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% Draw Hilbert curves.
% Credits: Based on code by Marc van Dongen
% See: http://www.fauskes.net/pgftikzexamples/hilbert-curve/
\title{Hilbert Curves}
\author{}
\date{}
\documentclass{tufte-handout}
\usepackage{tikz}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\usetikzlibrary{positioning}
\begin{document}
\newdimen\HilbertLastX
\newdimen\HilbertLastY
\newcounter{HilbertOrder}
\def\DrawToNext#1#2{%
\advance \HilbertLastX by #1
\advance \HilbertLastY by #2
\pgfpathlineto{\pgfqpoint{\HilbertLastX}{\HilbertLastY}}
% Alternative implementation using plot streams:
% \pgfplotstreampoint{\pgfqpoint{\HilbertLastX}{\HilbertLastY}}
}
% \Hilbert[right_x,right_y,left_x,left_x,up_x,up_y,down_x,down_y]
\def\Hilbert[#1,#2,#3,#4,#5,#6,#7,#8] {
\ifnum\value{HilbertOrder} > 0%
\addtocounter{HilbertOrder}{-1}
\Hilbert[#5,#6,#7,#8,#1,#2,#3,#4]
\DrawToNext {#1} {#2}
\Hilbert[#1,#2,#3,#4,#5,#6,#7,#8]
\DrawToNext {#5} {#6}
\Hilbert[#1,#2,#3,#4,#5,#6,#7,#8]
\DrawToNext {#3} {#4}
\Hilbert[#7,#8,#5,#6,#3,#4,#1,#2]
\addtocounter{HilbertOrder}{1}
\fi
}
% \hilbert((x,y),order)
\def\hilbert((#1,#2),#3){%
\advance \HilbertLastX by #1
\advance \HilbertLastY by #2
\pgfpathmoveto{\pgfqpoint{\HilbertLastX}{\HilbertLastY}}
% Alternative implementation using plot streams:
% \pgfplothandlerlineto
% \pgfplotstreamstart
% \pgfplotstreampoint{\pgfqpoint{\HilbertLastX}{\HilbertLastY}}
\setcounter{HilbertOrder}{#3}
\Hilbert[1mm,0mm,-1mm,0mm,0mm,1mm,0mm,-1mm]
\pgfusepath{stroke}%
}
\def\scalefac{1}
\maketitle
\begin{figure}[h!]
\begin{tikzpicture}[node distance=0cm,every path/.style={thin}]
\node[label={above:$n=1$}] (n1) {\tikz[scale=\scalefac*18] \hilbert((0mm,0mm),1);};
\node[label={above:$n=2$},right=of n1] (n2) {\tikz[scale=\scalefac*6] \hilbert((0mm,0mm),2);};
\node[label={above:$n=3$},right=of n2] (n3) {\tikz[scale=\scalefac*2.6] \hilbert((0mm,0mm),3);};
\node[label={above:$n=4$},right=of n3] (n4) {\tikz[scale=\scalefac*1.2] \hilbert((0mm,0mm),4);};
\node[label={above:$n=5$},right=of n4] (n5) {\tikz[scale=\scalefac*0.58] \hilbert((0mm,0mm),5);};
\end{tikzpicture}
\end{figure}
\end{document}
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