% 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}