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\title{Hilbert Curves}
\author{}
\date{}

\documentclass{tufte-handout}

\usepackage{tikz}

\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\usetikzlibrary{lindenmayersystems,positioning}

\begin{document}

\pgfdeclarelindenmayersystem{Hilbert curve}{
    \symbol{X}{\pgflsystemdrawforward}
    \symbol{+}{\pgflsystemturnright} % Explicitly define + and - symbols.
    \symbol{-}{\pgflsystemturnleft}
    \rule{A -> +BX-AXA-XB+}
    \rule{B -> -AX+BXB+XA-}
}

\def\scalefac{0.6}
% Draw a hilbert curve of order n
% Usage:
%  \hilbertvurve[scale]{order}
\newcommand\hilbertcurve[2][1]{
\tikz \draw[scale=\scalefac*#1,rotate=90,lindenmayer system={Hilbert curve, axiom=A, order=#2,angle=90}]
    lindenmayer system;
}
\maketitle

\begin{figure}[h!]
\begin{tikzpicture}[node distance=0cm,every path/.style={thin}]
    \node[label={above:$n=1$}] (n1) {\hilbertcurve[18]{1}};
    \node[label={above:$n=2$},right=of n1] (n2) {\hilbertcurve[6]{2}};
    \node[label={above:$n=3$},right=of n2] (n3) {\hilbertcurve[2.6]{3}};
    \node[label={above:$n=4$},right=of n3] (n4) {\hilbertcurve[1.2]{4}};
    \node[label={above:$n=5$},right=of n4] (n5) {\hilbertcurve[0.58]{5}};
\end{tikzpicture}
\end{figure}

\end{document}