    tand(54) * cosd(36) * \l__penrose_step_dim
+  }
+  \pgftransformyshift{\fp_to_dim:N \l__penrose_tmpa_fp}
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {P} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/2}
+  \pgftransformxshift{-\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim*tand(54)/2}
+  \pgftransformyshift{-\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ pentagon/.try,
+    every~
+    \seq_item:Nn \l__penrose_pentagon_parity_seq
+    {\l__penrose_pentagon_parity_int}
+    \space pentagon/.try,
+    every~ pentagon~ 5/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{pentagon~5}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {Q} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/2}
+  \pgftransformxshift{-\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim*tand(54)/2}
+  \pgftransformyshift{-\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ pentagon/.try,
+    every~
+    \seq_item:Nn \l__penrose_pentagon_parity_seq
+    {\l__penrose_pentagon_parity_int}
+    \space pentagon/.try,
+    every~ pentagon~ 3/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{pentagon~3}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {R} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/2}
+  \pgftransformxshift{-\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim*tand(54)/2}
+  \pgftransformyshift{-\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ pentagon/.try,
+    every~
+    \seq_item:Nn \l__penrose_pentagon_parity_seq
+    {\l__penrose_pentagon_parity_int}
+    \space pentagon/.try,
+    every~ pentagon~ 2/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{pentagon~2}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {G} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+%  \pgftransformrotate{198}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim*cosd(72)}
+  \pgftransformxshift{\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim*tand(54)*cosd(72)}
+  \pgftransformyshift{\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ pentagram/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{pentagram}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {B} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+%  \pgftransformrotate{198}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim*cosd(72)}
+  \pgftransformxshift{\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim*tand(54)*cosd(72)}
+  \pgftransformyshift{\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ boat/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{boat}
+  \group_end:
+}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\prop_put:Nnn \g__penrose_pentagon_lms_action_prop {D} {
+  \group_begin:
+  \int_gincr:N \l__penrose_tile_int
+  \pgftransformrotate{90}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim*cosd(18)}
+  \pgftransformxshift{-\fp_to_dim:N \l__penrose_tmpa_fp}
+  \fp_set:Nn \l__penrose_tmpa_fp {\l__penrose_step_dim/(1cm)}
+  \pgftransformscale{\fp_use:N \l__penrose_tmpa_fp}
+  \tl_set:Nx \l__penrose_tmpc_tl
+  {
+    {\int_use:N  \l__penrose_tile_int}
+    {\int_use:N \l__penrose_tiles_int}
+  }
+  \UsePenroseTile[
+    every~ Penrose~ tile/.try,
+    every~ diamond/.try,
+    Penrose~ tile~ \int_use:N \l__penrose_tile_int/.try,
+    Penrose~ tile/.try/.expand~ once=\l__penrose_tmpc_tl
+  ]{diamond}
+  \group_end:
+}
+%    \end{macrocode}
+%
+% \begin{macro}[internal]{\penrose_make_lms:Nnnn}
+% This creates the token list of actions, starting with the seed.
+% The arguments are: a token list to store the result in, the name of the system, the number of iterations, and the initial state.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \penrose_make_lms:Nnnn #1#2#3#4
+{
+  \group_begin:
+%    \end{macrocode}
+% On the first time round, we start with the given seed.
+%    \begin{macrocode}
+  \tl_set:Nn \l__penrose_tmpb_tl {#4}
+%    \end{macrocode}
+% We repeat the specified number of times.
+%    \begin{macrocode}
+  \prg_replicate:nn {#3} {
+%    \end{macrocode}
+% Duplicate the current state.
+%    \begin{macrocode}
+    \tl_set_eq:NN \l__penrose_tmpa_tl \l__penrose_tmpb_tl
+%    \end{macrocode}
+% Clear the receiving token list.
+%    \begin{macrocode}
+    \tl_clear:N \l__penrose_tmpb_tl
+%    \end{macrocode}
+% Walk through the current list, appending to the receiving list according to the rules.
+%    \begin{macrocode}
+    \tl_map_inline:Nn \l__penrose_tmpa_tl
+    {
+%    \end{macrocode}
+% If a rule exists, copy that.
+%    \begin{macrocode}
+      \prop_if_in:cnTF {g__penrose_#2_lms_rule_prop} {##1}
+      {
+        \tl_put_right:Nx \l__penrose_tmpb_tl
+        {\prop_item:cn {g__penrose_#2_lms_rule_prop} {##1} }
+      }
+      {
+%    \end{macrocode}
+% Otherwise, just copy the token.
+%    \begin{macrocode}
+        \tl_put_right:Nn \l__penrose_tmpb_tl {##1}
+      }
+    }
+  }
+%    \end{macrocode}
+% We've done all this inside a group, now pass the result outside.
+%    \begin{macrocode}
+  \tl_set:Nn \l__penrose_tmpa_tl {
+    \group_end:
+    \tl_set:Nn #1
+  }
+  \tl_put_right:Nx \l__penrose_tmpa_tl {{\tl_use:N \l__penrose_tmpb_tl}}
+  \tl_use:N \l__penrose_tmpa_tl
+}
+\cs_generate_variant:Nn \penrose_make_lms:Nnnn {Nnnx}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\penrose_invoke_lms:Nn}
+% This carries out the actions specified by the resulting rules.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \penrose_invoke_lms:Nn #1#2
+{
+  \group_begin:
+%    \end{macrocode}
+% Walk through the given list, carrying out the corresponding action if it exists.
+% If not, look at the default.
+% Otherwise, just do nothing.
+%    \begin{macrocode}
+  \tl_map_inline:Nn #1 {
+    \prop_if_in:cnTF {g__penrose_#2_lms_action_prop} {##1}
+    {
+      \prop_item:cn {g__penrose_#2_lms_action_prop} {##1}
+    }
+    {
+      \prop_if_in:cnT {g__penrose_default_lms_action_prop} {##1}
+      {
+        \prop_item:cn {g__penrose_default_lms_action_prop} {##1}
+      }
+    }
+  }
+  \group_end:
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% We keep track of the number of tiles.
+%    \begin{macrocode}
+\int_new:N \l__penrose_tile_int
+\int_new:N \l__penrose_tiles_int
+%    \end{macrocode}
+%
+% \begin{macro}[internal]{\PenroseDecomposition}
+% This is the user macro to invoke the decomposition.
+% The arguments are: optional styles, the name, number of iterations, and starting seed.
+%    \begin{macrocode}
+\NewDocumentCommand \PenroseDecomposition { O{} m m m }
+{
+  \group_begin:
+  \tikzset{#1}
+  \penrose_make_lms:Nnnx \l__penrose_tmpa_tl {#2} {#3} {#4}
+  \penrose_count_lms:N \l__penrose_tmpa_tl
+  \int_gzero:N \l__penrose_tile_int
+  \int_gset:Nn \l__penrose_pentagon_parity_int {2}
+  \penrose_invoke_lms:Nn \l__penrose_tmpa_tl {#2}
+  \group_end:
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}[internal]{\penrose_count_lms:N}
+% This counts the number of tiles in the string.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \penrose_count_lms:N #1
+{
+  \int_gzero:N \l__penrose_tiles_int
+  \tl_map_inline:Nn #1
+  {
+    \tl_if_eq:nnT {##1} {T}
+    {
+      \int_incr:N \l__penrose_tiles_int
+    }
+    \tl_if_eq:nnT {##1} {t}
+    {
+      \int_incr:N \l__penrose_tiles_int
+    }
+    \tl_if_eq:nnT {##1} {G}
+    {
+      \int_incr:N \l__penrose_tiles_int
+    }
+    \tl_if_eq:nnT {##1} {g}
+    {
+      \int_incr:N \l__penrose_tiles_int
+    }
+  }
+}
+%    \end{macrocode}
+% \end{macro}
+%
+% This is a \Verb+\tikzset+ mechanism for setting the dimensions of the tiling.
+%    \begin{macrocode}
+\tikzset{
+  Penrose~ step/.code={
+    \dim_set:Nn \l__penrose_step_dim {#1}
+  }
+}
+%    \end{macrocode}
+%
+% We're done with \LaTeX3, so turn off the syntax.
+%    \begin{macrocode}
+\ExplSyntaxOff
+%    \end{macrocode}
+%
+% \subsection{TikZ Pictures}
+%
+% New in TikZ3.0 is the ability to make pictures that can be reused.
+% Penrose tiles seems an obvious use for this.
+% These pictures can be placed alongside other tiles, matching by edge type.
+%
+% There are a variety of constants that are frequently used and reused, so we define them all here.
+% These are the PGF versions.
+%
+%    \begin{macrocode}
+\pgfmathsetmacro\pr@chphi{cos(18)}
+\pgfmathsetmacro\pr@shphi{sin(18)}
+\pgfmathsetmacro\pr@cphi{cos(36)}
+\pgfmathsetmacro\pr@sphi{sin(36)}
+\pgfmathsetmacro\pr@invphi{2/(sqrt(5)+1)}
+\pgfmathsetmacro\pr@phi{(sqrt(5)+1)/2}
+\pgfmathsetmacro\pr@invphisq{\pr@invphi*\pr@invphi}
+\pgfmathsetmacro\pr@ominvphisq{\pr@invphi - \pr@invphisq}
+\pgfmathsetmacro\pr@ominvphi{1 - \pr@invphi}
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\newif\if@edgealign
+\def\pr@getfirst#1#2\pr@stop{#1}%
+\def\test@edgealign#1{%
+  \pgfkeysgetvalue{/tikz/Penrose/alignment edge}{\@penrose@tmpa}%
+  \edef\@penrose@tmpb{#1}%
+  \edef\@penrose@tmpa{\expandafter\pr@getfirst\@penrose@tmpa.\pr@stop}%
+  \ifx\@penrose@tmpa\@penrose@tmpb
+  \@edgealigntrue
+  \else
+  \@edgealignfalse
+  \fi
+}%
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+\newif\if@newedge
+\def\test@newedge#1{%
+  \pgfkeysgetvalue{/tikz/Penrose/alignment new edge}{\@penrose@tmpa}%
+  \edef\@penrose@tmpb{#1}%
+  \edef\@penrose@tmpa{\@penrose@tmpa}%
+  \ifx\@penrose@tmpa\@penrose@tmpb
+  \@newedgetrue
+  \else
+  \@newedgefalse
+  \fi
+}%
+%    \end{macrocode}
+%
+% The implementation is essentially the same for each, so only the first will be commented.
+%    \begin{macrocode}
+\tikzset{
+%    \end{macrocode}
+% The key \Verb+align with=<tile> along <edge>+ is used to set the parameters for placing a tile next to an existing one.
+% For most tiles, that's enough to specify how the new tile should be placed.
+% Some, though, need more information.
+% For those, use \Verb+align with=<tile> along <edge> using <number>+. 
+%    \begin{macrocode}
+  align with/.code args={#1 along #2}{%
+    \pgfutil@in@{ using }{#2}
+    \ifpgfutil@in@%
+    \tikzset{
+      Penrose/alignment location=#1,
+      Penrose/alignment set edges=#2,
+    }%
+    \else
+    \tikzset{
+      Penrose/alignment location=#1,
+      Penrose/alignment edge=#2,
+    }%
+    \fi
+  },
+  Penrose/alignment set edges/.code args={#1 using #2}{%
+    \tikzset{
+      Penrose/alignment edge=#1,
+      Penrose/alignment new edge=#2
+    },
+  },
+  Penrose/alignment location/.initial={},
+  Penrose/alignment edge/.initial=a,
+  Penrose/alignment new edge/.initial={},
+%    \end{macrocode}
+% Default clipping style.
+%    \begin{macrocode}
+  every Penrose tile clip/.style={clip},
+%    \end{macrocode}
+% This is the code for setting up a \Verb+pic+.
+%    \begin{macrocode}
+  thin rhombus/.pic={
+    \begin{scope}
+%    \end{macrocode}
+% Were we given a tile to align ourselves against?
+%    \begin{macrocode}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+%    \end{macrocode}
+% Yes, we were.
+% So we adjust our position accordingly.
+% The first job is to transform so that we're along the edge of the receiving tile.
+%    \begin{macrocode}
+    \begingroup
+%    \end{macrocode}
+% We get the locations of the start and end of the receiving tile.
+% As \Verb+pic+ sets the node prefix, we have to temporarily suspend that (hence working in a group).
+%    \begin{macrocode}
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+%    \end{macrocode}
+% We store the initial points in \Verb+\pgf@xa+ and \Verb+\pgf@ya+ but we want \Verb+\pgf@xb+ and \Verb+\pgf@yb+ to be a vector along the edge.
+%    \begin{macrocode}
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+%    \end{macrocode}
+% We shift to the start of the edge.
+%    \begin{macrocode}
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+%    \end{macrocode}
+% And normalise the vector along it.
+%    \begin{macrocode}
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+%    \end{macrocode}
+% Now rotate so that the \(x\)--axis lies along the edge.
+%    \begin{macrocode}
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}
+%    \end{macrocode}
+% The next job is to shift and rotate the current tile so that the correct edge ends up against the receiving tile.
+%    \begin{macrocode}
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}b\relax
+    \pgftransformrotate{-18}%
+    \pgftransformshift{\pgfpoint{-\pr@chphi cm}{\pr@shphi cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}B\relax
+    \pgftransformrotate{18}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+    \pgftransformrotate{198}%
+    \pgftransformshift{\pgfpoint{-2*\pr@chphi cm}{0 cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+    \pgftransformrotate{162}%
+    \pgftransformshift{\pgfpoint{-\pr@chphi cm}{-\pr@shphi cm}}%
+    \fi\fi\fi\fi
+    \fi
+%    \end{macrocode}
+% Now that the transformation is finalised, we can render the tile.
+% We clip against the tile path so that the tiles don't ``bleed''.
+% If we didn't do this, drawing the tile would result in overlaps which can look a bit ugly.
+% On the other hand, tight clipping can lead to ``gaps'' between the tiles so we make this optional by enclosing it in a style.
+%    \begin{macrocode}
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every thin rhombus clip/.try
+    ]{thin rhombus}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every thin rhombus/.try,
+      pic actions
+    ]{thin rhombus}
+%    \end{macrocode}
+% These draw the arcs that designate the joining rules.
+% We draw full circles so that it doesn't matter what shape the tiles are.
+%    \begin{macrocode}
+    \UsePenroseTile[
+      every Penrose arc clip/.try,
+      every thin rhombus arc clip/.try
+    ]{thin rhombus}
+    \path[every circle arc/.try] (18:1) circle[radius=1/4];
+    \path[every long arc/.try] (-18:1) circle[radius=1/4];
+%    \end{macrocode}
+% Lastly, we put coordinates at each vertex, labelled by which edge they are.
+%    \begin{macrocode}
+\coordinate (-edge a start) at (0,0);
+\coordinate (-edge a end) at (18:1);
+\coordinate (-edge A start) at (18:1);
+\coordinate (-edge A end) at (2*\pr@chphi,0);
+\coordinate (-edge B start) at (2*\pr@chphi,0);
+\coordinate (-edge B end) at (-18:1);
+\coordinate (-edge b start) at (-18:1);
+\coordinate (-edge b end) at (0,0);
+    \end{scope}
+  },
+%    \end{macrocode}
+% This is a shortcut for installing the \Verb+pic+ type.
+%    \begin{macrocode}
+  thin rhombus/.style={
+    every Penrose pic/.try,
+    pic type=thin rhombus,
+  },
+%    \end{macrocode}
+% Same again, but for the thick rhombus.
+%    \begin{macrocode}
+  thick rhombus/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}b\relax
+    \pgftransformrotate{144}%
+    \pgftransformshift{\pgfpoint{-\pr@cphi cm}{-\pr@sphi cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}B\relax
+    \pgftransformrotate{36}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+    \pgftransformrotate{-36}%
+    \pgftransformshift{\pgfpoint{-\pr@cphi cm}{\pr@sphi cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+    \pgftransformrotate{216}%
+    \pgftransformshift{\pgfpoint{-2*\pr@cphi cm}{0 cm}}%
+    \fi\fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every thick rhombus clip/.try
+    ]{thick rhombus}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every thick rhombus/.try,
+      pic actions
+    ]{thick rhombus}
+    \UsePenroseTile[
+      every Penrose arc clip/.try,
+      every thick rhombus arc clip/.try
+    ]{thick rhombus}
+\path[every circle arc/.try] (2*\pr@cphi,0) circle[radius=1/4];
+\path[every long arc/.try] (0,0) circle[radius=3/4];
+\coordinate (-edge B start) at (0,0);
+\coordinate (-edge B end) at (36:1);
+\coordinate (-edge a start) at (36:1);
+\coordinate (-edge a end) at (2*\pr@cphi,0);
+\coordinate (-edge A start) at (2*\pr@cphi,0);
+\coordinate (-edge A end) at (-36:1);
+\coordinate (-edge b start) at (-36:1);
+\coordinate (-edge b end) at (0,0);
+    \end{scope}
+  },
+  thick rhombus/.style={
+    every Penrose pic/.try,
+    pic type=thick rhombus,
+  },
+%    \end{macrocode}
+% Now the kite.
+%    \begin{macrocode}
+  kite/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}c\relax
+    \pgftransformrotate{-72}%
+    \pgftransformshift{\pgfpoint{-\pr@cphi cm}{\pr@sphi cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}C\relax
+    \pgftransformrotate{-108}%
+    \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+    \pgftransformrotate{36}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+    \pgftransformrotate{144}%
+    \pgftransformshift{\pgfpoint{-\pr@cphi cm}{-\pr@sphi cm}}%
+    \fi\fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every kite clip/.try
+    ]{kite}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every kite/.try,
+      pic actions
+    ]{kite}
+    \UsePenroseTile[
+      every Penrose arc clip/.try,
+      every kite arc clip/.try
+    ]{kite}
+\path[every circle arc/.try] (0,0) circle[radius=\pr@invphi];
+\path[every long arc/.try] (1,0) circle[radius=\pr@invphisq];
+\coordinate (-edge a start) at (0,0);
+\coordinate (-edge a end) at (36:1);
+\coordinate (-edge c start) at (36:1);
+\coordinate (-edge c end) at (1,0);
+\coordinate (-edge C start) at (1,0);
+\coordinate (-edge C end) at (-36:1);
+\coordinate (-edge A start) at (-36:1);
+\coordinate (-edge A end) at (0,0);
+    \end{scope}
+  },
+%    \end{macrocode}
+% The dart is next.
+%    \begin{macrocode}
+  dart/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}c\relax
+    \pgftransformrotate{108}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}C\relax
+    \pgftransformrotate{72}%
+    \pgftransformshift%
+    {\pgfpoint{\pr@invphi*\pr@shphi cm}{-\pr@invphi*\pr@chphi cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+    \pgftransformrotate{-36}%
+    \pgftransformshift%
+    {\pgfpoint{\pr@invphi*\pr@shphi cm}{\pr@invphi*\pr@chphi cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+    \pgftransformrotate{216}%
+    \pgftransformshift{\pgfpoint{-\pr@invphi cm}{0 cm}}%
+    \fi\fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every dart clip/.try
+    ]{dart}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every dart/.try,
+      pic actions
+    ]{dart}
+    \UsePenroseTile[
+      every Penrose arc clip/.try,
+      every dart arc clip/.try
+    ]{dart}
+\path[every circle arc/.try] (\pr@invphi,0) circle[radius=\pr@ominvphi];
+\path[every long arc/.try] (0,0) circle[radius=\pr@ominvphisq];
+\coordinate (-edge c start) at (0,0);
+\coordinate (-edge c end) at (108:\pr@invphi);
+\coordinate (-edge a start) at (108:\pr@invphi);
+\coordinate (-edge a end) at (\pr@invphi,0);
+\coordinate (-edge A start) at (\pr@invphi,0);
+\coordinate (-edge A end) at (-108:\pr@invphi);
+\coordinate (-edge C start) at (-108:\pr@invphi);
+\coordinate (-edge C end) at (0,0);
+    \end{scope}
+  },
+  kite/.style={
+    every Penrose pic/.try,
+    pic type=kite,
+  },
+  dart/.style={
+    every Penrose pic/.try,
+    pic type=dart,
+  },
+%    \end{macrocode}
+% The golden triangle.
+%    \begin{macrocode}
+  golden triangle/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}B\relax
+    \pgftransformrotate{18}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}C\relax
+    \pgftransformrotate{-90}%
+    \pgftransformshift{\pgfpoint{-\pr@chphi cm}{\pr@shphi cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+    \pgftransformrotate{162}%
+    \pgftransformshift{\pgfpoint{-\pr@chphi cm}{-\pr@shphi cm}}%
+    \fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every golden triangle clip/.try
+    ]{golden triangle}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every golden triangle/.try,
+      pic actions
+    ]{golden triangle}
+\coordinate (-edge a start) at (0,0);
+\coordinate (-edge a end) at (18:1);
+\coordinate (-edge c start) at (18:1);
+\coordinate (-edge c end) at (-18:1);
+\coordinate (-edge b start) at (-18:1);
+\coordinate (-edge b end) at (0,0);
+    \end{scope}
+  },
+  golden triangle/.style={
+    every Penrose pic/.try,
+    pic type=golden triangle,
+  },
+%    \end{macrocode}
+% The reverse golden triangle (is there a better name?).
+%    \begin{macrocode}
+  reverse golden triangle/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}b\relax
+    \pgftransformrotate{162}%
+    \pgftransformshift{\pgfpoint{-\pr@chphi cm}{-\pr@shphi cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}c\relax
+    \pgftransformrotate{-90}%
+    \pgftransformshift{\pgfpoint{-\pr@chphi cm}{\pr@shphi cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+    \pgftransformrotate{18}%
+    \fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every reverse golden triangle clip/.try
+    ]{reverse golden triangle}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every reverse golden triangle/.try,
+      pic actions
+    ]{reverse golden triangle}
+\coordinate (-edge B start) at (0,0);
+\coordinate (-edge B end) at (18:1);
+\coordinate (-edge C start) at (18:1);
+\coordinate (-edge C end) at (-18:1);
+\coordinate (-edge A start) at (-18:1);
+\coordinate (-edge A end) at (0,0);
+    \end{scope}
+  },
+  reverse golden triangle/.style={
+    every Penrose pic/.try,
+    pic type=reverse golden triangle,
+  },
+%    \end{macrocode}
+% The golden gnomon.
+%    \begin{macrocode}
+  golden gnomon/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}c\relax
+    \pgftransformrotate{144}%
+    \pgftransformshift{\pgfpoint{-\pr@cphi cm}{-\pr@sphi cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}B\relax
+    \pgftransformrotate{-144}%
+    \pgftransformshift{\pgfpoint{-2*\pr@cphi cm}{0 cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}a\relax
+    \fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every golden gnomon clip/.try
+    ]{golden gnomon}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every golden gnomon/.try,
+      pic actions
+    ]{golden gnomon}
+\coordinate (-edge C start) at (0,0);
+\coordinate (-edge C end) at (36:1);
+\coordinate (-edge b start) at (36:1);
+\coordinate (-edge b end) at (2*\pr@cphi,0);
+\coordinate (-edge A start) at (2*\pr@cphi,0);
+\coordinate (-edge A end) at (0,0);
+    \end{scope}
+  },
+  golden gnomon/.style={
+    every Penrose pic/.try,
+    pic type=golden gnomon,
+  },
+%    \end{macrocode}
+% The reverse golden gnomon.
+%    \begin{macrocode}
+  reverse golden gnomon/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}C\relax
+    \pgftransformrotate{36}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}b\relax
+    \pgftransformrotate{-36}%
+    \pgftransformshift{\pgfpoint{-\pr@cphi cm}{\pr@sphi cm}}%
+    \else
+    \if\pgfkeysvalueof{/tikz/Penrose/alignment edge}A\relax
+    \pgftransformrotate{180}%
+    \pgftransformshift{\pgfpoint{-2*\pr@cphi cm}{0 cm}}%
+    \fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every reverse golden gnomon clip/.try
+    ]{reverse golden gnomon}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every reverse golden gnomon/.try,
+      pic actions
+    ]{reverse golden gnomon}
+\coordinate (-edge a start) at (0,0);
+\coordinate (-edge a end) at (2*\pr@cphi,0);
+\coordinate (-edge B start) at (2*\pr@cphi,0);
+\coordinate (-edge B end) at (-36:1);
+\coordinate (-edge c start) at (-36:1);
+\coordinate (-edge c end) at (0,0);
+    \end{scope}
+  },
+  reverse golden gnomon/.style={
+    every Penrose pic/.try,
+    pic type=reverse golden gnomon,
+  },
+%    \end{macrocode}
+% The primary pentagon.
+%    \begin{macrocode}
+  pentagon 5/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \test@newedge{1}%
+    \if@newedge
+    \pgftransformrotate{180}%
+    \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+    \else
+    \test@newedge{2}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{1 cm}{0 cm}}%
+    \pgftransformrotate{108}%
+    \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+    \else
+    \test@newedge{3}%
+    \if@newedge
+    \pgftransformshift%
+    {\pgfpoint{\pr@phi * \pr@shphi cm}{- \pr@phi * \pr@chphi cm}}%
+    \pgftransformrotate{36}%
+    \else
+    \test@newedge{4}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{- \pr@shphi cm}{-\pr@chphi cm}}%
+    \pgftransformrotate{-36}%
+    \else
+    \test@newedge{5}%
+    \if@newedge
+    \pgftransformrotate{-108}%
+    \fi\fi\fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every pentagon clip/.try,
+      every pentagon 5 clip/.try
+    ]{pentagon 5}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every pentagon/.try,
+      every pentagon 5/.try,
+      pic actions
+    ]{pentagon 5}
+\coordinate (-edge a1 start) at (0,0);
+\coordinate (-edge a1 end) at (1,0);
+\coordinate (-edge a2 start) at (1,0);
+\coordinate (-edge a2 end) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge a3 start) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge a3 end) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge a4 start) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge a4 end) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge a5 start) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge a5 end) at (0,0);
+    \end{scope}
+  },
+  pentagon 5/.style={
+    every Penrose pic/.try,
+    pic type=pentagon 5,
+  },
+%    \end{macrocode}
+% The secondary pentagon.
+%    \begin{macrocode}
+  pentagon 3/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \test@edgealign{a}%
+    \if@edgealign
+    \pgftransformrotate{180}%
+    \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+    \else
+    \test@edgealign{B}%
+    \if@edgealign%
+    \test@newedge{1}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{1 cm}{0 cm}}%
+    \pgftransformrotate{108}%
+    \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+    \else
+    \pgftransformrotate{-108}%
+    \fi
+    \else
+    \test@newedge{1}%
+    \if@newedge
+    \pgftransformshift%
+    {\pgfpoint{\pr@phi * \pr@shphi cm}{- \pr@phi * \pr@chphi cm}}%
+    \pgftransformrotate{36}%
+    \else
+    \pgftransformshift{\pgfpoint{- \pr@shphi cm}{-\pr@chphi cm}}%
+    \pgftransformrotate{-36}%
+    \fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every pentagon clip/.try,
+      every pentagon 3 clip/.try
+    ]{pentagon 3}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every pentagon/.try,
+      every pentagon 3/.try,
+      pic actions
+    ]{pentagon 3}
+\coordinate (-edge A start) at (0,0);
+\coordinate (-edge A end) at (1,0);
+\coordinate (-edge b1 start) at (1,0);
+\coordinate (-edge b1 end) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge a1 start) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge a1 end) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge a2 start) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge a2 end) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge b2 start) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge b2 end) at (0,0);
+    \end{scope}
+  },
+  pentagon 3/.style={
+    every Penrose pic/.try,
+    pic type=pentagon 3,
+  },
+%    \end{macrocode}
+% The tertiary pentagon.
+%    \begin{macrocode}
+  pentagon 2/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \test@edgealign{D}%
+    \if@edgealign
+    \pgftransformrotate{180}%
+    \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+    \else
+    \test@edgealign{a}%
+    \if@edgealign%
+    \test@newedge{1}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{1 cm}{0 cm}}%
+    \pgftransformrotate{108}%
+    \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+    \else
+    \pgftransformrotate{-108}%
+    \fi
+    \else
+    \test@newedge{1}%
+    \if@newedge
+    \pgftransformshift%
+    {\pgfpoint{\pr@phi * \pr@shphi cm}{- \pr@phi * \pr@chphi cm}}%
+    \pgftransformrotate{36}%
+    \else
+    \pgftransformshift{\pgfpoint{- \pr@shphi cm}{-\pr@chphi cm}}%
+    \pgftransformrotate{-36}%
+    \fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every pentagon clip/.try,
+      every pentagon 2 clip/.try
+    ]{pentagon 2}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every pentagon/.try,
+      every pentagon 2/.try,
+      pic actions
+    ]{pentagon 2}
+\coordinate (-edge d start) at (0,0);
+\coordinate (-edge d end) at (1,0);
+\coordinate (-edge A1 start) at (1,0);
+\coordinate (-edge A1 end) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge c1 start) at (1+\pr@shphi,\pr@chphi);
+\coordinate (-edge c1 end) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge c2 start) at (\pr@cphi-\pr@shphi,\pr@sphi+\pr@chphi);
+\coordinate (-edge c2 end) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge A2 start) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge A2 end) at (0,0);
+    \end{scope}
+  },
+  pentagon 2/.style={
+    every Penrose pic/.try,
+    pic type=pentagon 2,
+  },
+%    \end{macrocode}
+% The pentagram.
+%    \begin{macrocode}
+  pentagram/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \test@newedge{2}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{1 cm}{0 cm}}%
+    \pgftransformrotate{72}%
+    \else
+    \test@newedge{3}%
+    \if@newedge
+    \pgftransformrotate{-72}%
+    \pgftransformshift{\pgfpoint{2 * \pr@shphi cm}{0 cm}}%
+    \else
+    \test@newedge{4}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{1 cm + 2 * \pr@shphi cm}{0 cm}}%
+    \else
+    \test@newedge{5}%
+    \if@newedge
+    \pgftransformrotate{216}%
+    \pgftransformshift{\pgfpoint{\pr@cphi cm}{\pr@sphi cm}}%
+    \else
+    \test@newedge{6}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{1cm}{0cm}}%
+    \pgftransformrotate{-72}%
+    \pgftransformshift{\pgfpoint{\pr@cphi cm}{\pr@sphi cm}}%
+    \else
+    \test@newedge{7}%
+    \if@newedge
+    \pgftransformrotate{144}%
+    \pgftransformshift{\pgfpoint{\pr@shphi cm}{\pr@chphi cm}}%
+    \else
+    \test@newedge{8}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{1 cm + 2*\pr@shphi cm}{0cm}}%
+    \pgftransformrotate{216}%
+    \pgftransformshift{\pgfpoint{\pr@cphi cm}{\pr@sphi cm}}%
+    \else
+    \test@newedge{9}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{-2*\pr@shphi cm}{0cm}}%
+    \pgftransformrotate{72}%
+    \else
+    \test@newedge{10}%
+    \if@newedge
+    \pgftransformrotate{144}%
+    \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+    \else
+    \fi\fi\fi\fi\fi\fi\fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every pentagram clip/.try
+    ]{pentagram}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every pentagram/.try,
+      pic actions
+    ]{pentagram}
+\coordinate (-edge C1 start) at (1,0);
+\coordinate (-edge C1 end) at (0,0);
+\coordinate (-edge C2 start) at (0,0);
+\coordinate (-edge C2 end) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge C3 start) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge C3 end) at (-2*\pr@shphi,0);
+\coordinate (-edge C4 start) at (-2*\pr@shphi,0);
+\coordinate (-edge C4 end) at (-1-2*\pr@shphi,0);
+\coordinate (-edge C5 start) at (-1-2*\pr@shphi,0);
+\coordinate (-edge C5 end) at (-\pr@cphi,-\pr@sphi);
+\coordinate (-edge C6 start) at (-\pr@cphi,-\pr@sphi);
+\coordinate (-edge C6 end) at (-\pr@cphi-\pr@shphi,-\pr@sphi-\pr@chphi);
+\coordinate (-edge C7 start) at (-\pr@cphi-\pr@shphi,-\pr@sphi-\pr@chphi);
+\coordinate (-edge C7 end) at (-\pr@shphi,-\pr@chphi);
+\coordinate (-edge C8 start) at (-\pr@shphi,-\pr@chphi);
+\coordinate (-edge C8 end) at (1-\pr@cphi+\pr@shphi,-\pr@sphi-\pr@chphi);
+\coordinate (-edge C9 start) at (1-\pr@cphi+\pr@shphi,-\pr@sphi-\pr@chphi);
+\coordinate (-edge C9 end) at (1-\pr@cphi,-\pr@sphi);
+\coordinate (-edge C10 start) at (1-\pr@cphi,-\pr@sphi);
+\coordinate (-edge C10 end) at (1,0);
+    \end{scope}
+  },
+  pentagram/.style={
+    every Penrose pic/.try,
+    pic type=pentagram,
+  },
+%    \end{macrocode}
+% The boat.
+%    \begin{macrocode}
+  boat/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \test@edgealign{d}%
+    \if@edgealign
+    \pgftransformrotate{180}%
+    \pgftransformshift{\pgfpoint{\pr@cphi cm - 1cm}{\pr@sphi cm}}%
+    \else
+    \test@edgealign{b}%
+    \if@edgealign%
+    \test@newedge{2}%
+    \if@newedge
+    \pgftransformrotate{144}%
+    \pgftransformshift{\pgfpoint{-1 cm}{0 cm}}%
+    \else
+    \pgftransformrotate{216}%
+    \pgftransformshift{\pgfpoint{\pr@cphi cm}{\pr@sphi cm}}%
+    \fi
+    \else
+    \test@edgealign{c}%
+    \if@edgealign%
+    \test@newedge{2}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{1 cm}{0 cm}}%
+    \pgftransformrotate{72}%
+    \else
+    \test@newedge{3}%
+    \if@newedge
+    \pgftransformrotate{-72}%
+    \pgftransformshift{\pgfpoint{2 * \pr@shphi cm}{0 cm}}%
+    \else
+    \test@newedge{4}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{1 cm + 2 * \pr@shphi cm}{0 cm}}%
+    \else
+    \fi\fi\fi\fi\fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every boat clip/.try
+    ]{boat}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every boat/.try,
+      pic actions
+    ]{boat}
+\coordinate (-edge C1 start) at (1,0);
+\coordinate (-edge C1 end) at (0,0);
+\coordinate (-edge C2 start) at (0,0);
+\coordinate (-edge C2 end) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge C3 start) at (-\pr@shphi,\pr@chphi);
+\coordinate (-edge C3 end) at (-2*\pr@shphi,0);
+\coordinate (-edge C4 start) at (-2*\pr@shphi,0);
+\coordinate (-edge C4 end) at (-1-2*\pr@shphi,0);
+\coordinate (-edge B1 start) at (-1-2*\pr@shphi,0);
+\coordinate (-edge B1 end) at (-\pr@cphi,-\pr@sphi);
+\coordinate (-edge D start) at (-\pr@cphi,-\pr@sphi);
+\coordinate (-edge D end) at (1-\pr@cphi,-\pr@sphi);
+\coordinate (-edge B2 start) at (1-\pr@cphi,-\pr@sphi);
+\coordinate (-edge B2 end) at (1,0);
+    \end{scope}
+  },
+  boat/.style={
+    every Penrose pic/.try,
+    pic type=boat,
+  },
+%    \end{macrocode}
+% The diamond.
+%    \begin{macrocode}
+  diamond/.pic={
+    \begin{scope}
+    \pgfkeysgetvalue{/tikz/Penrose/alignment location}{\prloc}
+    \ifx\prloc\pgfutil@empty
+    \else
+    \begingroup
+    \tikzset{name prefix ..}%
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} start)%
+    \global\pgf@xa=\pgf@x
+    \global\pgf@ya=\pgf@y
+    \tikz@scan@one@point\pgfutil@firstofone%
+    (\prloc-edge \pgfkeysvalueof{/tikz/Penrose/alignment edge} end)%
+    \global\pgf@xb=\pgf@x
+    \global\pgf@yb=\pgf@y
+    \endgroup
+    \advance\pgf@xb by -\pgf@xa
+    \advance\pgf@yb by -\pgf@ya
+    \pgftransformshift{\pgfpoint{\pgf@xa}{\pgf@ya}}%
+    \pgfpointnormalised{\pgfpoint{\pgf@xb}{\pgf@yb}}
+    \pgf@xb=\pgf@x
+    \pgf@yb=\pgf@y
+    \pgftransformtriangle%
+    {\pgfpoint{0pt}{0pt}}%
+    {\pgfpoint{\pgf@xb}{\pgf@yb}}%
+    {\pgfpoint{-\pgf@yb}{\pgf@xb}}%
+    \test@edgealign{d}%
+    \if@edgealign%
+    \test@newedge{2}%
+    \if@newedge
+    \pgftransformshift{\pgfpoint{1cm}{0cm}}%
+    \pgftransformrotate{-162}%
+    \else
+    \pgftransformrotate{-18}%
+    \fi
+    \else
+    \test@newedge{2}%
+    \if@newedge
+    \pgftransformrotate{162}%
+    \pgftransformshift{\pgfpoint{- 2 * \pr@chphi cm}{0cm}}%
+    \else
+    \pgftransformshift{\pgfpoint{- \pr@cphi cm}{-\pr@sphi cm}}%
+    \pgftransformrotate{18}%
+    \fi\fi
+    \fi
+    \UsePenroseTile[
+      every Penrose tile clip/.try,
+      every diamond clip/.try
+    ]{diamond}
+    \UsePenroseTile[
+      every Penrose tile/.try,
+      every diamond/.try,
+      pic actions
+    ]{diamond}
+\coordinate (-edge D1 start) at (0,0);
+\coordinate (-edge D1 end) at (\pr@chphi,\pr@shphi);
+\coordinate (-edge B1 start) at (\pr@chphi,\pr@shphi);
+\coordinate (-edge B1 end) at (2*\pr@chphi,0);
+\coordinate (-edge B2 start) at (2*\pr@chphi,0);
+\coordinate (-edge B2 end) at (\pr@chphi,-\pr@shphi);
+\coordinate (-edge D2 start) at (\pr@chphi,-\pr@shphi);
+\coordinate (-edge D2 end) at (0,0);
+    \end{scope}
+  },
+  diamond/.style={
+    every Penrose pic/.try,
+    pic type=diamond,
+  },
+}
+%    \end{macrocode}
+%
+% \iffalse
+%</library>
+% \fi
+%\Finale
+\endinput