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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}