Scale and position Z-Curve using TikZ and the Lindenmayer system

Question

I want to draw a Z-Curve in LaTeX using TikZ and the Lindenmayer system. But I did not manage to position the curves central over each bullet point. Furthermore I do not find any elegant way such that all curves have the same size.

Here is what I get:

Here is my code:

\documentclass[a4paper,11pt]{article}

\usepackage{graphicx}          
\usepackage{caption}
\usepackage{subcaption} 
\usepackage{tikz}


\begin{document}
\usetikzlibrary{lindenmayersystems}
\pgfdeclarelindenmayersystem{z-curve}{
\symbol{I}{\pgftransformscale{+0.25\pgflsystemstep}}
\symbol{p}{%
  \pgfpathmoveto{\pgfqpoint{1pt}{3pt}}\pgfpathlineto{\pgfqpoint{3pt}{3pt}}%
  \pgfpathlineto{\pgfqpoint{1pt}{1pt}}\pgfpathlineto{\pgfqpoint{3pt}{1pt}}%
}
\symbol{q}{%
  \pgfpathlineto{\pgfqpoint{1pt}{3pt}}\pgfpathlineto{\pgfqpoint{3pt}{3pt}}%
  \pgfpathlineto{\pgfqpoint{1pt}{1pt}}\pgfpathlineto{\pgfqpoint{3pt}{1pt}}%
}
\symbol{S}{\pgftransformscale{+0.5pt}}
\symbol{A}{\pgftransformshift{\pgfqpoint{0pt}{4pt}}}
\symbol{B}{\pgftransformshift{\pgfqpoint{4pt}{4pt}}}
\symbol{C}{\pgftransformshift{\pgfqpoint{4pt}{0pt}}}
\symbol{[}{\bgroup}
\symbol{]}{\egroup}
\rule{Z -> Ip}
\rule{p -> S[Ap][Bq][q][Cq]}
\rule{q -> S[Aq][Bq][q][Cq]}
}

\begin{figure}[ht]
\centering
\subcaptionbox{}
{\begin{tikzpicture}[scale=2]
\draw [l-system={z-curve, step=1cm, axiom=Z, order=1}] l-system;
\end{tikzpicture}}
\hspace{1cm}
\subcaptionbox{}
{\begin{tikzpicture}[scale=2]
\draw [l-system={z-curve, step=1cm, axiom=Z, order=2}] l-system;
\end{tikzpicture}}
\hspace{1cm}
\subcaptionbox{}
{\begin{tikzpicture}[scale=2]
\draw [l-system={z-curve, step=1cm, axiom=Z, order=3}] l-system;
\end{tikzpicture}}
\hspace{1cm}
\subcaptionbox{}
{\begin{tikzpicture}[scale=2]
\draw [l-system={z-curve, step=1cm, axiom=Z, order=4}] l-system;
\end{tikzpicture}}
\end{figure}

\end{document}

Any suggestion what I should change to get what I want?

Answer 1

1. Manage to position the curves central over each bullet point:

I changed the symbols p and q (horizontal domain: 0pt to 2pt; instead of 1pt to 3pt) to achive a horizontal centering. Vertically it also start from 0pt instead of 1pt. With \draw(<x>,<y>)... you could place the curves later arbitrary. For example with \draw(0,0).

\symbol{p}{%
  \pgfpathmoveto{\pgfqpoint{0pt}{2pt}}\pgfpathlineto{\pgfqpoint{2pt}{2pt}}%
  \pgfpathlineto{\pgfqpoint{0pt}{0pt}}\pgfpathlineto{\pgfqpoint{2pt}{0pt}}%
}
\symbol{q}{%
  \pgfpathlineto{\pgfqpoint{0pt}{2pt}}\pgfpathlineto{\pgfqpoint{2pt}{2pt}}%
  \pgfpathlineto{\pgfqpoint{0pt}{0pt}}\pgfpathlineto{\pgfqpoint{2pt}{0pt}}%
}

2. Same size of all curves:

With \resizebox{<horizontal size>}{<vertical size>}{...} (see: 4.3.2 Scaling to a requested size, p.8 in the manual ["Packages in the ‘graphics’ bundle"]) you could set the horizontal and vertical size of the tikzpicture. If you want the tikzpicture to be scaled proportionally, you can give one of the sizes and put ! in the other.

\resizebox{!}{2cm}{
\begin{tikzpicture}
\draw[black](0,0) l-system [l-system={z-curve, step=1cm, axiom=Z, order=1}];
\end{tikzpicture}
}

3. Note

I used \subfloat and reduced the import of packages, because TikZ loads graphicx automatically.

---

Result:

---

MWE:

\documentclass[a4paper,11pt]{article}
\usepackage{tikz}
\usepackage{subfig}
\begin{document}
\usetikzlibrary{lindenmayersystems}
\pgfdeclarelindenmayersystem{z-curve}{
\symbol{I}{\pgftransformscale{+0.25\pgflsystemstep}}
\symbol{p}{%
  \pgfpathmoveto{\pgfqpoint{0pt}{2pt}}\pgfpathlineto{\pgfqpoint{2pt}{2pt}}%
  \pgfpathlineto{\pgfqpoint{0pt}{0pt}}\pgfpathlineto{\pgfqpoint{2pt}{0pt}}%
}
\symbol{q}{%
  \pgfpathlineto{\pgfqpoint{0pt}{2pt}}\pgfpathlineto{\pgfqpoint{2pt}{2pt}}%
  \pgfpathlineto{\pgfqpoint{0pt}{0pt}}\pgfpathlineto{\pgfqpoint{2pt}{0pt}}%
}
\symbol{S}{\pgftransformscale{+0.5pt}}
\symbol{A}{\pgftransformshift{\pgfqpoint{0pt}{4pt}}}
\symbol{B}{\pgftransformshift{\pgfqpoint{4pt}{4pt}}}
\symbol{C}{\pgftransformshift{\pgfqpoint{4pt}{0pt}}}
\symbol{[}{\bgroup}
\symbol{]}{\egroup}
\rule{Z -> Ip}
\rule{p -> S[Ap][Bq][q][Cq]}
\rule{q -> S[Aq][Bq][q][Cq]}
}

\begin{figure}[h!]
\centering
\subfloat[]{\label{fig:a}
\resizebox{!}{2cm}{
\begin{tikzpicture}
\draw[black](0,0) l-system [l-system={z-curve, step=1cm, axiom=Z, order=1}];
\end{tikzpicture}
}
}
\hfill
\subfloat[]{\label{fig:a}
\resizebox{!}{2cm}{
\begin{tikzpicture}
\draw [red](0,0) l-system  [l-system={z-curve, step=1cm, axiom=Z, order=2}];
\end{tikzpicture}
}
}
\hfill
\subfloat[]{\label{fig:a}
\resizebox{!}{2cm}{
\begin{tikzpicture}
\draw [blue](0,0) l-system  [l-system={z-curve, step=1cm, axiom=Z, order=3}];
\end{tikzpicture}
}
}
\hfill
\subfloat[]{\label{fig:a}
\resizebox{!}{2cm}{
\begin{tikzpicture}
\draw [green](0,0) l-system  [l-system={z-curve, step=1cm, axiom=Z, order=4}];
\end{tikzpicture}
}
}
\hfill
\caption{Z-Curve using TikZ and the Lindenmayer system}\label{fig:LabelFigOne}
\end{figure}
\end{document}