penrose-gen.tex

% via
% <http://tex.stackexchange.com/questions/61437/penrose-tiling-in-tikz/61623#61623>
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}

% phi = golden ratio = (1+sqrt(5))/2
% invphi = 1/phi
% n: number of decompositions left to do
% ver: starting vertex
% angle: direction of first edge
% len: lenght of first edge
% rot: sense of rotation (0 => anticlockwise, 1 => clockwise)

\pgfmathsetmacro{\invphi}{2/(1+sqrt(5))}

% default styles
\tikzset{
  % borders style
  penrose line/.style={draw=black,line join=round},
  % semikites and semidarts styles
  penrose clockwise semikite/.style={penrose line},
  penrose anticlockwise semikite/.style={penrose line},
  penrose clockwise semidart/.style={penrose line},
  penrose anticlockwise semidart/.style={penrose line},
  % kites and darts styles
  penrose kite/.style={penrose line},
  penrose dart/.style={penrose line},
  % the three paths (and the three corresponding reverse paths)
  penrose common/.style={},
  penrose path 1/.style={penrose common},
  penrose path 2/.style={penrose common},
  penrose path 3/.style={penrose common},
  penrose rev path 1/.style={penrose common},
  penrose rev path 2/.style={penrose common},
  penrose rev path 3/.style={penrose common},
}

\newcommand\penrosedrawclockwisesemikite[3]{% ver, angle, len
  % semikite (clockwise)
  \path (#1) +(#2:#3) coordinate (#1-b) +(#2-36:#3) coordinate (#1-c);
  \path[penrose anticlockwise semikite] (#1)
  to[penrose path 1] (#1-b)
  to[penrose path 2] (#1-c)
  to[penrose path 3] (#1);
}

\newcommand\penrosedrawanticlockwisesemikite[3]{% ver, angle, len
  % semikite (anticlockwise)
  \path (#1) +(#2:#3) coordinate (#1-b) +(#2+36:#3) coordinate (#1-c);
  \path[penrose clockwise semikite] (#1)
  to[penrose path 1] (#1-b)
  to[penrose path 2] (#1-c)
  to[penrose path 3] (#1);
}

\newcommand\penrosesemikite[5]{% n, ver, angle, len, rot
  \ifnum#1=0 % draw or recursive decomposition ?
  \ifnum#5=1 % anticlockwise or clockwise ?
  \penrosedrawclockwisesemikite{#2}{#3}{#4}
  \else
  \penrosedrawanticlockwisesemikite{#2}{#3}{#4}
  \fi
  \else
  {
    % decomposition (semikite => 2 semikites and 1 semidart)
    \edef\dep{#1}
    \edef\ver{#2}
    \edef\angle{#3}
    \edef\len{#4}
    \edef\rot{#5}
    \pgfmathtruncatemacro{\n}{\dep-1}
    \edef\namex{\ver\n}
    \pgfmathsetlengthmacro{\newlen}{\len*\invphi}
    \ifnum#5=1 % anticlockwise or clockwise ?
    \path (\ver) ++(\angle-36:\len) coordinate (\namex);
    \pgfmathtruncatemacro{\newanglea}{mod(\angle+108,360)}
    \penrosesemikite{\n}{\namex}{\newanglea}{\newlen}{1}
    \penrosesemikite{\n}{\namex}{\newanglea}{\newlen}{0}
    \penrosesemidart{\n}{\ver}{\angle}{\newlen}{1}
    \else
    \path (\ver) ++(\angle+36:\len) coordinate (\namex);
    \pgfmathtruncatemacro{\newanglea}{mod(\angle-108,360)}
    \penrosesemikite{\n}{\namex}{\newanglea}{\newlen}{0}
    \penrosesemikite{\n}{\namex}{\newanglea}{\newlen}{1}
    \penrosesemidart{\n}{\ver}{\angle}{\newlen}{0}
    \fi
  }
  \fi
}

\newcommand\penrosedrawkite[3]{% ver, angle, len
  % kite (current clockwise semikite + opposite anticlockwise semikite)
  \path (#1)
  +(#2+36:#3) coordinate (#1-b)
  +(#2:#3)    coordinate (#1-c)
  +(#2-36:#3) coordinate (#1-d);
  \pgfmathparse{0.9*rnd+0.3}
  \definecolor{MyColor}{rgb}{\pgfmathresult,\pgfmathresult,\pgfmathresult}
  \path[penrose kite] (#1)
  to[penrose path 1] (#1-b)
  to[penrose rev path 2] (#1-c)
  to[penrose path 2] (#1-d)
  to[penrose rev path 1] (#1);
}

\newcommand\penrosekite[5]{% n, ver, angle, len, rot
  \ifnum#1=0 % draw or recursive decomposition ?
  \ifnum#5=1 % draw kite if current semikite is clockwise
  \penrosedrawkite{#2}{#3}{#4}
  \fi
  \else
  {
    % decomposition (semikite => 2 semikites and 1 semidart)
    \edef\dep{#1}
    \edef\ver{#2}
    \edef\angle{#3}
    \edef\len{#4}
    \edef\rot{#5}
    \pgfmathtruncatemacro{\n}{\dep-1}
    \edef\namex{\ver\n}
    \pgfmathsetlengthmacro{\newlen}{\len*\invphi}
    \ifnum#5=1 % anticlockwise or clockwise ?
    \path (\ver) ++(\angle-36:\len) coordinate (\namex);
    \pgfmathtruncatemacro{\newanglea}{mod(\angle+108,360)}
    \penrosekite{\n}{\namex}{\newanglea}{\newlen}{1}
    \penrosekite{\n}{\namex}{\newanglea}{\newlen}{0}
    \penrosedart{\n}{\ver}{\angle}{\newlen}{1}
    \else
    \path (\ver) ++(\angle+36:\len) coordinate (\namex);
    \pgfmathtruncatemacro{\newanglea}{mod(\angle-108,360)}
    \penrosekite{\n}{\namex}{\newanglea}{\newlen}{0}
    \penrosekite{\n}{\namex}{\newanglea}{\newlen}{1}
    \penrosedart{\n}{\ver}{\angle}{\newlen}{0}
    \fi
  }
  \fi
}

\newcommand\penrosedrawclockwisesemidart[3]{
  % semidart (clockwise)
  \path (#1)
  +(#2:#3)            coordinate (#1-b)
  +(#2-36:#3*\invphi) coordinate (#1-c);
  \path[penrose anticlockwise semidart] (#1)
  to[penrose path 3] (#1-b)
  to[penrose path 2] (#1-c)
  to[penrose path 1] (#1);
}

\newcommand\penrosedrawanticlockwisesemidart[3]{
  % semidart (anticlockwise)
 \path (#1)
  +(#2:#3)            coordinate (#1-b)
  +(#2+36:#3*\invphi) coordinate (#1-c);
  \path[penrose clockwise semidart] (#1)
  to[penrose path 3] (#1-b)
  to[penrose path 2] (#1-c)
  to[penrose path 1] (#1);
 }

\newcommand\penrosesemidart[5]{% n, ver, angle, len, rot
  \ifnum#1=0 % draw or recursive decomposition ?
  \ifnum#5=1 % anticlockwise or clockwise ?
  \penrosedrawclockwisesemidart{#2}{#3}{#4}
  \else
  \penrosedrawanticlockwisesemidart{#2}{#3}{#4}
  \fi
  \else
  {
    % decomposition (semidart => 1 semikite and 1 semidart)
    \edef\dep{#1}
    \edef\ver{#2}
    \edef\angle{#3}
    \edef\len{#4}
    \edef\rot{#5}
    \pgfmathtruncatemacro{\n}{\dep-1}
    \edef\namex{\ver\n}
    \pgfmathsetlengthmacro{\newlen}{\len*\invphi}
    \path (\ver) ++(\angle:\len) coordinate (\namex);
    \ifnum#5=1 % anticlockwise or clockwise
    \pgfmathsetmacro{\newanglea}{mod(\angle-144,360)}
    \pgfmathsetmacro{\newangleb}{mod(\angle-36,360)}
    \penrosesemidart{\n}{\namex}{\newanglea}{\newlen}{1}
    \penrosesemikite{\n}{\ver}{\newangleb}{\newlen}{0}
    \else
    \pgfmathtruncatemacro{\newanglea}{mod(\angle+144,360)}
    \pgfmathtruncatemacro{\newangleb}{mod(\angle+36,360)}
    \penrosesemidart{\n}{\namex}{\newanglea}{\newlen}{0}
    \penrosesemikite{\n}{\ver}{\newangleb}{\newlen}{1}
    \fi
  }
  \fi
}

\newcommand\penrosedrawdart[3]{
  % dart (current clockwise semidart + opposite anticlockwise semidart)
  \path (#1)
  +(#2:#3)            coordinate (#1-b)
  +(#2-36:#3*\invphi) coordinate (#1-c)
  +(#2-72:#3)         coordinate (#1-d);
  \path[penrose dart] (#1)
  to[penrose path 3] (#1-b)
  to[penrose path 2] (#1-c)
  to[penrose rev path 2] (#1-d)
  to[penrose rev path 3] (#1);
}

\newcommand\penrosedart[5]{% n, ver, angle, len, rot
  \ifnum#1=0 % draw or recursive decomposition ?
  \ifnum#5=1 % draw dart if current semidart is clockwise
  \penrosedrawdart{#2}{#3}{#4}
  \fi
  \else
  {
    % decomposition (semidart => 1 semikite and 1 semidart)
    \edef\dep{#1}
    \edef\ver{#2}
    \edef\angle{#3}
    \edef\len{#4}
    \edef\rot{#5}
    \pgfmathtruncatemacro{\n}{\dep-1}
    \edef\namex{\ver\n}
    \pgfmathsetlengthmacro{\newlen}{\len*\invphi}
    \path (\ver) ++(\angle:\len) coordinate (\namex);
    \ifnum#5=1 % anticlockwise or clockwise
    \pgfmathsetmacro{\newanglea}{mod(\angle-144,360)}
    \pgfmathsetmacro{\newangleb}{mod(\angle-36,360)}
    \penrosedart{\n}{\namex}{\newanglea}{\newlen}{1}
    \penrosekite{\n}{\ver}{\newangleb}{\newlen}{0}
    \else
    \pgfmathtruncatemacro{\newanglea}{mod(\angle+144,360)}
    \pgfmathtruncatemacro{\newangleb}{mod(\angle+36,360)}
    \penrosedart{\n}{\namex}{\newanglea}{\newlen}{0}
    \penrosekite{\n}{\ver}{\newangleb}{\newlen}{1}
    \fi
  }
  \fi
}

\newcommand\setveclength[5]{%
  %\typeout{-#1-#2-#3-#4-}%
  \pgfpointanchor{#2}{#3}
  \pgfgetlastxy{\penrosexa}{\penroseya}
  \pgfpointanchor{#4}{#5}
  \pgfgetlastxy{\penrosexb}{\penroseyb}
  \pgfmathparse{veclen(\penrosexb-\penrosexa,\penroseyb-\penroseya)}
  \edef#1{\pgfmathresult}
}

\tikzset{
  semipenrose sym fill/.style={
    path picture={
      \setveclength{\mylen}%
      {path picture bounding box}{center}%
      {path picture bounding box}{north west}
      \pgfmathsetmacro{\len}{1.17*\mylen}
      \begin{scope}[shift={(path picture bounding box.center)}]
        \foreach \level in {0,...,4}{
          \begin{scope}[rotate=\level*72+9]
            \coordinate (a) at (0,0);
            \penrosesemikite{#1}{a}{0}{\len pt}{0}
            \penrosesemikite{#1}{a}{0}{\len pt}{1}
          \end{scope}
        }
      \end{scope}
    }
  },
  semipenrose fill/.style={
    path picture={
      \setveclength{\mylen}%
      {path picture bounding box}{center}%
      {path picture bounding box}{west}
      \pgfmathsetmacro{\len}{1.33*\mylen}
      \begin{scope}[shift={(path picture bounding box.center)},rotate=9]
        \coordinate (a) at (-\len pt,0);
        \path (a) +(36:2*\len pt) coordinate (b);
        \path (a) +(-36:2*\len pt) coordinate (c);
        \penrosesemidart{#1}{b}{36-180}{2*\len pt}{1}
        \penrosesemikite{#1}{a}{0}{2*\len pt}{0}
        \penrosesemikite{#1}{a}{0}{2*\len pt}{1}
        \penrosesemidart{#1}{c}{180-36}{2*\len pt}{0}
      \end{scope}
    }
  },
  penrose sym fill/.style={
    path picture={
      \setveclength{\mylen}%
      {path picture bounding box}{center}%
      {path picture bounding box}{north west}
      \pgfmathsetmacro{\len}{1.23*\mylen}
      \begin{scope}[shift={(path picture bounding box.center)}]
        \foreach \level in {0,...,4}{
          \begin{scope}[rotate=\level*72+9]
            \coordinate (a) at (0,0);
            \penrosekite{#1}{a}{18}{\len pt}{0}
            \penrosekite{#1}{a}{18}{\len pt}{1}
          \end{scope}
        }
      \end{scope}
    }
  },
  penrose fill/.style={
    path picture={
      \setveclength{\mylen}%
      {path picture bounding box}{center}%
      {path picture bounding box}{west}
      \pgfmathsetmacro{\len}{2.38*\mylen}
      \begin{scope}[shift={(path picture bounding box.center)},rotate=9]
        \coordinate (a) at (-\len pt,0);
        \path (a) +(36:2*\len pt) coordinate (b);
        \path (a) +(-36:2*\len pt) coordinate (c);
        \penrosedart{#1}{b}{36-180}{2*\len pt}{1}
        \penrosekite{#1}{a}{0}{2*\len pt}{0}
        \penrosekite{#1}{a}{0}{2*\len pt}{1}
        \penrosedart{#1}{c}{180-36}{2*\len pt}{0}
      \end{scope}
    }
  },
}

\usetikzlibrary{shapes.arrows}
\pgfmathsetlengthmacro{\len}{4cm}
\pgfmathtruncatemacro{\recurs}{5}
\begin{document}
\begin{tikzpicture}
  \tikzset{
    gray arrow/.style={
      fill=gray,minimum height=.5cm,rotate=-90,
      single arrow,single arrow head extend=1mm,
    },
  }
  \tikzset{
    % style for borders
    line/.style={draw=white,rounded corners=0pt},
    % styles for semikites and semidarts
    penrose clockwise semikite/.style={fill=orange,line},
    penrose anticlockwise semikite/.style={fill=orange!50!black,line},
    penrose clockwise semidart/.style={fill=cyan!80,line},
    penrose anticlockwise semidart/.style={fill=cyan!50,line},
    % styles for kites and darts
    penrose kite/.style={fill=red!75!black,line},
    penrose dart/.style={fill=olive!75!white,line},
  }
  % example of semidarts and semikites
  \begin{scope}[yshift=-2*\len]
    \foreach \level in {0,...,7}{
      \begin{scope}[rotate=\level*72]
        \coordinate (a) at (0,0);
        \penrosesemikite{\recurs}{a}{0}{\len}{0}
        \penrosesemikite{\recurs}{a}{0}{\len}{1}
      \end{scope}
    }
  \end{scope}
\end{tikzpicture}
\end{document}