Information: the material between BODY and ENDBODY is a plain TeX file which, when TeXed, will unfold some postscript files (for the graphics) in the same directory; these postscript files will automatically be included when the dvi file is printed. BODY % This file was generated from % text11.tex jfig1.ps jfig2.ps jfig7new.ps fig6-1.eps fig6-2.eps pinwheel3.ps square.eps squares2.ps Penrose6.ai by /public/bin/texpsinclude. % This file contains included PostScript. % TeX writes out the included PostScript to files. % Here are the macros for writing out the included PostScript: % Macros for dumping included Postscript to files. % Requires Plain TeX. Maybe other flavors will work too? % Jamie Stephens, jamies@math.utexas.edu, 28 Nov 94 % If you're in the UT Math Department, see % /usr/local/doc/tex/texpsinclude.text and /public/bin/texpsinclude. % Parts of these files are attached at the end of this file. % Adapted from Knuth's \answer macro in the TeXbook. \def\endofps{EndOfTheIncludedPostscriptMagicCookie} \chardef\other=12 \newwrite\psdumphandle \outer\def\psdump#1{\par\medbreak \immediate\openout\psdumphandle=#1 \copytoblankline} \def\copytoblankline{\begingroup\setupcopy\copypsline} \def\setupcopy{\def\do##1{\catcode`##1=\other}\dospecials \catcode`\\=\other \obeylines} {\obeylines \gdef\copypsline#1 {\def\next{#1}% \ifx\next\endofps\let\next=\endgroup % \else\immediate\write\psdumphandle{\next} \let\next=\copypsline\fi\next}} \outer\def\closepsdump{ \immediate\closeout\psdumphandle} %% %% Here's a shell script for automating the use of psdump.tex %% % #!/bin/bash % % PSDUMP=/usr/local/tex/macros/local/psdump.tex % TEXPSINCLUDEHELP=/usr/local/doc/tex/texpsinclude.help % % if [ $# -eq 0 ]; then % echo "Usage: $0 file.tex {files.ps} > output.tex" >&2 % echo "See $TEXPSINCLUDEHELP for more information." >&2 % exit 1 % fi % % echo "% This file was generated from" % echo "% $@ by $0." % echo "% This file contains included PostScript." % echo "% TeX writes out the included PostScript to files." % echo % echo "% Here are the macros for writing out the included PostScript:" % cat $PSDUMP % echo % % for argument in $@; do % if [ $argument != $1 ]; then % echo "% Here's the Postscript for $argument:" % echo "\message{Writing file $argument}" % echo -n "\psdump{$argument}" % echo "Including $argument." >&2 % cat $argument % echo "EndOfTheIncludedPostscriptMagicCookie" % echo % echo "\closepsdump" % fi % done % % echo % echo "% Finally, here is $1:" % % cat $1 %% %% Here's some documentation: %% % This file documents how to use the texpsinclude command in /public/bin. % Here's the problem that texpsinclude solves: % You have a TeX file called foo.tex that you want to distribute as a % single TeX file. The problem is that foo.tex needs two Postscript % files, bar1.ps and bar2.ps, for embedded figures. You'd like a single % TeX file which somehow includes bar1.ps and bar2.ps. When TeX % processes foo.tex, TeX should extract bar1.ps and bar2.ps from % foo.tex. % Here's how to do what you want to do: % texpsinclude foo.tex. bar1.ps bar2.ps > bigfoo.tex % (In general: "texpsinclude > ".) If you % enter this command, the result is a new file called bigfoo.tex. The % file bigfoo.tex contains bar1.ps and bar2.ps. If you give bigfoo.tex % to a friend, she can make your document with: % tex bigfoo.tex % This command writes out bar1.ps and bar2.ps, and the command also % TeX's foo.tex. % Note: If *you* run tex on bigfoo.tex in the same directory, then TeX % will write over your .ps files. Be careful when testing your % bigfoo.tex. %% %% Here's another way to use psdump.tex %% % EXAMPLE (remove the leading % signs to make it work): % %\psdump{example.ps}These three lines %are going be dumped "as is" %to the file example.ps %EndOfTheIncludedPostscriptMagicCookie %\closepsdump % Here's the Postscript for jfig1.ps: \message{Writing file jfig1.ps} \psdump{jfig1.ps}%!PS-Adobe-2.0 EPSF-2.0 %%Creator: gnuplot %%DocumentFonts: Courier %%BoundingBox: 50 50 554 554 %%EndComments /gnudict 40 dict def gnudict begin /Color false def /gnulinewidth 5.000 def /vshift -46 def /dl {10 mul} def /hpt 31.5 def /vpt 31.5 def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke moveto 0 vshift rmoveto show } def /Rshow { currentpoint stroke moveto dup stringwidth pop neg vshift rmoveto show } def /Cshow { currentpoint stroke moveto dup stringwidth pop -2 div vshift rmoveto show } def /DL { Color {setrgbcolor [] 0 setdash pop} {pop pop pop 0 setdash} ifelse } def /BL { stroke gnulinewidth 2 mul setlinewidth } def /AL { stroke gnulinewidth 2 div setlinewidth } def /PL { stroke gnulinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 0 1 0 DL } def /LT1 { PL [4 dl 2 dl] 0 0 1 DL } def /LT2 { PL [2 dl 3 dl] 1 0 0 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /M {moveto} def /L {lineto} def /P { stroke [] 0 setdash currentlinewidth 2 div sub moveto 0 currentlinewidth rlineto stroke } def /D { stroke [] 0 setdash 2 copy vpt add moveto hpt neg vpt neg rlineto hpt vpt neg rlineto hpt vpt rlineto hpt neg vpt rlineto closepath stroke P } def /A { stroke [] 0 setdash vpt sub moveto 0 vpt2 rlineto currentpoint stroke moveto hpt neg vpt neg rmoveto hpt2 0 rlineto stroke } def /B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add moveto 0 vpt2 neg rlineto hpt2 0 rlineto 0 vpt2 rlineto hpt2 neg 0 rlineto closepath stroke P } def /C { stroke [] 0 setdash exch hpt sub exch vpt add moveto hpt2 vpt2 neg rlineto currentpoint stroke moveto hpt2 neg 0 rmoveto hpt2 vpt2 rlineto stroke } def /T { stroke [] 0 setdash 2 copy vpt 1.12 mul add moveto hpt neg vpt -1.62 mul rlineto hpt 2 mul 0 rlineto hpt neg vpt 1.62 mul rlineto closepath stroke P } def /S { 2 copy A C} def end %%EndProlog gnudict begin gsave 50 50 translate 0.070 0.100 scale 0 setgray /Courier findfont 140 scalefont setfont newpath LTa LTb LTb 3989 -2307 M (Figure 4) Cshow LT0 LT0 1670 491 M 1564 547 L 1882 659 L 2001 491 L 1564 1107 M 1564 1107 L 1564 547 L 1882 659 L 1564 1107 L 1564 547 M 1564 547 L 1564 1107 L 1246 995 L 1564 547 L 1564 547 M 1564 547 L 1008 841 L 1008 911 M 1246 995 L 1564 547 L 1008 957 M 1405 1331 L 1564 1107 L 1008 911 L 1056 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4353 M 3631 4353 L 2995 4689 L 2995 4689 M 2931 4443 L 3631 4353 L 2995 4689 M 2518 4241 L 2868 4196 L 2995 4689 L 2741 3704 M 2741 3704 L 2518 4241 L 2868 4196 L 2741 3704 L 2518 4241 M 2518 4241 L 2741 3704 L 2391 3749 L 2518 4241 L 2518 4241 M 2518 4241 L 2041 3793 L 2391 3749 L 2518 4241 L 2041 3793 M 2041 3793 L currentpoint stroke moveto 2677 3458 L 2741 3704 L 2041 3793 L 2995 4689 M 2518 4241 L 2359 4465 L 2995 4689 L 1723 4241 M 1723 4241 L 2518 4241 L 2359 4465 L 1723 4241 L 2518 4241 M 2518 4241 L 1723 4241 L 1882 4017 L 2518 4241 L 2518 4241 M 2518 4241 L 2041 3793 L 1882 4017 L 2518 4241 L 2041 3793 M 2041 3793 L 1405 4129 L 1723 4241 L 2041 3793 L 1405 4129 M 1405 4129 L 2041 3793 L 1723 3681 L 1405 4129 L 2041 3234 M 2041 3234 L 2041 3793 L 1723 3681 L 2041 3234 L 2041 3793 M 2041 3793 L 2041 3234 L 2359 3346 L 2041 3793 L 2041 3793 M 2041 3793 L 2677 3458 L 2359 3346 L 2041 3793 L 2677 3458 M 2677 3458 L 2200 3010 L 2041 3234 L 2677 3458 L 2200 3010 M 2200 3010 L 1564 3346 L 1882 3458 L 2200 3010 L 1564 3905 M 1564 3905 L 1564 3346 L 1882 3458 L 1564 3905 L 1564 3346 M 1564 3346 L 1564 3905 L 1246 3793 L 1564 3346 L 1564 3346 M 1564 3346 L 1008 3640 L 1008 3709 M 1246 3793 L 1564 3346 L 1008 3756 M 1405 4129 L 1564 3905 L 1008 3709 L 1056 4174 M 1056 4174 L 1008 4164 L 1008 4180 M 1056 4174 L 1008 4164 M 1056 4174 L 1008 3989 L 1008 3756 M 1405 4129 L 1056 4174 L 1008 3989 L 1405 4129 M 1405 4129 L 1008 4339 L 1008 4180 M 1405 4129 L 1405 4129 M 1405 4129 L 1008 4339 L 1008 4549 M 1087 4577 L 1405 4129 L 1008 4549 M 1087 4577 L 1008 4689 L 1564 3346 M 1564 3346 L 1008 3640 L 1008 3417 M 1564 3346 L 1215 3390 M 1215 3390 L 1008 3348 L 1008 3417 M 1215 3390 L 1008 3348 M 1215 3390 L 1151 3144 L 1008 3162 L 1008 2940 M 1087 2898 L 1151 3144 L 1008 3162 L 1087 2898 M 1087 2898 L 1564 3346 L 1215 3390 L 1087 2898 L 1008 2940 M 1087 2898 L 1008 2870 L 1087 2898 M 1087 2898 L 1008 2823 L 1008 2870 M 1087 2898 L 1008 2823 M 1087 2898 L 1246 2674 L 1008 2590 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1405 1890 M 1405 1890 L 1405 2450 L 1723 2338 L 1405 1890 L 1405 2450 M 1405 2450 L 2200 2450 L 2041 2226 L 1405 2450 L 1405 1331 M 1405 1331 L 1405 1890 L 1087 1778 L 1405 1331 L 1008 2100 M 1405 1890 L 1087 1778 L 1008 1890 L 1405 1890 M 1405 1890 L 1008 2100 L 1008 2310 M 1087 2338 L 1405 1890 L 1405 1890 M 1405 1890 L 1405 2450 L 1087 2338 L 1405 1890 L 1405 2450 M 1405 2450 L 1008 2450 L 1008 2310 M 1405 2450 L 1008 2450 M 1405 2450 L 1246 2674 L 1008 2590 L 1882 2898 M 1882 2898 L 1405 2450 L 1246 2674 L 1882 2898 L 1405 2450 M 1405 2450 L 1882 2898 L 2041 2674 L 1405 2450 L 1405 2450 M 1405 2450 L 2200 2450 L 2041 2674 L 1405 2450 L 2200 2450 M 2200 2450 L 2200 3010 L 1882 2898 L 2200 2450 L 2200 3010 M 2200 3010 L 2200 2450 L 2518 2562 L 2200 3010 L 2836 2114 M 2836 2114 L 2200 2450 L 2518 2562 L 2836 2114 L 2200 2450 M 2200 2450 L 2836 2114 L 2518 2002 L 2200 2450 L 2200 2450 M 2200 2450 L 2200 1890 L 2518 2002 L 2200 2450 L 2200 1890 M 2200 1890 L 2995 1890 L 2836 2114 L 2200 1890 L 2200 771 M 2200 771 L 2200 1331 L 2518 1219 L 2200 771 L 2836 1666 M 2836 1666 L 2200 1331 L 2518 1219 L 2836 1666 L 2200 1331 M 2200 1331 L 2836 1666 L 2518 1778 L 2200 1331 L 2200 1331 M 2200 1331 L 2200 1890 L 2518 1778 L 2200 1331 L 2200 1890 M 2200 1890 L 2995 1890 L 2836 1666 L 2200 1890 L 2995 1890 M 2995 1890 L 2995 1331 L 2677 1443 L 2995 1890 L 2359 995 M 2359 995 L 2995 1331 L 2677 1443 L 2359 995 L 2995 1331 M 2995 1331 L 2359 995 L 2677 883 L 2995 1331 L 2995 1331 M 2995 1331 L 2995 771 L 2677 883 L 2995 1331 L 2995 771 M 2995 771 L 2200 771 L 2359 995 L 2995 771 L 2995 1890 M 2995 1890 L 2995 1331 L 3313 1443 L 2995 1890 L 3631 995 M 3631 995 L 2995 1331 L 3313 1443 L 3631 995 L 2995 1331 M 2995 1331 L 3631 995 L 3313 883 L 2995 1331 L 2995 1331 M 2995 1331 L 2995 771 L 3313 883 L 2995 1331 L 2995 771 M 2995 771 L 3790 771 L 3631 995 L 2995 771 L 3790 771 M 3790 771 L 2995 771 L 3154 547 L 3790 771 L 2697 491 M 2995 771 L 3154 547 L 2995 491 L 2995 771 M 2995 771 L 2697 491 L 2399 491 M 2359 547 L 2995 771 L 2995 771 M 2995 771 L 2200 771 L 2359 547 L currentpoint stroke moveto 2995 771 L 2200 771 M 2200 771 L 2200 491 L 2399 491 M 2200 771 L 2200 3010 M 2200 3010 L 2836 2674 L 2518 2562 L 2200 3010 L 2836 2114 M 2836 2114 L 2836 2674 L 2518 2562 L 2836 2114 L 2836 2674 M 2836 2674 L 2836 2114 L 3154 2226 L 2836 2674 L 2836 2674 M 2836 2674 L 3472 2338 L 3154 2226 L 2836 2674 L 3472 2338 M 3472 2338 L 2995 1890 L 2836 2114 L 3472 2338 L 4744 1666 M 4744 1666 L 4108 2002 L 4044 1756 L 4744 1666 L 3345 1846 M 3345 1846 L 4108 2002 L 4044 1756 L 3345 1846 L 4108 2002 M 4108 2002 L 3345 1846 L 3408 2092 L 4108 2002 L 4108 2002 M 4108 2002 L 3472 2338 L 3408 2092 L 4108 2002 L 3472 2338 M 3472 2338 L 2995 1890 L 3345 1846 L 3472 2338 L 2995 1890 M 2995 1890 L 3631 1554 L 3694 1801 L 2995 1890 L 4394 1711 M 4394 1711 L 3631 1554 L 3694 1801 L 4394 1711 L 3631 1554 M 3631 1554 L 4394 1711 L 4330 1465 L 3631 1554 L 3631 1554 M 3631 1554 L 4267 1219 L 4330 1465 L 3631 1554 L 4267 1219 M 4267 1219 L 4744 1666 L 4394 1711 L 4267 1219 L 2995 1890 M 2995 1890 L 3631 1554 L 3313 1443 L 2995 1890 L 3631 995 M 3631 995 L 3631 1554 L 3313 1443 L 3631 995 L 3631 1554 M 3631 1554 L 3631 995 L 3949 1107 L 3631 1554 L 3631 1554 M 3631 1554 L 4267 1219 L 3949 1107 L 3631 1554 L 4267 1219 M 4267 1219 L 3790 771 L 3631 995 L 4267 1219 L 3790 771 M 3790 771 L 4267 1219 L 4426 995 L 3790 771 L 5061 1219 M 5061 1219 L 4267 1219 L 4426 995 L 5061 1219 L 4267 1219 M 4267 1219 L 5061 1219 L 4903 1443 L 4267 1219 L 4267 1219 M 4267 1219 L 4744 1666 L 4903 1443 L 4267 1219 L 4744 1666 M 4744 1666 L 5379 1331 L 5061 1219 L 4744 1666 L 5379 1331 M 5379 1331 L 4903 883 L 4744 1107 L 5379 1331 L 4108 883 M 4108 883 L 4903 883 L 4744 1107 L 4108 883 L 4903 883 M 4903 883 L 4108 883 L 4267 659 L 4903 883 L 4903 883 M 4903 883 L 4485 491 L 4386 491 M 4267 659 L 4903 883 L 4320 491 M 3790 771 L 4108 883 L 4386 491 L 3726 525 M 3726 525 L 3740 491 L 3718 491 M 3726 525 L 3740 491 M 3726 525 L 3988 491 L 4320 491 M 3790 771 L 3726 525 L 3989 491 L 3790 771 M 3790 771 L 3492 491 L 3718 491 M 3790 771 L 3790 771 M 3790 771 L 3492 491 L 3194 491 M 3154 547 L 3790 771 L 3194 491 M 3154 547 L 2995 491 L 4903 883 M 4903 883 L 4485 491 L 4801 491 M 4903 883 L 4839 637 M 4839 637 L 4899 491 L 4801 491 M 4839 637 L 4899 491 M 4839 637 L 5189 592 L 5163 491 L 5479 491 M 5538 547 L 5189 592 L 5163 491 L 5538 547 M 5538 547 L 4903 883 L 4839 637 L 5538 547 L 5479 491 M 5538 547 L 5578 491 L 5538 547 M 5538 547 L 5644 491 L 5578 491 M 5538 547 L 5644 491 M 5538 547 L 5856 659 L 5976 491 L 5538 1107 M 5538 1107 L 5538 547 L 5856 659 L 5538 1107 L 5538 547 M 5538 547 L 5538 1107 L 5220 995 L 5538 547 L 5538 547 M 5538 547 L 4903 883 L 5220 995 L 5538 547 L 4903 883 M 4903 883 L 5379 1331 L 5538 1107 L 4903 883 L 6174 1331 M 6174 1331 L 6969 1331 L 6969 1331 M 6810 1107 L 6174 1331 L 6969 1331 M 6810 1107 L 6969 1051 L 6492 1219 M 6492 1219 L 6969 771 L 6969 1051 M 6492 1219 L 6969 771 M 6492 1219 L 6333 995 L 6969 771 L 6969 771 M 6174 771 L 6333 995 L 6969 771 L 6174 771 M 6174 771 L 6174 1331 L 6492 1219 L 6174 771 L 6373 491 M 6333 547 L 6969 771 L 6969 771 M 6174 771 L 6333 547 L 6969 771 L 6174 771 M 6174 771 L 6174 491 L 6373 491 M 6174 771 L 6174 491 M 6174 771 L 5856 659 L 5976 491 L 5538 1107 M 5538 1107 L 6174 771 L 5856 659 L 5538 1107 L 6174 771 M 6174 771 L 5538 1107 L 5856 1219 L 6174 771 L 6174 771 M 6174 771 L 6174 1331 L 5856 1219 L 6174 771 L 6174 1331 M 6174 1331 L 5379 1331 L 5538 1107 L 6174 1331 L 5379 1331 M 5379 1331 L 6174 1331 L 6015 1554 L 5379 1331 L 6651 1778 M 6651 1778 L 6174 1331 L 6015 1554 L 6651 1778 L 6174 1331 M 6174 1331 L 6651 1778 L 6810 1554 L 6174 1331 L 6174 1331 M 6174 1331 L 6969 1331 L 6969 1331 M 6810 1554 L 6174 1331 L 6969 1890 M 6651 1778 L 6969 1331 L 5379 1331 M 5379 1331 L 5856 1778 L 6015 1554 L 5379 1331 L 6651 1778 M 6651 1778 L 5856 1778 L 6015 1554 L 6651 1778 L 5856 1778 M 5856 1778 L 6651 1778 L 6492 2002 L 5856 1778 L 5856 1778 M 5856 1778 L 6333 2226 L 6492 2002 L 5856 1778 L 6333 2226 M 6333 2226 L 6969 1890 L 6969 1890 M 6651 1778 L 6333 2226 L 6969 2823 M 6810 2674 L 6969 2654 L 6969 2290 M 6810 2674 L 6969 2654 L 6810 2674 M 6810 2674 L 6969 2290 L 6969 2145 M 6683 2181 L 6810 2674 L 6810 2674 M 6810 2674 L 6333 2226 L 6683 2181 L 6810 2674 L 6333 2226 M 6333 2226 L 6969 1890 L 6969 2145 M 6333 2226 L stroke grestore end showpage %%Trailer EndOfTheIncludedPostscriptMagicCookie \closepsdump % Here's the Postscript for jfig2.ps: \message{Writing file jfig2.ps} \psdump{jfig2.ps}%!PS-Adobe-3.0 EPSF-3.0 %%Creator: Adobe Illustrator(TM) 3.0.1. %%For: () () %%Title: (/d1/grad/strauss/Penrose6.ai) %%CreationDate: (6/15/94) (16:04) %%BoundingBox: -46 175 389 646 %%DocumentProcessColors: Black %%DocumentSuppliedResources: procset Adobe_packedarray 2.0 0 %%+ procset Adobe_cmykcolor 1.1 0 %%+ procset Adobe_cshow 1.1 0 %%+ procset Adobe_customcolor 1.0 0 %%+ procset Adobe_IllustratorA_AI3 1.0 1 %AI3_ColorUsage: Black&White %AI3_TemplateBox: 306 396 306 396 %AI3_TileBox: 30 31 582 761 %AI3_DocumentPreview: Header %%Template: %%PageOrigin:30 31 %%AI3_PaperRect:0 792 612 0 %%AI3_Margin:30 31 30 31 %%EndComments %%BeginProlog %%BeginResource: procset Adobe_packedarray 2.0 0 %%Title: (Packed Array Operators) %%Version: 2.0 %%CreationDate: (8/2/90) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) userdict /Adobe_packedarray 5 dict dup begin put /initialize % - initialize - { /packedarray where { pop } { Adobe_packedarray begin Adobe_packedarray { dup xcheck { bind } if userdict 3 1 roll put } forall end } ifelse } def /terminate % - terminate - { } def /packedarray % arguments count packedarray array { array astore readonly } def /setpacking % boolean setpacking - { pop } def /currentpacking % - setpacking boolean { false } def currentdict readonly pop end %%EndResource Adobe_packedarray /initialize get exec %%BeginResource: procset Adobe_cmykcolor 1.1 0 %%Title: (CMYK Color Operators) %%Version: 1.1 %%CreationDate: (1/23/89) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_cmykcolor 4 dict dup begin put /initialize % - initialize - { /setcmykcolor where { pop } { userdict /Adobe_cmykcolor_vars 2 dict dup begin put /_setrgbcolor /setrgbcolor load def /_currentrgbcolor /currentrgbcolor load def Adobe_cmykcolor begin Adobe_cmykcolor { dup xcheck { bind } if pop pop } forall end end Adobe_cmykcolor begin } ifelse } def /terminate % - terminate - { currentdict Adobe_cmykcolor eq { end } if } def /setcmykcolor % cyan magenta yellow black setcmykcolor - { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat Adobe_cmykcolor_vars /_setrgbcolor get exec pop } def /currentcmykcolor % - currentcmykcolor cyan magenta yellow black { Adobe_cmykcolor_vars /_currentrgbcolor get exec 3 { 1 sub neg 3 1 roll } repeat 0 } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_cshow 1.1 0 %%Title: (cshow Operator) %%Version: 1.1 %%CreationDate: (1/23/89) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_cshow 3 dict dup begin put /initialize % - initialize - { /cshow where { pop } { userdict /Adobe_cshow_vars 1 dict dup begin put /_cshow % - _cshow proc {} def Adobe_cshow begin Adobe_cshow { dup xcheck { bind } if userdict 3 1 roll put } forall end end } ifelse } def /terminate % - terminate - { } def /cshow % proc string cshow - { exch Adobe_cshow_vars exch /_cshow exch put { 0 0 Adobe_cshow_vars /_cshow get exec } forall } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_customcolor 1.0 0 %%Title: (Custom Color Operators) %%Version: 1.0 %%CreationDate: (5/9/88) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_customcolor 5 dict dup begin put /initialize % - initialize - { /setcustomcolor where { pop } { Adobe_customcolor begin Adobe_customcolor { dup xcheck { bind } if pop pop } forall end Adobe_customcolor begin } ifelse } def /terminate % - terminate - { currentdict Adobe_customcolor eq { end } if } def /findcmykcustomcolor % cyan magenta yellow black name findcmykcustomcolor object { 5 packedarray } def /setcustomcolor % object tint setcustomcolor - { exch aload pop pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } def /setoverprint % boolean setoverprint - { pop } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_IllustratorA_AI3 1.0 1 %%Title: (Adobe Illustrator (R) Version 3.0 Abbreviated Prolog) %%Version: 1.0 %%CreationDate: (7/22/89) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_IllustratorA_AI3 61 dict dup begin put % initialization /initialize % - initialize - { % 47 vars, but leave slack of 10 entries for custom Postscript fragments userdict /Adobe_IllustratorA_AI3_vars 57 dict dup begin put % paint operands /_lp /none def /_pf {} def /_ps {} def /_psf {} def /_pss {} def /_pjsf {} def /_pjss {} def /_pola 0 def /_doClip 0 def % paint operators /cf currentflat def % - cf flatness % typography operands /_tm matrix def /_renderStart [/e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0] def /_renderEnd [null null null null /i1 /i1 /i1 /i1] def /_render -1 def /_rise 0 def /_ax 0 def % x character spacing (_ax, _ay, _cx, _cy follows awidthshow naming convention) /_ay 0 def % y character spacing /_cx 0 def % x word spacing /_cy 0 def % y word spacing /_leading [0 0] def /_ctm matrix def /_mtx matrix def /_sp 16#020 def /_hyphen (-) def /_fScl 0 def /_cnt 0 def /_hs 1 def /_nativeEncoding 0 def /_useNativeEncoding 0 def /_tempEncode 0 def /_pntr 0 def /_tDict 2 dict def % typography operators /Tx {} def /Tj {} def % compound path operators /CRender {} def % printing /_AI3_savepage {} def % color operands /_gf null def /_cf 4 array def /_if null def /_of false def /_fc {} def /_gs null def /_cs 4 array def /_is null def /_os false def /_sc {} def /_i null def Adobe_IllustratorA_AI3 begin Adobe_IllustratorA_AI3 { dup xcheck { bind } if pop pop } forall end end Adobe_IllustratorA_AI3 begin Adobe_IllustratorA_AI3_vars begin newpath } def /terminate % - terminate - { end end } def % definition operators /_ % - _ null null def /ddef % key value ddef - { Adobe_IllustratorA_AI3_vars 3 1 roll put } def /xput % key value literal xput - { dup load dup length exch maxlength eq { dup dup load dup length 2 mul dict copy def } if load begin def end } def /npop % integer npop - { { pop } repeat } def % marking operators /sw % ax ay string sw x y { dup length exch stringwidth exch 5 -1 roll 3 index 1 sub mul add 4 1 roll 3 1 roll 1 sub mul add } def /swj % cx cy fillchar ax ay string swj x y { dup 4 1 roll dup length exch stringwidth exch 5 -1 roll 3 index 1 sub mul add 4 1 roll 3 1 roll 1 sub mul add 6 2 roll /_cnt 0 ddef {1 index eq {/_cnt _cnt 1 add ddef} if} forall pop exch _cnt mul exch _cnt mul 2 index add 4 1 roll 2 index add 4 1 roll pop pop } def /ss % ax ay string matrix ss - { 4 1 roll { % matrix ax ay char 0 0 {proc} - 2 npop (0) exch 2 copy 0 exch put pop gsave false charpath currentpoint 4 index setmatrix stroke grestore moveto 2 copy rmoveto } exch cshow 3 npop } def /jss % cx cy fillchar ax ay string matrix jss - { 4 1 roll { % cx cy fillchar matrix ax ay char 0 0 {proc} - 2 npop (0) exch 2 copy 0 exch put gsave _sp eq { exch 6 index 6 index 6 index 5 -1 roll widthshow currentpoint } { false charpath currentpoint 4 index setmatrix stroke }ifelse grestore moveto 2 copy rmoveto } exch cshow 6 npop } def % path operators /sp % ax ay string sp - { { 2 npop (0) exch 2 copy 0 exch put pop false charpath 2 copy rmoveto } exch cshow 2 npop } def /jsp % cx cy fillchar ax ay string jsp - { { % cx cy fillchar ax ay char 0 0 {proc} - 2 npop (0) exch 2 copy 0 exch put _sp eq { exch 5 index 5 index 5 index 5 -1 roll widthshow } { false charpath }ifelse 2 copy rmoveto } exch cshow 5 npop } def % path construction operators /pl % x y pl x y { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } def /setstrokeadjust where { pop true setstrokeadjust /c % x1 y1 x2 y2 x3 y3 c - { curveto } def /C /c load def /v % x2 y2 x3 y3 v - { currentpoint 6 2 roll curveto } def /V /v load def /y % x1 y1 x2 y2 y - { 2 copy curveto } def /Y /y load def /l % x y l - { lineto } def /L /l load def /m % x y m - { moveto } def } {%else /c { pl curveto } def /C /c load def /v { currentpoint 6 2 roll pl curveto } def /V /v load def /y { pl 2 copy curveto } def /Y /y load def /l { pl lineto } def /L /l load def /m { pl moveto } def }ifelse % graphic state operators /d % array phase d - { setdash } def /cf {} def % - cf flatness /i % flatness i - { dup 0 eq { pop cf } if setflat } def /j % linejoin j - { setlinejoin } def /J % linecap J - { setlinecap } def /M % miterlimit M - { setmiterlimit } def /w % linewidth w - { setlinewidth } def % path painting operators /H % - H - {} def /h % - h - { closepath } def /N % - N - { _pola 0 eq { _doClip 1 eq {clip /_doClip 0 ddef} if newpath } { /CRender {N} ddef }ifelse } def /n % - n - {N} def /F % - F - { _pola 0 eq { _doClip 1 eq { gsave _pf grestore clip newpath /_lp /none ddef _fc /_doClip 0 ddef } { _pf }ifelse } { /CRender {F} ddef }ifelse } def /f % - f - { closepath F } def /S % - S - { _pola 0 eq { _doClip 1 eq { gsave _ps grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { _ps }ifelse } { /CRender {S} ddef }ifelse } def /s % - s - { closepath S } def /B % - B - { _pola 0 eq { _doClip 1 eq % F clears _doClip gsave F grestore { gsave S grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { S }ifelse } { /CRender {B} ddef }ifelse } def /b % - b - { closepath B } def /W % - W - { /_doClip 1 ddef } def /* % - [string] * - { count 0 ne { dup type (stringtype) eq {pop} if } if _pola 0 eq {newpath} if } def % group operators /u % - u - {} def /U % - U - {} def /q % - q - { _pola 0 eq {gsave} if } def /Q % - Q - { _pola 0 eq {grestore} if } def /*u % - *u - { _pola 1 add /_pola exch ddef } def /*U % - *U - { _pola 1 sub /_pola exch ddef _pola 0 eq {CRender} if } def /D % polarized D - {pop} def /*w % - *w - {} def /*W % - *W - {} def % place operators /` % matrix llx lly urx ury string ` - { /_i save ddef 6 1 roll 4 npop concat userdict begin /showpage {} def false setoverprint pop } def /~ % - ~ - { end _i restore } def % color operators /O % flag O - { 0 ne /_of exch ddef /_lp /none ddef } def /R % flag R - { 0 ne /_os exch ddef /_lp /none ddef } def /g % gray g - { /_gf exch ddef /_fc { _lp /fill ne { _of setoverprint _gf setgray /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /G % gray G - { /_gs exch ddef /_sc { _lp /stroke ne { _os setoverprint _gs setgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /k % cyan magenta yellow black k - { _cf astore pop /_fc { _lp /fill ne { _of setoverprint _cf aload pop setcmykcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /K % cyan magenta yellow black K - { _cs astore pop /_sc { _lp /stroke ne { _os setoverprint _cs aload pop setcmykcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /x % cyan magenta yellow black name gray x - { /_gf exch ddef findcmykcustomcolor /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /X % cyan magenta yellow black name gray X - { /_gs exch ddef findcmykcustomcolor /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def % locked object operator /A % value A - { pop } def currentdict readonly pop end setpacking % annotate page operator /annotatepage { } def %%EndResource %AI3-Grid.0 18 18 3 0 0 0 3 %%EndProlog %%BeginSetup Adobe_cmykcolor /initialize get exec Adobe_cshow /initialize get exec Adobe_customcolor /initialize get exec Adobe_IllustratorA_AI3 /initialize get exec %%EndSetup 0 A u u u u 0 R 0 G 0 i 0 J 0 j 1 w 4 M []0 d %AI3_Note: 0 D 103.8711 412.8662 m 134.8572 390.3529 L 103.8706 367.8406 L 111.1857 390.3537 L 103.8706 412.8666 L 103.8711 412.8662 L s U u 65.5686 367.8405 m 34.5839 390.3542 L 22.7471 353.9286 L 46.4184 353.9279 L 65.5689 367.8411 L 65.5686 367.8405 L s U u 84.7177 308.9012 m 115.7044 331.4135 L 84.7182 353.9268 L 77.4031 331.4137 L 84.7181 308.9008 L 84.7177 308.9012 L s U u 84.7197 353.9272 m 115.7044 331.4135 L 127.5412 367.8391 L 103.8699 367.8398 L 84.7194 353.9266 L 84.7197 353.9272 L s U u 46.4183 353.9272 m 84.7197 353.9272 L 72.8838 390.3536 L 65.5686 367.8405 L 46.4178 353.9271 L 46.4183 353.9272 L s U u 111.1856 390.3527 m 72.8849 390.3538 L 84.7197 353.9272 L 103.8706 367.8406 L 111.1855 390.3533 L 111.1856 390.3527 L s U u 84.7197 353.9272 m 46.4189 353.9283 L 58.2537 317.5017 L 77.4046 331.4151 L 84.7196 353.9278 L 84.7197 353.9272 L s U u 103.8685 294.9884 m 65.5678 294.9895 L 77.4046 331.4151 L 84.7189 308.9021 L 103.8691 294.9883 L 103.8685 294.9884 L s U U u s U U u u u 1 w 127.5397 367.8398 m 115.7026 331.4149 L 154.0028 331.4132 L 146.6889 353.926 L 127.5391 367.8399 L 127.5397 367.8398 L s U u 103.8682 367.8407 m 134.8548 390.3523 L 146.6889 353.926 L 127.5388 367.8401 L 103.8677 367.8404 L 103.8682 367.8407 L s U u 158.5257 390.3513 m 196.8266 390.3507 L 184.9913 426.7769 L 177.676 404.2642 L 158.5251 390.3512 L 158.5257 390.3513 L s U u 134.8548 390.3523 m 146.6889 353.926 L 177.6755 376.4375 L 158.5253 390.3517 L 134.8543 390.352 L 134.8548 390.3523 L s U u 177.6759 404.2634 m 146.692 426.7772 L 134.8548 390.3523 L 158.5257 390.3513 L 177.6762 404.264 L 177.6759 404.2634 L s U U u s U U u u u 1 w 77.4019 258.5626 m 65.5666 294.989 L 103.8672 294.9884 L 84.7166 281.0748 L 77.402 258.562 L 77.4019 258.5626 L s U u 134.8538 272.4756 m 146.6877 236.0498 L 177.6739 258.561 L 158.524 272.475 L 134.8533 272.4753 L 134.8538 272.4756 L s U u 154.0052 331.4132 m 115.7046 331.4138 L 127.5398 294.9875 L 146.6905 308.9011 L 154.0051 331.4139 L 154.0052 331.4132 L s U u 127.5384 294.9881 m 115.7046 331.4138 L 84.7184 308.9027 L 103.8683 294.9887 L 127.539 294.9883 L 127.5384 294.9881 L s U u 158.5245 272.4755 m 127.5384 294.9881 L 115.7032 258.5619 L 134.8538 272.4756 L 158.525 272.4752 L 158.5245 272.4755 L s U u 84.7173 281.0756 m 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repeat 0 } def currentdict readonly pop end setpacking currentpacking true setpacking userdict /Adobe_cshow 3 dict dup begin put /initialize % - initialize - { /cshow where { pop } { userdict /Adobe_cshow_vars 1 dict dup begin put /_cshow % - _cshow proc {} def Adobe_cshow begin Adobe_cshow { dup xcheck { bind } if userdict 3 1 roll put } forall end end } ifelse } def /terminate % - terminate - { } def /cshow % proc string cshow - { exch Adobe_cshow_vars exch /_cshow exch put { 0 0 Adobe_cshow_vars /_cshow get exec } forall } def currentdict readonly pop end setpacking currentpacking true setpacking userdict /Adobe_customcolor 5 dict dup begin put /initialize % - initialize - { /setcustomcolor where { pop } { Adobe_customcolor begin Adobe_customcolor { dup xcheck { bind } if pop pop } forall end Adobe_customcolor begin } ifelse } def /terminate % - terminate - { currentdict Adobe_customcolor eq { end } if } def /findcmykcustomcolor % cyan magenta yellow black name findcmykcustomcolor object { 5 packedarray } def /setcustomcolor % object tint setcustomcolor - { exch aload pop pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } def /setoverprint % boolean setoverprint - { pop } def currentdict readonly pop end setpacking currentpacking true setpacking userdict /Adobe_IllustratorA_AI3 61 dict dup begin put % initialization /initialize % - initialize - { % 47 vars, but leave slack of 10 entries for custom Postscript fragments userdict /Adobe_IllustratorA_AI3_vars 57 dict dup begin put % paint operands /_lp /none def /_pf {} def /_ps {} def /_psf {} def /_pss {} def /_pjsf {} def /_pjss {} def /_pola 0 def /_doClip 0 def % paint operators /cf currentflat def % - cf flatness % typography operands /_tm matrix def /_renderStart [/e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0] def /_renderEnd [null null null null /i1 /i1 /i1 /i1] def /_render -1 def /_rise 0 def /_ax 0 def % x character spacing (_ax, _ay, _cx, _cy follows awidthshow naming convention) /_ay 0 def % y 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6 index 6 index 5 -1 roll widthshow currentpoint } { false charpath currentpoint 4 index setmatrix stroke }ifelse grestore moveto 2 copy rmoveto } exch cshow 6 npop } def % path operators /sp % ax ay string sp - { { 2 npop (0) exch 2 copy 0 exch put pop false charpath 2 copy rmoveto } exch cshow 2 npop } def /jsp % cx cy fillchar ax ay string jsp - { { % cx cy fillchar ax ay char 0 0 {proc} - 2 npop (0) exch 2 copy 0 exch put _sp eq { exch 5 index 5 index 5 index 5 -1 roll widthshow } { false charpath }ifelse 2 copy rmoveto } exch cshow 5 npop } def % path construction operators /pl % x y pl x y { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } def /setstrokeadjust where { pop true setstrokeadjust /c % x1 y1 x2 y2 x3 y3 c - { curveto } def /C /c load def /v % x2 y2 x3 y3 v - { currentpoint 6 2 roll curveto } def /V /v load def /y % x1 y1 x2 y2 y - { 2 copy curveto } def /Y /y load def /l % x y l - { lineto } def /L /l load def /m % x y m - { moveto } def } {%else /c { pl curveto } def /C /c load def /v { currentpoint 6 2 roll pl curveto } def /V /v load def /y { pl 2 copy curveto } def /Y /y load def /l { pl lineto } def /L /l load def /m { pl moveto } def }ifelse % graphic state operators /d % array phase d - { setdash } def /cf {} def % - cf flatness /i % flatness i - { dup 0 eq { pop cf } if setflat } def /j % linejoin j - { setlinejoin } def /J % linecap J - { setlinecap } def /M % miterlimit M - { setmiterlimit } def /w % linewidth w - { setlinewidth } def % path painting operators /H % - H - {} def /h % - h - { closepath } def /N % - N - { _pola 0 eq { _doClip 1 eq {clip /_doClip 0 ddef} if newpath } { /CRender {N} ddef }ifelse } def /n % - n - {N} def /F % - F - { _pola 0 eq { _doClip 1 eq { gsave _pf grestore clip newpath /_lp /none ddef _fc /_doClip 0 ddef } { _pf }ifelse } { /CRender {F} ddef }ifelse } def /f % - f - { closepath F } def /S % - S - { _pola 0 eq { _doClip 1 eq { gsave _ps grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { _ps }ifelse } { /CRender {S} ddef }ifelse } def /s % - s - { closepath S } def /B % - B - { _pola 0 eq { _doClip 1 eq % F clears _doClip gsave F grestore { gsave S grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { S }ifelse } { /CRender {B} ddef }ifelse } def /b % - b - { closepath B } def /W % - W - { /_doClip 1 ddef } def /* % - [string] * - { count 0 ne { dup type (stringtype) eq {pop} if } if _pola 0 eq {newpath} if } def % group operators /u % - u - {} def /U % - U - {} def /q % - q - { _pola 0 eq {gsave} if } def /Q % - Q - { _pola 0 eq {grestore} if } def /*u % - *u - { _pola 1 add /_pola exch ddef } def /*U % - *U - { _pola 1 sub /_pola exch ddef _pola 0 eq {CRender} if } def /D % polarized D - {pop} def /*w % - *w - {} def /*W % - *W - {} def % place operators /` % matrix llx lly urx ury string ` - { /_i save ddef 6 1 roll 4 npop concat userdict begin /showpage {} def false setoverprint pop } def /~ % - ~ - { end _i restore } def % color operators /O % flag O - { 0 ne /_of exch ddef /_lp /none ddef } def /R % flag R - { 0 ne /_os exch ddef /_lp /none ddef } def /g % gray g - { /_gf exch ddef /_fc { _lp /fill ne { _of setoverprint _gf setgray /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /G % gray G - { /_gs exch ddef /_sc { _lp /stroke ne { _os setoverprint _gs setgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /k % cyan magenta yellow black k - { _cf astore pop /_fc { _lp /fill ne { _of setoverprint _cf aload pop setcmykcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /K % cyan magenta yellow black K - { _cs astore pop /_sc { _lp /stroke ne { _os setoverprint _cs aload pop setcmykcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /x % cyan magenta yellow black name gray x - { /_gf exch ddef findcmykcustomcolor /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /X % cyan magenta yellow black name gray X - { /_gs exch ddef findcmykcustomcolor /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def % locked object operator /A % value A - { pop } def currentdict readonly pop end setpacking % annotate page operator /annotatepage { } def %AI3-Grid.0 18 18 3 0 0 0 3 Adobe_cmykcolor /initialize get exec Adobe_cshow /initialize get exec Adobe_customcolor /initialize get exec Adobe_IllustratorA_AI3 /initialize get exec 0 A u u u u 0 R 0 G 0 i 0 J 0 j 3 w 4 M []0 d %AI3_Note: 0 D 330.6263 275.4581 m 277.0221 285.2985 l 223.4178 295.1389 l 340.4667 329.0623 l 330.6263 275.4581 L s U u 1 w 270.2364 308.7083 m 246.8271 301.9236 l 223.4178 295.1389 l 277.0211 285.2991 l 270.2364 308.7083 L s U u 323.8396 298.8685 m 300.4303 292.0838 l 277.0211 285.2991 l 330.6243 275.4592 l 323.8396 298.8685 L s U u 323.8401 298.8678 m 300.4306 292.0834 l 277.0211 285.2991 l 317.0558 322.2773 l 323.8401 298.8678 L s U U u u 3 w 233.2582 348.7432 m 286.8625 338.9027 l 340.4667 329.0623 l 223.4178 295.1389 l 233.2582 348.7432 L s U u 1 w 293.6482 315.4929 m 317.0574 322.2776 l 340.4667 329.0623 l 286.8635 338.9022 l 293.6482 315.4929 L s U u 240.0449 325.3328 m 263.4542 332.1175 l 286.8635 338.9022 l 233.2602 348.742 l 240.0449 325.3328 L s U u 240.0444 325.3335 m 263.4539 332.1178 l 286.8635 338.9022 l 246.8288 301.9239 l 240.0444 325.3335 L s U U u u 3 w 233.2582 348.7432 m 179.654 358.5836 l 126.0498 368.424 l 223.4178 295.1389 l 233.2582 348.7432 L s U u 1 w 164.9961 339.1103 m 145.5229 353.7671 l 126.0498 368.424 l 179.6529 358.5834 l 164.9961 339.1103 L s U u 218.5992 329.2697 m 199.126 343.9265 l 179.6529 358.5834 l 233.256 348.7428 l 218.5992 329.2697 L s U u 218.5999 329.2702 m 199.1264 343.9268 l 179.6529 358.5834 l 203.9433 309.7967 l 218.5999 329.2702 L s U U u u 3 w 330.6263 275.4581 m 277.0221 285.2985 l 223.4178 295.1389 l 320.7859 221.8539 l 330.6263 275.4581 L s U u 1 w 262.3641 265.8252 m 242.8909 280.4821 l 223.4178 295.1389 l 277.0209 285.2983 l 262.3641 265.8252 L s U u 315.9672 255.9846 m 296.494 270.6415 l 277.0209 285.2983 l 330.624 275.4578 l 315.9672 255.9846 L s U u 315.9679 255.9851 m 296.4944 270.6417 l 277.0209 285.2983 l 301.3113 236.5116 l 315.9679 255.9851 L s U U u u 3 w 340.4667 329.0623 m 330.6263 275.4581 l 320.7859 221.8539 l 394.0709 319.2219 l 340.4667 329.0623 L s U u 1 w 350.0996 260.8001 m 335.4427 241.327 l 320.7859 221.8539 l 330.6265 275.4569 l 350.0996 260.8001 L s U u 359.9402 314.4032 m 345.2833 294.9301 l 330.6265 275.4569 l 340.4671 329.0601 l 359.9402 314.4032 L s U u 359.9397 314.4039 m 345.2831 294.9304 l 330.6265 275.4569 l 379.4132 299.7473 l 359.9397 314.4039 L s U U U U u u u u 3 w 189.4944 412.1878 m 243.0987 402.3474 l 296.7029 392.507 l 179.654 358.5836 l 189.4944 412.1878 L s U u 1 w 249.8844 378.9376 m 273.2936 385.7223 l 296.7029 392.507 l 243.0997 402.3468 l 249.8844 378.9376 L s U u 196.2811 388.7774 m 219.6904 395.5621 l 243.0997 402.3468 l 189.4964 412.1867 l 196.2811 388.7774 L s U u 196.2806 388.7781 m 219.6901 395.5625 l 243.0997 402.3468 l 203.065 365.3686 l 196.2806 388.7781 L s U U u u 3 w 286.8625 338.9027 m 233.2582 348.7432 l 179.654 358.5836 l 296.7029 392.507 l 286.8625 338.9027 L s U u 1 w 226.4725 372.153 m 203.0633 365.3683 l 179.654 358.5836 l 233.2573 348.7437 l 226.4725 372.153 L s U u 280.0758 362.3131 m 256.6665 355.5284 l 233.2573 348.7437 l 286.8605 338.9039 l 280.0758 362.3131 L s U u 280.0763 362.3124 m 256.6668 355.5281 l 233.2573 348.7437 l 273.292 385.7219 l 280.0763 362.3124 L s U U u u 3 w 286.8625 338.9027 m 340.4667 329.0623 l 394.0709 319.2219 l 296.7029 392.507 l 286.8625 338.9027 L s U u 1 w 355.1247 348.5356 m 374.5978 333.8787 l 394.0709 319.2219 l 340.4679 329.0625 l 355.1247 348.5356 L s U u 301.5216 358.3762 m 320.9947 343.7193 l 340.4679 329.0625 l 286.8647 338.9031 l 301.5216 358.3762 L s U u 301.5209 358.3757 m 320.9944 343.7191 l 340.4679 329.0625 l 316.1775 377.8492 l 301.5209 358.3757 L s U U u u 3 w 189.4944 412.1878 m 243.0987 402.3474 l 296.7029 392.507 l 199.3349 465.792 l 189.4944 412.1878 L s U u 1 w 257.7567 421.8207 m 277.2298 407.1638 l 296.7029 392.507 l 243.0998 402.3475 l 257.7567 421.8207 L s U u 204.1536 431.6613 m 223.6267 417.0044 l 243.0998 402.3475 l 189.4967 412.1882 l 204.1536 431.6613 L s U u 204.1528 431.6608 m 223.6263 417.0042 l 243.0998 402.3475 l 218.8094 451.1343 l 204.1528 431.6608 L s U U u u 3 w 179.654 358.5836 m 189.4944 412.1878 l 199.3349 465.792 l 126.0498 368.424 l 179.654 358.5836 L s U u 1 w 170.0212 426.8458 m 184.678 446.3189 l 199.3349 465.792 l 189.4943 412.1889 l 170.0212 426.8458 L s U u 160.1806 373.2427 m 174.8374 392.7158 l 189.4943 412.1889 l 179.6537 358.5858 l 160.1806 373.2427 L s U u 160.181 373.242 m 174.8376 392.7155 l 189.4943 412.1889 l 140.7076 387.8986 l 160.181 373.242 L s U U U U u u u u 3 w 271.9997 197.5631 m 247.7092 246.3509 l 223.4187 295.1388 l 223.2118 173.2725 l 271.9997 197.5631 L s U u 1 w 223.3356 246.3933 m 223.3771 270.766 l 223.4187 295.1388 l 247.7083 246.3517 l 223.3356 246.3933 L s U u 247.6252 197.6062 m 247.6668 221.9789 l 247.7083 246.3517 l 271.998 197.5647 l 247.6252 197.6062 L s U u 247.6261 197.6059 m 247.6672 221.9788 l 247.7083 246.3517 l 223.2532 197.647 l 247.6261 197.6059 L s U U u u 3 w 174.6308 270.8483 m 198.9213 222.0604 l 223.2118 173.2725 l 223.4187 295.1388 l 174.6308 270.8483 L s U u 1 w 223.2949 222.0181 m 223.2533 197.6453 l 223.2118 173.2725 l 198.9221 222.0596 l 223.2949 222.0181 L s U u 199.0052 270.8051 m 198.9636 246.4324 l 198.9221 222.0596 l 174.6324 270.8467 l 199.0052 270.8051 L s U u 199.0044 270.8054 m 198.9632 246.4325 l 198.9221 222.0596 l 223.3773 270.7643 l 199.0044 270.8054 L s U U u u 3 w 174.6308 270.8483 m 150.3403 319.6361 l 126.0498 368.424 l 223.4187 295.1388 l 174.6308 270.8483 L s U u 1 w 164.9968 339.1108 m 145.5233 353.7674 l 126.0498 368.424 l 150.3401 319.6373 l 164.9968 339.1108 L s U u 189.2871 290.324 m 169.8136 304.9807 l 150.3401 319.6373 l 174.6305 270.8505 l 189.2871 290.324 L s U u 189.2869 290.3232 m 169.8135 304.9802 l 150.3401 319.6373 l 203.9439 309.7965 l 189.2869 290.3232 L s U U u u 3 w 271.9997 197.5631 m 247.7092 246.3509 l 223.4187 295.1388 l 320.7875 221.8535 l 271.9997 197.5631 L s U u 1 w 262.3656 265.8255 m 242.8921 280.4821 l 223.4187 295.1388 l 247.709 246.352 l 262.3656 265.8255 L s U u 286.656 217.0388 m 267.1825 231.6954 l 247.709 246.352 l 271.9994 197.5653 l 286.656 217.0388 L s U u 286.6557 217.038 m 267.1823 231.695 l 247.709 246.352 l 301.3128 236.5113 l 286.6557 217.038 L s U U u u 3 w 223.2118 173.2725 m 271.9997 197.5631 l 320.7875 221.8535 l 247.5023 124.4847 l 223.2118 173.2725 L s U u 1 w 291.4743 182.9066 m 306.1309 202.38 l 320.7875 221.8535 l 272.0008 197.5632 l 291.4743 182.9066 L s U u 242.6875 158.6162 m 257.3441 178.0897 l 272.0008 197.5632 l 223.214 173.2729 l 242.6875 158.6162 L s U u 242.6867 158.6165 m 257.3437 178.0898 l 272.0008 197.5632 l 262.16 143.9594 l 242.6867 158.6165 L s U U U U u u u u 3 w 150.5472 441.5023 m 126.2567 490.2902 l 101.9662 539.078 l 101.7593 417.2118 l 150.5472 441.5023 L s U u 1 w 101.8831 490.3325 m 101.9246 514.7053 l 101.9662 539.078 l 126.2558 490.291 l 101.8831 490.3325 L s U u 126.1728 441.5455 m 126.2143 465.9182 l 126.2558 490.291 l 150.5455 441.5039 l 126.1728 441.5455 L s U u 126.1736 441.5452 m 126.2147 465.9181 l 126.2558 490.291 l 101.8007 441.5863 l 126.1736 441.5452 L s U U u u 3 w 53.1783 514.7876 m 77.4688 465.9997 l 101.7593 417.2118 l 101.9662 539.078 l 53.1783 514.7876 L s U u 1 w 101.8424 465.9574 m 101.8009 441.5846 l 101.7593 417.2118 l 77.4696 465.9989 l 101.8424 465.9574 L s U u 77.5527 514.7445 m 77.5111 490.3717 l 77.4696 465.9989 l 53.1799 514.786 l 77.5527 514.7445 L s U u 77.5519 514.7447 m 77.5107 490.3718 l 77.4696 465.9989 l 101.9248 514.7036 l 77.5519 514.7447 L s U U u u 3 w 53.1783 514.7876 m 28.8878 563.5754 l 4.5973 612.3633 l 101.9662 539.078 l 53.1783 514.7876 L s U u 1 w 43.5443 583.05 m 24.0708 597.7067 l 4.5973 612.3633 l 28.8877 563.5766 l 43.5443 583.05 L s U u 67.8346 534.2633 m 48.3611 548.9199 l 28.8877 563.5766 l 53.178 514.7898 l 67.8346 534.2633 L s U u 67.8344 534.2625 m 48.361 548.9195 l 28.8877 563.5766 l 82.4914 553.7358 l 67.8344 534.2625 L s U U u u 3 w 150.5472 441.5023 m 126.2567 490.2902 l 101.9662 539.078 l 199.335 465.7929 l 150.5472 441.5023 L s U u 1 w 140.9131 509.7648 m 121.4396 524.4215 l 101.9662 539.078 l 126.2565 490.2913 l 140.9131 509.7648 L s U u 165.2035 460.9781 m 145.73 475.6347 l 126.2565 490.2913 l 150.5469 441.5046 l 165.2035 460.9781 L s U u 165.2032 460.9773 m 145.7299 475.6343 l 126.2565 490.2913 l 179.8603 480.4506 l 165.2032 460.9773 L s U U u u 3 w 101.7593 417.2118 m 150.5472 441.5023 l 199.335 465.7929 l 126.0498 368.424 l 101.7593 417.2118 L s U u 1 w 170.0218 426.8459 m 184.6784 446.3194 l 199.335 465.7929 l 150.5483 441.5025 l 170.0218 426.8459 L s U u 121.235 402.5555 m 135.8917 422.029 l 150.5483 441.5025 l 101.7615 417.2121 l 121.235 402.5555 L s U u 121.2342 402.5558 m 135.8912 422.0291 l 150.5483 441.5025 l 140.7076 387.8987 l 121.2342 402.5558 L s U U U U u u u u 3 w 418.3614 270.434 m 369.5736 246.1435 l 320.7857 221.853 l 442.6519 221.6462 l 418.3614 270.434 L s U u 1 w 369.5312 221.77 m 345.1585 221.8115 l 320.7857 221.853 l 369.5728 246.1427 l 369.5312 221.77 L s U u 418.3183 246.0596 m 393.9455 246.1012 l 369.5728 246.1427 l 418.3598 270.4324 l 418.3183 246.0596 L s U u 418.3186 246.0605 m 393.9457 246.1016 l 369.5728 246.1427 l 418.2775 221.6876 l 418.3186 246.0605 L s U U u u 3 w 345.0762 173.0652 m 393.8641 197.3557 l 442.6519 221.6462 l 320.7857 221.853 l 345.0762 173.0652 L s U u 1 w 393.9064 221.7292 m 418.2792 221.6877 l 442.6519 221.6462 l 393.8649 197.3565 l 393.9064 221.7292 L s U u 345.1194 197.4396 m 369.4921 197.398 l 393.8649 197.3565 l 345.0778 173.0668 l 345.1194 197.4396 L s U u 345.1191 197.4387 m 369.492 197.3976 l 393.8649 197.3565 l 345.1602 221.8116 l 345.1191 197.4387 L s U U u u 3 w 345.0762 173.0652 m 296.2884 148.7747 l 247.5005 124.4842 l 320.7857 221.853 l 345.0762 173.0652 L s U u 1 w 276.8137 163.4311 m 262.1571 143.9577 l 247.5005 124.4842 l 296.2872 148.7745 l 276.8137 163.4311 L s U u 325.6005 187.7215 m 310.9438 168.248 l 296.2872 148.7745 l 345.074 173.0649 l 325.6005 187.7215 L s U u 325.6013 187.7213 m 310.9443 168.2479 l 296.2872 148.7745 l 306.128 202.3783 l 325.6013 187.7213 L s U U u u 3 w 418.3614 270.434 m 369.5736 246.1435 l 320.7857 221.853 l 394.0709 319.2219 l 418.3614 270.434 L s U u 1 w 350.0989 260.8 m 335.4423 241.3265 l 320.7857 221.853 l 369.5724 246.1434 l 350.0989 260.8 L s U u 398.8857 285.0904 m 384.2291 265.6168 l 369.5724 246.1434 l 418.3592 270.4338 l 398.8857 285.0904 L s U u 398.8865 285.0901 m 384.2295 265.6167 l 369.5724 246.1434 l 379.4132 299.7471 l 398.8865 285.0901 L s U U u u 3 w 442.6519 221.6462 m 418.3614 270.434 l 394.0709 319.2219 l 491.4398 245.9367 l 442.6519 221.6462 L s U u 1 w 433.0179 289.9086 m 413.5444 304.5653 l 394.0709 319.2219 l 418.3613 270.4352 l 433.0179 289.9086 L s U u 457.3083 241.1219 m 437.8348 255.7785 l 418.3613 270.4352 l 442.6516 221.6484 l 457.3083 241.1219 L s U u 457.308 241.1211 m 437.8347 255.7781 l 418.3613 270.4352 l 471.965 260.5944 l 457.308 241.1211 L s U U U U u u u u 3 w 165.4108 582.8419 m 219.015 573.0015 l 272.6193 563.161 l 155.5704 529.2377 l 165.4108 582.8419 L s U u 1 w 225.8007 549.5916 m 249.21 556.3764 l 272.6193 563.161 l 219.016 573.0009 l 225.8007 549.5916 L s U u 172.1975 559.4315 m 195.6068 566.2162 l 219.016 573.0009 l 165.4128 582.8407 l 172.1975 559.4315 L s U u 172.197 559.4322 m 195.6065 566.2165 l 219.016 573.0009 l 178.9813 536.0227 l 172.197 559.4322 L s U U u u 3 w 262.7789 509.5568 m 209.1746 519.3973 l 155.5704 529.2377 l 272.6193 563.161 l 262.7789 509.5568 L s U u 1 w 202.3889 542.8071 m 178.9796 536.0224 l 155.5704 529.2377 l 209.1736 519.3978 l 202.3889 542.8071 L s U u 255.9922 532.9672 m 232.5829 526.1825 l 209.1736 519.3978 l 262.7769 509.558 l 255.9922 532.9672 L s U u 255.9927 532.9665 m 232.5832 526.1821 l 209.1736 519.3978 l 249.2083 556.376 l 255.9927 532.9665 L s U U u u 3 w 262.7789 509.5568 m 316.3831 499.7164 l 369.9873 489.876 l 272.6193 563.161 l 262.7789 509.5568 L s U u 1 w 331.041 519.1897 m 350.5142 504.5328 l 369.9873 489.876 l 316.3842 499.7166 l 331.041 519.1897 L s U u 277.438 529.0303 m 296.9111 514.3734 l 316.3842 499.7166 l 262.7811 509.5572 l 277.438 529.0303 L s U u 277.4372 529.0298 m 296.9107 514.3732 l 316.3842 499.7166 l 292.0938 548.5033 l 277.4372 529.0298 L s U U u u 3 w 165.4108 582.8419 m 219.015 573.0015 l 272.6193 563.161 l 175.2512 636.4461 l 165.4108 582.8419 L s U u 1 w 233.673 592.4748 m 253.1461 577.8179 l 272.6193 563.161 l 219.0162 573.0017 l 233.673 592.4748 L s U u 180.0699 602.3154 m 199.543 587.6585 l 219.0162 573.0017 l 165.4131 582.8422 l 180.0699 602.3154 L s U u 180.0692 602.3149 m 199.5427 587.6582 l 219.0162 573.0017 l 194.7258 621.7884 l 180.0692 602.3149 L s U U u u 3 w 155.5704 529.2377 m 165.4108 582.8419 l 175.2512 636.4461 l 101.9662 539.0781 l 155.5704 529.2377 L s U u 1 w 145.9375 597.4999 m 160.5944 616.973 l 175.2512 636.4461 l 165.4106 582.843 l 145.9375 597.4999 L s U u 136.0969 543.8968 m 150.7538 563.3699 l 165.4106 582.843 l 155.57 529.2399 l 136.0969 543.8968 L s U u 136.0974 543.8961 m 150.754 563.3695 l 165.4106 582.843 l 116.6239 558.5527 l 136.0974 543.8961 L s U U U U u u u u 3 w 306.5426 446.1122 m 252.9384 455.9526 l 199.3342 465.793 l 316.3831 499.7164 l 306.5426 446.1122 L s U u 1 w 246.1527 479.3624 m 222.7434 472.5777 l 199.3342 465.793 l 252.9374 455.9532 l 246.1527 479.3624 L s U u 299.7559 469.5226 m 276.3467 462.7379 l 252.9374 455.9532 l 306.5407 446.1133 l 299.7559 469.5226 L s U u 299.7565 469.5219 m 276.347 462.7375 l 252.9374 455.9532 l 292.9721 492.9314 l 299.7565 469.5219 L s U U u u 3 w 209.1746 519.3973 m 262.7789 509.5568 l 316.3831 499.7164 l 199.3342 465.793 l 209.1746 519.3973 L s U u 1 w 269.5645 486.147 m 292.9738 492.9317 l 316.3831 499.7164 l 262.7798 509.5563 l 269.5645 486.147 L s U u 215.9613 495.9869 m 239.3706 502.7716 l 262.7798 509.5563 l 209.1766 519.3961 l 215.9613 495.9869 L s U u 215.9608 495.9876 m 239.3703 502.7719 l 262.7798 509.5563 l 222.7451 472.5781 l 215.9608 495.9876 L s U U u u 3 w 209.1746 519.3973 m 155.5704 529.2377 l 101.9662 539.0781 l 199.3342 465.793 l 209.1746 519.3973 L s U u 1 w 140.9124 509.7644 m 121.4393 524.4212 l 101.9662 539.0781 l 155.5692 529.2375 l 140.9124 509.7644 L s U u 194.5155 499.9238 m 175.0424 514.5807 l 155.5692 529.2375 l 209.1724 519.3969 l 194.5155 499.9238 L s U u 194.5162 499.9243 m 175.0427 514.5809 l 155.5692 529.2375 l 179.8596 480.4508 l 194.5162 499.9243 L s U U u u 3 w 306.5426 446.1122 m 252.9384 455.9526 l 199.3342 465.793 l 296.7022 392.508 l 306.5426 446.1122 L s U u 1 w 238.2804 436.4793 m 218.8073 451.1362 l 199.3342 465.793 l 252.9373 455.9524 l 238.2804 436.4793 L s U u 291.8835 426.6387 m 272.4104 441.2956 l 252.9373 455.9524 l 306.5404 446.1118 l 291.8835 426.6387 L s U u 291.8843 426.6392 m 272.4108 441.2958 l 252.9373 455.9524 l 277.2277 407.1657 l 291.8843 426.6392 L s U U u u 3 w 316.3831 499.7164 m 306.5426 446.1122 l 296.7022 392.508 l 369.9873 489.876 l 316.3831 499.7164 L s U u 1 w 326.016 431.4542 m 311.3591 411.9811 l 296.7022 392.508 l 306.5428 446.1111 l 326.016 431.4542 L s U u 335.8565 485.0573 m 321.1997 465.5842 l 306.5428 446.1111 l 316.3834 499.7142 l 335.8565 485.0573 L s U u 335.8561 485.058 m 321.1994 465.5845 l 306.5428 446.1111 l 355.3295 470.4014 l 335.8561 485.058 L s U U U U u u u u 3 w 224.0374 660.7369 m 248.3279 611.9491 l 272.6184 563.1612 l 272.8253 685.0274 l 224.0374 660.7369 L s U u 1 w 272.7015 611.9067 m 272.66 587.534 l 272.6184 563.1612 l 248.3288 611.9483 l 272.7015 611.9067 L s U u 248.4118 660.6938 m 248.3703 636.321 l 248.3288 611.9483 l 224.0391 660.7353 l 248.4118 660.6938 L s U u 248.411 660.6941 m 248.3699 636.3212 l 248.3288 611.9483 l 272.7839 660.6529 l 248.411 660.6941 L s U U u u 3 w 321.4063 587.4517 m 297.1158 636.2396 l 272.8253 685.0274 l 272.6184 563.1612 l 321.4063 587.4517 L s U u 1 w 272.7422 636.2819 m 272.7838 660.6547 l 272.8253 685.0274 l 297.115 636.2404 l 272.7422 636.2819 L s U u 297.0319 587.4948 m 297.0735 611.8676 l 297.115 636.2404 l 321.4047 587.4533 l 297.0319 587.4948 L s U u 297.0327 587.4945 m 297.0739 611.8674 l 297.115 636.2404 l 272.6598 587.5357 l 297.0327 587.4945 L s U U u u 3 w 321.4063 587.4517 m 345.6968 538.6638 l 369.9873 489.876 l 272.6184 563.1612 l 321.4063 587.4517 L s U u 1 w 331.0403 519.1892 m 350.5138 504.5326 l 369.9873 489.876 l 345.697 538.6627 l 331.0403 519.1892 L s U u 306.75 567.976 m 326.2235 553.3193 l 345.697 538.6627 l 321.4066 587.4495 l 306.75 567.976 L s U u 306.7502 567.9768 m 326.2236 553.3198 l 345.697 538.6627 l 292.0932 548.5034 l 306.7502 567.9768 L s U U u u 3 w 224.0374 660.7369 m 248.3279 611.9491 l 272.6184 563.1612 l 175.2496 636.4464 l 224.0374 660.7369 L s U u 1 w 233.6715 592.4745 m 253.145 577.8179 l 272.6184 563.1612 l 248.3281 611.9479 l 233.6715 592.4745 L s U u 209.3811 641.2612 m 228.8546 626.6046 l 248.3281 611.9479 l 224.0377 660.7347 l 209.3811 641.2612 L s U u 209.3814 641.262 m 228.8547 626.605 l 248.3281 611.9479 l 194.7243 621.7886 l 209.3814 641.262 L s U U u u 3 w 272.8253 685.0274 m 224.0374 660.7369 l 175.2496 636.4464 l 248.5348 733.8153 l 272.8253 685.0274 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l 369.7806 368.0086 l 316.1768 377.8494 l 330.8339 397.3227 L s U U u u 3 w 394.2778 441.0881 m 345.4899 416.7976 l 296.7021 392.5072 l 369.9873 489.876 l 394.2778 441.0881 L s U u 1 w 326.0153 431.4541 m 311.3587 411.9806 l 296.7021 392.5072 l 345.4888 416.7975 l 326.0153 431.4541 L s U u 374.8021 455.7444 m 360.1454 436.271 l 345.4888 416.7975 l 394.2756 441.0878 l 374.8021 455.7444 L s U u 374.8029 455.7442 m 360.1459 436.2708 l 345.4888 416.7975 l 355.3295 470.4012 l 374.8029 455.7442 L s U U U U u u u u 3 w 77.6757 587.8659 m 126.4635 612.1565 l 175.2514 636.4469 l 53.3852 636.6538 l 77.6757 587.8659 L s U u 1 w 126.5059 636.53 m 150.8786 636.4885 l 175.2514 636.4469 l 126.4643 612.1573 l 126.5059 636.53 L s U u 77.7188 612.2404 m 102.0916 612.1988 l 126.4643 612.1573 l 77.6772 587.8676 l 77.7188 612.2404 L s U u 77.7185 612.2395 m 102.0914 612.1984 l 126.4643 612.1573 l 77.7596 636.6125 l 77.7185 612.2395 L s U U u u 3 w 150.9609 685.2348 m 102.173 660.9443 l 53.3852 636.6538 l 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151.1703 807.0998 l 165.8273 826.5731 L s U u 190.117 777.7857 m 170.6436 792.4427 l 151.1703 807.0998 l 175.4599 758.3123 l 190.117 777.7857 L s U u 190.1167 777.7848 m 170.6435 792.4423 l 151.1703 807.0998 l 204.7742 797.2581 l 190.1167 777.7848 L s U U u u 3 w 175.6691 880.1771 m 199.959 831.3885 l 224.2488 782.5999 l 126.8806 855.8872 l 175.6691 880.1771 L s U u 1 w 185.3021 811.914 m 204.7754 797.2569 l 224.2488 782.5999 l 199.9591 831.3874 l 185.3021 811.914 L s U u 161.0124 860.7014 m 180.4858 846.0444 l 199.9591 831.3874 l 175.6694 880.1748 l 161.0124 860.7014 L s U u 161.0126 860.7023 m 180.4859 846.0448 l 199.9591 831.3874 l 146.3552 841.229 l 161.0126 860.7023 L s U U u u 3 w 175.6691 880.1771 m 151.3793 928.9656 l 127.0895 977.7542 l 126.8806 855.8872 l 175.6691 880.1771 L s U u 1 w 127.0056 929.0083 m 127.0476 953.3813 l 127.0895 977.7542 l 151.3785 928.9664 l 127.0056 929.0083 L s U u 151.2946 880.2206 m 151.3365 904.5935 l 151.3785 928.9664 l 175.6675 880.1786 l 151.2946 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957.8653 L s U u 331.8733 1006.652 m 351.3468 991.9954 l 370.8203 977.3388 l 346.5299 1026.1255 l 331.8733 1006.652 L s U u 331.8735 1006.6529 m 351.3469 991.9958 l 370.8203 977.3388 l 317.2165 987.1795 l 331.8735 1006.6529 L s U U u u 3 w 395.3175 1050.4183 m 346.5296 1026.1278 l 297.7418 1001.8373 l 371.027 1099.2061 l 395.3175 1050.4183 L s U u 1 w 327.055 1040.7843 m 312.3984 1021.3108 l 297.7418 1001.8373 l 346.5285 1026.1276 l 327.055 1040.7843 L s U u 375.8418 1065.0746 m 361.1851 1045.6011 l 346.5285 1026.1276 l 395.3152 1050.418 l 375.8418 1065.0746 L s U u 375.8426 1065.0743 m 361.1855 1045.601 l 346.5285 1026.1276 l 356.3692 1079.7314 l 375.8426 1065.0743 L s U U U U u u u u 3 w 467.9821 782.1885 m 492.2726 733.4006 l 516.5631 684.6128 l 516.77 806.479 l 467.9821 782.1885 L s U u 1 w 516.6462 733.3583 m 516.6047 708.9855 l 516.5631 684.6128 l 492.2734 733.3999 l 516.6462 733.3583 L s U u 492.3565 782.1454 m 492.315 757.7726 l 492.2734 733.3999 l 467.9838 782.1869 l 492.3565 782.1454 L s U u 492.3557 782.1457 m 492.3145 757.7727 l 492.2734 733.3999 l 516.7286 782.1045 l 492.3557 782.1457 L s U U u u 3 w 565.351 708.9033 m 541.0605 757.6911 l 516.77 806.479 l 516.5631 684.6128 l 565.351 708.9033 L s U u 1 w 516.6869 757.7335 m 516.7284 782.1062 l 516.77 806.479 l 541.0597 757.6919 l 516.6869 757.7335 L s U u 540.9766 708.9464 m 541.0181 733.3192 l 541.0597 757.6919 l 565.3493 708.9049 l 540.9766 708.9464 L s U u 540.9774 708.9461 m 541.0185 733.319 l 541.0597 757.6919 l 516.6045 708.9872 l 540.9774 708.9461 L s U U u u 3 w 565.351 708.9033 m 589.6415 660.1154 l 613.932 611.3275 l 516.5631 684.6128 l 565.351 708.9033 L s U u 1 w 574.985 640.6408 m 594.4585 625.9842 l 613.932 611.3275 l 589.6416 660.1143 l 574.985 640.6408 L s U u 550.6947 689.4275 m 570.1681 674.7709 l 589.6416 660.1143 l 565.3513 708.901 l 550.6947 689.4275 L s U u 550.6949 689.4283 m 570.1683 674.7713 l 589.6416 660.1143 l 536.0379 669.955 l 550.6949 689.4283 L s U U u u 3 w 467.9821 782.1885 m 492.2726 733.4006 l 516.5631 684.6128 l 419.1943 757.898 l 467.9821 782.1885 L s U u 1 w 477.6161 713.926 m 497.0896 699.2694 l 516.5631 684.6128 l 492.2728 733.3995 l 477.6161 713.926 L s U u 453.3258 762.7127 m 472.7993 748.0561 l 492.2728 733.3995 l 467.9824 782.1862 l 453.3258 762.7127 L s U u 453.326 762.7136 m 472.7994 748.0565 l 492.2728 733.3995 l 438.669 743.2402 l 453.326 762.7136 L s U U u u 3 w 516.77 806.479 m 467.9821 782.1885 l 419.1943 757.898 l 492.4795 855.2669 l 516.77 806.479 L s U u 1 w 448.5075 796.845 m 433.8509 777.3715 l 419.1943 757.898 l 467.981 782.1883 l 448.5075 796.845 L s U u 497.2942 821.1353 m 482.6376 801.6618 l 467.981 782.1883 l 516.7677 806.4787 l 497.2942 821.1353 L s U u 497.2951 821.1351 m 482.638 801.6617 l 467.981 782.1883 l 477.8217 835.7921 l 497.2951 821.1351 L s U U U U u u u u 3 w 200.1678 953.2568 m 248.9557 977.5473 l 297.7436 1001.8378 l 175.8774 1002.0447 l 200.1678 953.2568 L s U u 1 w 248.998 1001.9209 m 273.3708 1001.8793 l 297.7436 1001.8378 l 248.9565 977.5481 l 248.998 1001.9209 L s U u 200.211 977.6312 m 224.5838 977.5897 l 248.9565 977.5481 l 200.1694 953.2584 l 200.211 977.6312 L s U u 200.2107 977.6304 m 224.5836 977.5892 l 248.9565 977.5481 l 200.2518 1002.0033 l 200.2107 977.6304 L s U U u u 3 w 273.453 1050.6257 m 224.6652 1026.3352 l 175.8774 1002.0447 l 297.7436 1001.8378 l 273.453 1050.6257 L s U u 1 w 224.6229 1001.9616 m 200.2501 1002.0031 l 175.8774 1002.0447 l 224.6644 1026.3343 l 224.6229 1001.9616 L s U u 273.4099 1026.2513 m 249.0372 1026.2928 l 224.6644 1026.3343 l 273.4515 1050.624 l 273.4099 1026.2513 L s U u 273.4102 1026.2521 m 249.0373 1026.2932 l 224.6644 1026.3343 l 273.3691 1001.8792 l 273.4102 1026.2521 L s U U u u 3 w 273.453 1050.6257 m 322.2409 1074.9161 l 371.0288 1099.2066 l 297.7436 1001.8378 l 273.453 1050.6257 L s U u 1 w 341.7156 1060.2597 m 356.3722 1079.7332 l 371.0288 1099.2066 l 322.242 1074.9163 l 341.7156 1060.2597 L s U u 292.9288 1035.9693 m 307.5854 1055.4428 l 322.242 1074.9163 l 273.4553 1050.626 l 292.9288 1035.9693 L s U u 292.928 1035.9696 m 307.585 1055.4429 l 322.242 1074.9163 l 312.4013 1021.3126 l 292.928 1035.9696 L s U U u u 3 w 200.1678 953.2568 m 248.9557 977.5473 l 297.7436 1001.8378 l 224.4583 904.4689 l 200.1678 953.2568 L s U u 1 w 268.4303 962.8908 m 283.0869 982.3643 l 297.7436 1001.8378 l 248.9568 977.5475 l 268.4303 962.8908 L s U u 219.6436 938.6005 m 234.3002 958.074 l 248.9568 977.5475 l 200.1701 953.2571 l 219.6436 938.6005 L s U u 219.6427 938.6007 m 234.2998 958.0741 l 248.9568 977.5475 l 239.1161 923.9437 l 219.6427 938.6007 L s U U u u 3 w 175.8774 1002.0447 m 200.1678 953.2568 l 224.4583 904.4689 l 127.0895 977.7542 l 175.8774 1002.0447 L s U u 1 w 185.5114 933.7822 m 204.9849 919.1256 l 224.4583 904.4689 l 200.168 953.2557 l 185.5114 933.7822 L s U u 161.221 982.5689 m 180.6945 967.9123 l 200.168 953.2557 l 175.8776 1002.0424 l 161.221 982.5689 L s U u 161.2212 982.5698 m 180.6946 967.9127 l 200.168 953.2557 l 146.5642 963.0964 l 161.2212 982.5698 L s U U U U u u u u 3 w 453.1185 640.8489 m 399.5142 650.6894 l 345.91 660.5298 l 462.9589 694.4532 l 453.1185 640.8489 L s U u 1 w 392.7286 674.0992 m 369.3193 667.3145 l 345.91 660.5298 l 399.5132 650.6899 l 392.7286 674.0992 L s U u 446.3318 664.2593 m 422.9225 657.4746 l 399.5132 650.6899 l 453.1165 640.8501 l 446.3318 664.2593 L s U u 446.3323 664.2586 m 422.9228 657.4743 l 399.5132 650.6899 l 439.5479 687.6681 l 446.3323 664.2586 L s U U u u 3 w 355.7504 714.134 m 409.3547 704.2936 l 462.9589 694.4532 l 345.91 660.5298 l 355.7504 714.134 L s U u 1 w 416.1404 680.8838 m 439.5496 687.6685 l 462.9589 694.4532 l 409.3556 704.293 l 416.1404 680.8838 L s U u 362.5371 690.7236 m 385.9464 697.5083 l 409.3556 704.293 l 355.7524 714.1329 l 362.5371 690.7236 L s U u 362.5366 690.7243 m 385.9461 697.5087 l 409.3556 704.293 l 369.3209 667.3148 l 362.5366 690.7243 L s U U u u 3 w 355.7504 714.134 m 302.1462 723.9744 l 248.542 733.8148 l 345.91 660.5298 l 355.7504 714.134 L s U u 1 w 287.4882 704.5011 m 268.0151 719.158 l 248.542 733.8148 l 302.1451 723.9743 l 287.4882 704.5011 L s U u 341.0913 694.6605 m 321.6182 709.3174 l 302.1451 723.9743 l 355.7482 714.1337 l 341.0913 694.6605 L s U u 341.0921 694.661 m 321.6186 709.3176 l 302.1451 723.9743 l 326.4354 675.1875 l 341.0921 694.661 L s U U u u 3 w 453.1185 640.8489 m 399.5142 650.6894 l 345.91 660.5298 l 443.278 587.2447 l 453.1185 640.8489 L s U u 1 w 384.8562 631.2161 m 365.3831 645.8729 l 345.91 660.5298 l 399.5131 650.6892 l 384.8562 631.2161 L s U u 438.4594 621.3755 m 418.9862 636.0323 l 399.5131 650.6892 l 453.1162 640.8486 l 438.4594 621.3755 L s U u 438.4601 621.3759 m 418.9866 636.0326 l 399.5131 650.6892 l 423.8035 601.9024 l 438.4601 621.3759 L s U U u u 3 w 462.9589 694.4532 m 453.1185 640.8489 l 443.278 587.2447 l 516.5631 684.6127 l 462.9589 694.4532 L s U u 1 w 472.5917 626.191 m 457.9349 606.7178 l 443.278 587.2447 l 453.1186 640.8478 l 472.5917 626.191 L s U u 482.4324 679.7941 m 467.7755 660.3209 l 453.1186 640.8478 l 462.9592 694.4509 l 482.4324 679.7941 L s U u 482.4319 679.7948 m 467.7753 660.3213 l 453.1186 640.8478 l 501.9054 665.1382 l 482.4319 679.7948 L s U U U U u u u u 3 w 311.9866 777.5787 m 365.5908 767.7382 l 419.1951 757.8978 l 302.1462 723.9744 l 311.9866 777.5787 L s U u 1 w 372.3766 744.3284 m 395.7858 751.1131 l 419.1951 757.8978 l 365.5918 767.7377 l 372.3766 744.3284 L s U u 318.7733 754.1683 m 342.1826 760.953 l 365.5918 767.7377 l 311.9886 777.5776 l 318.7733 754.1683 L s U u 318.7728 754.169 m 342.1823 760.9533 l 365.5918 767.7377 l 325.5571 730.7594 l 318.7728 754.169 L s U U u u 3 w 409.3547 704.2936 m 355.7504 714.134 l 302.1462 723.9744 l 419.1951 757.8978 l 409.3547 704.2936 L s U u 1 w 348.9647 737.5438 m 325.5555 730.7591 l 302.1462 723.9744 l 355.7494 714.1346 l 348.9647 737.5438 L s U u 402.568 727.704 m 379.1587 720.9193 l 355.7494 714.1346 l 409.3527 704.2947 l 402.568 727.704 L s U u 402.5685 727.7033 m 379.1589 720.9189 l 355.7494 714.1346 l 395.7841 751.1128 l 402.5685 727.7033 L s U U u u 3 w 409.3547 704.2936 m 462.9589 694.4532 l 516.5631 684.6127 l 419.1951 757.8978 l 409.3547 704.2936 L s U u 1 w 477.6168 713.9265 m 497.09 699.2696 l 516.5631 684.6127 l 462.96 694.4533 l 477.6168 713.9265 L s U u 424.0138 723.767 m 443.4869 709.1102 l 462.96 694.4533 l 409.3569 704.2939 l 424.0138 723.767 L s U u 424.013 723.7666 m 443.4865 709.11 l 462.96 694.4533 l 438.6696 743.2401 l 424.013 723.7666 L s U U u u 3 w 311.9866 777.5787 m 365.5908 767.7382 l 419.1951 757.8978 l 321.827 831.1829 l 311.9866 777.5787 L s U u 1 w 380.2488 787.2115 m 399.722 772.5547 l 419.1951 757.8978 l 365.592 767.7384 l 380.2488 787.2115 L s U u 326.6457 797.0521 m 346.1188 782.3953 l 365.592 767.7384 l 311.9889 777.579 l 326.6457 797.0521 L s U u 326.645 797.0516 m 346.1185 782.395 l 365.592 767.7384 l 341.3016 816.5251 l 326.645 797.0516 L s U U u u 3 w 302.1462 723.9744 m 311.9866 777.5787 l 321.827 831.1829 l 248.542 733.8148 l 302.1462 723.9744 L s U u 1 w 292.5133 792.2366 m 307.1702 811.7098 l 321.827 831.1829 l 311.9865 777.5798 l 292.5133 792.2366 L s U u 282.6727 738.6335 m 297.3296 758.1067 l 311.9865 777.5798 l 302.1459 723.9767 l 282.6727 738.6335 L s U u 282.6732 738.6328 m 297.3298 758.1063 l 311.9865 777.5798 l 263.1997 753.2894 l 282.6732 738.6328 L s U U U U u u u u 3 w 394.4918 562.9539 m 370.2014 611.7418 l 345.9108 660.5296 l 345.7039 538.6634 l 394.4918 562.9539 L s U u 1 w 345.8278 611.7841 m 345.8693 636.1569 l 345.9108 660.5296 l 370.2005 611.7425 l 345.8278 611.7841 L s U u 370.1174 562.997 m 370.159 587.3698 l 370.2005 611.7425 l 394.4902 562.9555 l 370.1174 562.997 L s U u 370.1183 562.9967 m 370.1594 587.3697 l 370.2005 611.7425 l 345.7454 563.0379 l 370.1183 562.9967 L s U U u u 3 w 297.123 636.2391 m 321.4135 587.4512 l 345.7039 538.6634 l 345.9108 660.5296 l 297.123 636.2391 L s U u 1 w 345.787 587.409 m 345.7455 563.0362 l 345.7039 538.6634 l 321.4143 587.4505 l 345.787 587.409 L s U u 321.4974 636.196 m 321.4558 611.8232 l 321.4143 587.4505 l 297.1246 636.2375 l 321.4974 636.196 L s U u 321.4965 636.1963 m 321.4554 611.8234 l 321.4143 587.4505 l 345.8694 636.1551 l 321.4965 636.1963 L s U U u u 3 w 297.123 636.2391 m 272.8325 685.027 l 248.542 733.8148 l 345.9108 660.5296 l 297.123 636.2391 L s U u 1 w 287.4889 704.5016 m 268.0154 719.1582 l 248.542 733.8148 l 272.8323 685.0281 l 287.4889 704.5016 L s U u 311.7793 655.7149 m 292.3058 670.3715 l 272.8323 685.0281 l 297.1227 636.2414 l 311.7793 655.7149 L s U u 311.779 655.714 m 292.3057 670.3711 l 272.8323 685.0281 l 326.4361 675.1874 l 311.779 655.714 L s U U u u 3 w 394.4918 562.9539 m 370.2014 611.7418 l 345.9108 660.5296 l 443.2797 587.2444 l 394.4918 562.9539 L s U u 1 w 384.8578 631.2164 m 365.3843 645.873 l 345.9108 660.5296 l 370.2012 611.7429 l 384.8578 631.2164 L s U u 409.1481 582.4297 m 389.6746 597.0863 l 370.2012 611.7429 l 394.4915 562.9562 l 409.1481 582.4297 L s U u 409.1479 582.4288 m 389.6745 597.0858 l 370.2012 611.7429 l 423.8049 601.9022 l 409.1479 582.4288 L s U U u u 3 w 345.7039 538.6634 m 394.4918 562.9539 l 443.2797 587.2444 l 369.9944 489.8756 l 345.7039 538.6634 L s U u 1 w 413.9664 548.2974 m 428.6231 567.7709 l 443.2797 587.2444 l 394.493 562.9541 l 413.9664 548.2974 L s U u 365.1797 524.0071 m 379.8363 543.4806 l 394.493 562.9541 l 345.7062 538.6637 l 365.1797 524.0071 L s U u 365.1789 524.0073 m 379.8359 543.4807 l 394.493 562.9541 l 384.6522 509.3503 l 365.1789 524.0073 L s U U U U u u u u 3 w 273.0393 806.8932 m 248.7488 855.6811 l 224.4583 904.4689 l 224.2515 782.6027 l 273.0393 806.8932 L s U u 1 w 224.3753 855.7234 m 224.4168 880.0962 l 224.4583 904.4689 l 248.748 855.6819 l 224.3753 855.7234 L s U u 248.6649 806.9363 m 248.7065 831.3091 l 248.748 855.6819 l 273.0377 806.8948 l 248.6649 806.9363 L s U u 248.6658 806.936 m 248.7069 831.309 l 248.748 855.6819 l 224.2929 806.9772 l 248.6658 806.936 L s U U u u 3 w 175.6705 880.1784 m 199.961 831.3906 l 224.2515 782.6027 l 224.4583 904.4689 l 175.6705 880.1784 L s U u 1 w 224.3346 831.3482 m 224.293 806.9755 l 224.2515 782.6027 l 199.9618 831.3898 l 224.3346 831.3482 L s U u 200.0448 880.1353 m 200.0033 855.7625 l 199.9618 831.3898 l 175.6721 880.1768 l 200.0448 880.1353 L s U u 200.0441 880.1356 m 200.0029 855.7627 l 199.9618 831.3898 l 224.417 880.0944 l 200.0441 880.1356 L s U U u u 3 w 175.6705 880.1784 m 151.38 928.9663 l 127.0895 977.7542 l 224.4583 904.4689 l 175.6705 880.1784 L s U u 1 w 166.0364 948.4409 m 146.563 963.0975 l 127.0895 977.7542 l 151.3798 928.9674 l 166.0364 948.4409 L s U u 190.3268 899.6542 m 170.8533 914.3108 l 151.3798 928.9674 l 175.6702 880.1807 l 190.3268 899.6542 L s U u 190.3266 899.6533 m 170.8532 914.3104 l 151.3798 928.9674 l 204.9836 919.1267 l 190.3266 899.6533 L s U U u u 3 w 273.0393 806.8932 m 248.7488 855.6811 l 224.4583 904.4689 l 321.8272 831.1837 l 273.0393 806.8932 L s U u 1 w 263.4053 875.1557 m 243.9318 889.8123 l 224.4583 904.4689 l 248.7487 855.6822 l 263.4053 875.1557 L s U u 287.6956 826.3689 m 268.2222 841.0256 l 248.7487 855.6822 l 273.039 806.8955 l 287.6956 826.3689 L s U u 287.6954 826.3681 m 268.2221 841.0252 l 248.7487 855.6822 l 302.3524 845.8415 l 287.6954 826.3681 L s U U u u 3 w 224.2515 782.6027 m 273.0393 806.8932 l 321.8272 831.1837 l 248.542 733.8148 l 224.2515 782.6027 L s U u 1 w 292.514 792.2367 m 307.1706 811.7102 l 321.8272 831.1837 l 273.0404 806.8934 l 292.514 792.2367 L s U u 243.7272 767.9464 m 258.3839 787.4199 l 273.0404 806.8934 l 224.2537 782.603 l 243.7272 767.9464 L s U u 243.7264 767.9466 m 258.3834 787.42 l 273.0404 806.8934 l 263.1997 753.2896 l 243.7264 767.9466 L s U U U U u u u u 3 w 540.8536 635.8249 m 492.0657 611.5344 l 443.2779 587.2439 l 565.1441 587.037 l 540.8536 635.8249 L s U u 1 w 492.0234 587.1608 m 467.6506 587.2023 l 443.2779 587.2439 l 492.0649 611.5336 l 492.0234 587.1608 L s U u 540.8105 611.4505 m 516.4377 611.492 l 492.0649 611.5336 l 540.852 635.8232 l 540.8105 611.4505 L s U u 540.8108 611.4513 m 516.4379 611.4924 l 492.0649 611.5336 l 540.7696 587.0784 l 540.8108 611.4513 L s U U u u 3 w 467.5684 538.456 m 516.3562 562.7465 l 565.1441 587.037 l 443.2779 587.2439 l 467.5684 538.456 L s U u 1 w 516.3986 587.1201 m 540.7713 587.0786 l 565.1441 587.037 l 516.357 562.7473 l 516.3986 587.1201 L s U u 467.6115 562.8304 m 491.9843 562.7889 l 516.357 562.7473 l 467.57 538.4577 l 467.6115 562.8304 L s U u 467.6112 562.8296 m 491.9841 562.7884 l 516.357 562.7473 l 467.6524 587.2025 l 467.6112 562.8296 L s U U u u 3 w 467.5684 538.456 m 418.7805 514.1655 l 369.9927 489.875 l 443.2779 587.2439 l 467.5684 538.456 L s U u 1 w 399.3059 528.822 m 384.6493 509.3485 l 369.9927 489.875 l 418.7794 514.1654 l 399.3059 528.822 L s U u 448.0927 553.1123 m 433.436 533.6389 l 418.7794 514.1654 l 467.5661 538.4557 l 448.0927 553.1123 L s U u 448.0935 553.1121 m 433.4365 533.6388 l 418.7794 514.1654 l 428.6201 567.7691 l 448.0935 553.1121 L s U U u u 3 w 540.8536 635.8249 m 492.0657 611.5344 l 443.2779 587.2439 l 516.5631 684.6127 l 540.8536 635.8249 L s U u 1 w 472.5911 626.1909 m 457.9345 606.7174 l 443.2779 587.2439 l 492.0646 611.5342 l 472.5911 626.1909 L s U u 521.3779 650.4812 m 506.7212 631.0077 l 492.0646 611.5342 l 540.8514 635.8246 l 521.3779 650.4812 L s U u 521.3787 650.481 m 506.7217 631.0076 l 492.0646 611.5342 l 501.9054 665.138 l 521.3787 650.481 L s U U u u 3 w 565.1441 587.037 m 540.8536 635.8249 l 516.5631 684.6127 l 613.932 611.3275 l 565.1441 587.037 L s U u 1 w 555.5101 655.2995 m 536.0366 669.9561 l 516.5631 684.6127 l 540.8535 635.826 l 555.5101 655.2995 L s U u 579.8004 606.5128 m 560.327 621.1694 l 540.8535 635.826 l 565.1438 587.0393 l 579.8004 606.5128 L s U u 579.8002 606.5119 m 560.3268 621.169 l 540.8535 635.826 l 594.4572 625.9853 l 579.8002 606.5119 L s U U U U u u u u 3 w 540.5616 465.2124 m 516.105 416.5077 l 491.6483 367.8029 l 589.2664 440.7558 l 540.5616 465.2124 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m 515.9372 319.0134 l 515.8956 294.6407 l 540.3515 343.3446 l 515.9787 343.3862 L s U u 515.9795 343.3865 m 515.9376 319.0136 l 515.8956 294.6407 l 491.6066 343.4284 l 515.9795 343.3865 L s U U u u 3 w 540.5616 465.2124 m 516.105 416.5077 l 491.6483 367.8029 l 491.8569 489.6691 l 540.5616 465.2124 L s U u 1 w 491.7314 416.5484 m 491.6899 392.1757 l 491.6483 367.8029 l 516.1042 416.5069 l 491.7314 416.5484 L s U u 516.1873 465.2524 m 516.1457 440.8796 l 516.1042 416.5069 l 540.56 465.2108 l 516.1873 465.2524 L s U u 516.1881 465.2527 m 516.1461 440.8798 l 516.1042 416.5069 l 491.8152 465.2946 l 516.1881 465.2527 L s U U u u 3 w 589.2664 440.7558 m 540.5616 465.2124 l 491.8569 489.6691 l 613.723 489.4606 l 589.2664 440.7558 L s U u 1 w 540.6024 489.586 m 516.2296 489.6276 l 491.8569 489.6691 l 540.5608 465.2133 l 540.6024 489.586 L s U u 589.3064 465.1302 m 564.9336 465.1717 l 540.5608 465.2133 l 589.2648 440.7574 l 589.3064 465.1302 L s U u 589.3067 465.1294 m 564.9337 465.1713 l 540.5608 465.2133 l 589.3486 489.5023 l 589.3067 465.1294 L s U U U U u u u u 3 w 564.6012 270.1848 m 589.0579 318.8896 l 613.5145 367.5944 l 515.8965 294.6415 l 564.6012 270.1848 L s U u 1 w 574.4679 338.414 m 593.9912 353.0042 l 613.5145 367.5944 l 589.058 318.8907 l 574.4679 338.414 L s U u 550.0114 289.7104 m 569.5347 304.3006 l 589.058 318.8907 l 564.6016 270.1871 l 550.0114 289.7104 L s U u 550.0116 289.7096 m 569.5348 304.3001 l 589.058 318.8907 l 535.421 309.2328 l 550.0116 289.7096 L s U U u u 3 w 564.8097 392.051 m 540.3531 343.3462 l 515.8965 294.6415 l 613.5145 367.5944 l 564.8097 392.051 L s U u 1 w 554.9431 323.8218 m 535.4198 309.2316 l 515.8965 294.6415 l 540.353 343.3451 l 554.9431 323.8218 L s U u 579.3996 372.5254 m 559.8763 357.9353 l 540.353 343.3451 l 564.8095 392.0488 l 579.3996 372.5254 L s U u 579.3994 372.5263 m 559.8762 357.9357 l 540.353 343.3451 l 593.9899 353.0031 l 579.3994 372.5263 L s U U u u 3 w 564.8097 392.051 m 589.2664 440.7558 l 613.723 489.4606 l 613.5145 367.5944 l 564.8097 392.051 L s U u 1 w 613.64 440.715 m 613.6815 465.0878 l 613.723 489.4606 l 589.2672 440.7566 l 613.64 440.715 L s U u 589.1841 392.011 m 589.2257 416.3838 l 589.2672 440.7566 l 564.8114 392.0526 l 589.1841 392.011 L s U u 589.1833 392.0108 m 589.2253 416.3837 l 589.2672 440.7566 l 613.5562 391.9688 l 589.1833 392.0108 L s U U u u 3 w 564.6012 270.1848 m 589.0579 318.8896 l 613.5145 367.5944 l 613.306 245.7282 l 564.6012 270.1848 L s U u 1 w 613.4315 318.8488 m 613.473 343.2216 l 613.5145 367.5944 l 589.0587 318.8904 l 613.4315 318.8488 L s U u 588.9756 270.1449 m 589.0172 294.5176 l 589.0587 318.8904 l 564.6029 270.1864 l 588.9756 270.1449 L s U u 588.9748 270.1446 m 589.0167 294.5175 l 589.0587 318.8904 l 613.3477 270.1026 l 588.9748 270.1446 L s U U u u 3 w 515.8965 294.6415 m 564.6012 270.1848 l 613.306 245.7282 l 491.4398 245.9367 l 515.8965 294.6415 L s U u 1 w 564.5605 245.8112 m 588.9332 245.7697 l 613.306 245.7282 l 564.602 270.184 l 564.5605 245.8112 L s U u 515.8565 270.2671 m 540.2293 270.2255 l 564.602 270.184 l 515.898 294.6398 l 515.8565 270.2671 L s U u 515.8562 270.2679 m 540.2292 270.226 l 564.602 270.184 l 515.8143 245.895 l 515.8562 270.2679 L s U U U U u u u u 3 w 443.069 465.3808 m 467.3589 416.5922 l 491.6487 367.8036 l 394.2805 441.0909 l 443.069 465.3808 L s U u 1 w 452.702 397.1177 m 472.1753 382.4607 l 491.6487 367.8036 l 467.359 416.5911 l 452.702 397.1177 L s U u 428.4123 445.9051 m 447.8856 431.2481 l 467.359 416.5911 l 443.0693 465.3785 l 428.4123 445.9051 L s U u 428.4125 445.906 m 447.8858 431.2485 l 467.359 416.5911 l 413.7551 426.4327 l 428.4125 445.906 L s U U u u 3 w 442.8601 343.5138 m 418.5703 392.3024 l 394.2805 441.0909 l 491.6487 367.8036 l 442.8601 343.5138 L s U u 1 w 433.2272 411.7769 m 413.7538 426.4339 l 394.2805 441.0909 l 418.5702 392.3035 l 433.2272 411.7769 L s U u 457.5169 362.9894 m 438.0435 377.6465 l 418.5702 392.3035 l 442.8598 343.5161 l 457.5169 362.9894 L s U u 457.5166 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l 517.0192 952.7148 L s U U u u 3 w 541.6013 1074.5407 m 517.1446 1025.8359 l 492.688 977.1312 l 492.8965 1098.9974 l 541.6013 1074.5407 L s U u 1 w 492.771 1025.8767 m 492.7295 1001.5039 l 492.688 977.1312 l 517.1438 1025.8352 l 492.771 1025.8767 L s U u 517.2269 1074.5807 m 517.1853 1050.2079 l 517.1438 1025.8352 l 541.5996 1074.5391 l 517.2269 1074.5807 L s U u 517.2277 1074.581 m 517.1858 1050.2081 l 517.1438 1025.8352 l 492.8548 1074.6229 l 517.2277 1074.581 L s U U u u 3 w 590.306 1050.0841 m 541.6013 1074.5407 l 492.8965 1098.9974 l 614.7627 1098.7888 l 590.306 1050.0841 L s U u 1 w 541.642 1098.9143 m 517.2693 1098.9559 l 492.8965 1098.9974 l 541.6005 1074.5416 l 541.642 1098.9143 L s U u 590.346 1074.4585 m 565.9732 1074.5 l 541.6005 1074.5416 l 590.3045 1050.0857 l 590.346 1074.4585 L s U u 590.3463 1074.4577 m 565.9734 1074.4996 l 541.6005 1074.5416 l 590.3883 1098.8306 l 590.3463 1074.4577 L s U U U U u u u u 3 w 565.6408 879.5131 m 590.0975 928.2179 l 614.5542 976.9226 l 516.9361 903.9698 l 565.6408 879.5131 L s U u 1 w 575.5075 947.7423 m 595.0308 962.3325 l 614.5542 976.9226 l 590.0977 928.219 l 575.5075 947.7423 L s U u 551.051 899.0387 m 570.5743 913.6288 l 590.0977 928.219 l 565.6412 879.5153 l 551.051 899.0387 L s U u 551.0513 899.0379 m 570.5745 913.6284 l 590.0977 928.219 l 536.4607 918.5611 l 551.0513 899.0379 L s U U u u 3 w 565.8494 1001.3793 m 541.3927 952.6745 l 516.9361 903.9698 l 614.5542 976.9226 l 565.8494 1001.3793 L s U u 1 w 555.9828 933.1501 m 536.4594 918.5599 l 516.9361 903.9698 l 541.3926 952.6734 l 555.9828 933.1501 L s U u 580.4393 981.8537 m 560.9159 967.2635 l 541.3926 952.6734 l 565.8491 1001.377 l 580.4393 981.8537 L s U u 580.439 981.8546 m 560.9158 967.264 l 541.3926 952.6734 l 595.0296 962.3313 l 580.439 981.8546 L s U U u u 3 w 565.8494 1001.3793 m 590.306 1050.0841 l 614.7627 1098.7888 l 614.5542 976.9226 l 565.8494 1001.3793 L s U u 1 w 614.6796 1050.0433 m 614.7212 1074.4161 l 614.7627 1098.7888 l 590.3069 1050.0849 l 614.6796 1050.0433 L s U u 590.2238 1001.3393 m 590.2653 1025.7121 l 590.3069 1050.0849 l 565.851 1001.3809 l 590.2238 1001.3393 L s U u 590.223 1001.3391 m 590.2649 1025.712 l 590.3069 1050.0849 l 614.5959 1001.2971 l 590.223 1001.3391 L s U U u u 3 w 565.6408 879.5131 m 590.0975 928.2179 l 614.5542 976.9226 l 614.3456 855.0564 l 565.6408 879.5131 L s U u 1 w 614.4711 928.1771 m 614.5126 952.5499 l 614.5542 976.9226 l 590.0983 928.2187 l 614.4711 928.1771 L s U u 590.0153 879.4731 m 590.0568 903.8459 l 590.0983 928.2187 l 565.6425 879.5147 l 590.0153 879.4731 L s U u 590.0144 879.4729 m 590.0564 903.8458 l 590.0983 928.2187 l 614.3873 879.4309 l 590.0144 879.4729 L s U U u u 3 w 516.9361 903.9698 m 565.6408 879.5131 l 614.3456 855.0564 l 492.4794 855.2649 l 516.9361 903.9698 L s U u 1 w 565.6001 855.1395 m 589.9729 855.098 l 614.3456 855.0564 l 565.6417 879.5123 l 565.6001 855.1395 L s U u 516.8962 879.5953 m 541.2689 879.5538 l 565.6417 879.5123 l 516.9377 903.9681 l 516.8962 879.5953 L s U u 516.8959 879.5962 m 541.2688 879.5542 l 565.6417 879.5123 l 516.8539 855.2233 l 516.8959 879.5962 L s U U U U u u u u 3 w 444.1087 1074.709 m 468.3985 1025.9205 l 492.6883 977.1319 l 395.3201 1050.4192 l 444.1087 1074.709 L s U u 1 w 453.7416 1006.446 m 473.215 991.7889 l 492.6883 977.1319 l 468.3986 1025.9194 l 453.7416 1006.446 L s U u 429.4519 1055.2334 m 448.9253 1040.5764 l 468.3986 1025.9194 l 444.109 1074.7068 l 429.4519 1055.2334 L s U u 429.4522 1055.2343 m 448.9254 1040.5768 l 468.3986 1025.9194 l 414.7947 1035.761 l 429.4522 1055.2343 L s U U u u 3 w 443.8998 952.8421 m 419.6099 1001.6307 l 395.3201 1050.4192 l 492.6883 977.1319 l 443.8998 952.8421 L s U u 1 w 434.2668 1021.1051 m 414.7935 1035.7622 l 395.3201 1050.4192 l 419.6098 1001.6318 l 434.2668 1021.1051 L s U u 458.5565 972.3177 m 439.0831 986.9748 l 419.6098 1001.6318 l 443.8995 952.8443 l 458.5565 972.3177 L s U u 458.5563 972.3169 m 439.083 986.9743 l 419.6098 1001.6318 l 473.2137 991.7901 l 458.5563 972.3169 L s U U u u 3 w 443.8998 952.8421 m 468.1896 904.0535 l 492.4794 855.2649 l 492.6883 977.1319 l 443.8998 952.8421 L s U u 1 w 492.5633 904.0108 m 492.5213 879.6379 l 492.4794 855.2649 l 468.1904 904.0527 l 492.5633 904.0108 L s U u 468.2743 952.7985 m 468.2323 928.4256 l 468.1904 904.0527 l 443.9014 952.8405 l 468.2743 952.7985 L s U u 468.2735 952.7988 m 468.2319 928.4258 l 468.1904 904.0527 l 492.6465 952.7573 l 468.2735 952.7988 L s U U u u 3 w 444.1087 1074.709 m 468.3985 1025.9205 l 492.6883 977.1319 l 492.8972 1098.9989 l 444.1087 1074.709 L s U u 1 w 492.7722 1025.8777 m 492.7303 1001.5048 l 492.6883 977.1319 l 468.3993 1025.9197 l 492.7722 1025.8777 L s U u 468.4832 1074.6655 m 468.4413 1050.2926 l 468.3993 1025.9197 l 444.1103 1074.7075 l 468.4832 1074.6655 L s U u 468.4824 1074.6658 m 468.4408 1050.2928 l 468.3993 1025.9197 l 492.8554 1074.6243 l 468.4824 1074.6658 L s U U u u 3 w 395.3201 1050.4192 m 444.1087 1074.709 l 492.8972 1098.9989 l 371.0303 1099.2078 l 395.3201 1050.4192 L s U u 1 w 444.1514 1099.0828 m 468.5243 1099.0408 l 492.8972 1098.9989 l 444.1095 1074.7098 l 444.1514 1099.0828 L s U u 395.3637 1074.7937 m 419.7366 1074.7518 l 444.1095 1074.7098 l 395.3217 1050.4208 l 395.3637 1074.7937 L s U u 395.3633 1074.7929 m 419.7364 1074.7514 l 444.1095 1074.7098 l 395.4049 1099.166 l 395.3633 1074.7929 L s U U U U u u u u 3 w 565.5578 830.7662 m 589.8477 781.9777 l 614.1375 733.1891 l 516.7693 806.4764 l 565.5578 830.7662 L s U u 1 w 575.1908 762.5032 m 594.6641 747.8462 l 614.1375 733.1891 l 589.8478 781.9765 l 575.1908 762.5032 L s U u 550.9011 811.2906 m 570.3744 796.6336 l 589.8478 781.9765 l 565.5581 830.764 l 550.9011 811.2906 L s U u 550.9013 811.2915 m 570.3746 796.634 l 589.8478 781.9765 l 536.2439 791.8182 l 550.9013 811.2915 L s U U u u 3 w 565.3489 708.8993 m 541.0591 757.6878 l 516.7693 806.4764 l 614.1375 733.1891 l 565.3489 708.8993 L s U u 1 w 555.716 777.1623 m 536.2426 791.8194 l 516.7693 806.4764 l 541.0589 757.689 l 555.716 777.1623 L s U u 580.0057 728.3749 m 560.5323 743.0319 l 541.0589 757.689 l 565.3486 708.9015 l 580.0057 728.3749 L s U u 580.0054 728.3741 m 560.5322 743.0315 l 541.0589 757.689 l 594.6629 747.8473 l 580.0054 728.3741 L s U U u u 3 w 565.3489 708.8993 m 589.6388 660.1107 l 613.9286 611.3221 l 614.1375 733.1891 l 565.3489 708.8993 L s U u 1 w 614.0125 660.068 m 613.9705 635.6951 l 613.9286 611.3221 l 589.6396 660.1099 l 614.0125 660.068 L s U u 589.7234 708.8557 m 589.6815 684.4828 l 589.6396 660.1099 l 565.3506 708.8977 l 589.7234 708.8557 L s U u 589.7226 708.856 m 589.6811 684.483 l 589.6396 660.1099 l 614.0957 708.8145 l 589.7226 708.856 L s U U u u 3 w 565.5578 830.7662 m 589.8477 781.9777 l 614.1375 733.1891 l 614.3464 855.0561 l 565.5578 830.7662 L s U u 1 w 614.2214 781.9349 m 614.1795 757.562 l 614.1375 733.1891 l 589.8484 781.9769 l 614.2214 781.9349 L s U u 589.9323 830.7227 m 589.8904 806.3498 l 589.8484 781.9769 l 565.5594 830.7647 l 589.9323 830.7227 L s U u 589.9315 830.723 m 589.89 806.3499 l 589.8484 781.9769 l 614.3046 830.6815 l 589.9315 830.723 L s U U u u 3 w 516.7693 806.4764 m 565.5578 830.7662 l 614.3464 855.0561 l 492.4794 855.2649 l 516.7693 806.4764 L s U u 1 w 565.6006 855.14 m 589.9735 855.098 l 614.3464 855.0561 l 565.5586 830.767 l 565.6006 855.14 L s U u 516.8128 830.8509 m 541.1857 830.809 l 565.5586 830.767 l 516.7709 806.478 l 516.8128 830.8509 L s U u 516.8125 830.8501 m 541.1856 830.8086 l 565.5586 830.767 l 516.854 855.2232 l 516.8125 830.8501 L s U U U U u u u u 3 w 590.4729 1147.5774 m 541.6843 1123.2876 l 492.8957 1098.9977 l 566.183 1196.366 l 590.4729 1147.5774 L s U u 1 w 522.2098 1137.9445 m 507.5528 1118.4711 l 492.8957 1098.9977 l 541.6832 1123.2874 l 522.2098 1137.9445 L s U u 570.9972 1162.2342 m 556.3402 1142.7608 l 541.6832 1123.2874 l 590.4706 1147.5772 l 570.9972 1162.2342 L s U u 570.9981 1162.2339 m 556.3406 1142.7607 l 541.6832 1123.2874 l 551.5248 1176.8914 l 570.9981 1162.2339 L 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1099.4133 l 200.4613 1123.8698 l 219.9846 1138.46 L s U u 171.281 1162.9165 m 185.8711 1143.3932 l 200.4613 1123.8698 l 151.7576 1148.3263 l 171.281 1162.9165 L s U u 171.2801 1162.9162 m 185.8707 1143.393 l 200.4613 1123.8698 l 190.8033 1177.5068 l 171.2801 1162.9162 L s U U u u 3 w 273.6216 1148.1181 m 224.9168 1172.5748 l 176.212 1197.0314 l 249.165 1099.4133 l 273.6216 1148.1181 L s U u 1 w 205.3924 1157.9848 m 190.8022 1177.5081 l 176.212 1197.0314 l 224.9157 1172.5749 l 205.3924 1157.9848 L s U u 254.096 1133.5282 m 239.5058 1153.0516 l 224.9157 1172.5749 l 273.6193 1148.1184 l 254.096 1133.5282 L s U u 254.0968 1133.5285 m 239.5063 1153.0517 l 224.9157 1172.5749 l 234.5737 1118.9379 l 254.0968 1133.5285 L s U U u u 3 w 273.6216 1148.1181 m 322.3264 1123.6614 l 371.0311 1099.2048 l 249.165 1099.4133 l 273.6216 1148.1181 L s U u 1 w 322.2856 1099.2879 m 346.6584 1099.2463 l 371.0311 1099.2048 l 322.3272 1123.6606 l 322.2856 1099.2879 L s U u 273.5816 1123.7437 m 297.9544 1123.7022 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-1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 94 464 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 134 464 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 54 464 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 174 504 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 54 504 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 94 504 m gs 1 -1 scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 134 504 m gs 1 -1 scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 174 424 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 94 424 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 134 424 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 54 424 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 174 224 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 54 224 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 94 224 m gs 1 -1 scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 129 224 m gs 1 -1 scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 174 304 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 94 304 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 134 304 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 54 304 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 174 344 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 54 344 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 94 344 m gs 1 -1 scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont 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findfont 12.00 scalefont setfont 454 224 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 494 224 m gs 1 -1 scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 414 304 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 454 304 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 494 304 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 374 304 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 374 344 m gs 1 -1 scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 414 344 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 454 344 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 414 264 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 454 264 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 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scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 174 144 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 54 184 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 94 184 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 134 184 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 174 184 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 54 64 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 94 64 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 54 104 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 94 104 m gs 1 -1 scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 134 64 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 174 64 m gs 1 -1 scale (D) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 134 104 m gs 1 -1 scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 174 104 m gs 1 -1 scale (C) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 615 383 m gs 1 -1 scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 614 224 m gs 1 -1 scale (A) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 615 544 m gs 1 -1 scale (B) col-1 show gr /Times-Roman findfont 12.00 scalefont setfont 614 584 m gs 1 -1 scale (A) col-1 show gr showpage $F2psEnd EndOfTheIncludedPostscriptMagicCookie \closepsdump % Here's the Postscript for Penrose6.ai: \message{Writing file Penrose6.ai} \psdump{Penrose6.ai}%!PS-Adobe-3.0 EPSF-3.0 %%Creator: Adobe Illustrator(TM) 3.0.1. %%For: () () %%Title: (/d1/grad/strauss/Penrose6.ai) %%CreationDate: (6/15/94) (16:04) %%BoundingBox: -46 175 389 646 %%DocumentProcessColors: Black %%DocumentSuppliedResources: procset Adobe_packedarray 2.0 0 %%+ procset Adobe_cmykcolor 1.1 0 %%+ procset Adobe_cshow 1.1 0 %%+ procset Adobe_customcolor 1.0 0 %%+ procset Adobe_IllustratorA_AI3 1.0 1 %AI3_ColorUsage: Black&White %AI3_TemplateBox: 306 396 306 396 %AI3_TileBox: 30 31 582 761 %AI3_DocumentPreview: Header %%Template: %%PageOrigin:30 31 %%AI3_PaperRect:0 792 612 0 %%AI3_Margin:30 31 30 31 %%EndComments %%BeginProlog %%BeginResource: procset Adobe_packedarray 2.0 0 %%Title: (Packed Array Operators) %%Version: 2.0 %%CreationDate: (8/2/90) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) userdict /Adobe_packedarray 5 dict dup begin put /initialize % - initialize - { /packedarray where { pop } { Adobe_packedarray begin Adobe_packedarray { dup xcheck { bind } if userdict 3 1 roll put } forall end } ifelse } def /terminate % - terminate - { } def /packedarray % arguments count packedarray array { array astore readonly } def /setpacking % boolean setpacking - { pop } def /currentpacking % - setpacking boolean { false } def currentdict readonly pop end %%EndResource Adobe_packedarray /initialize get exec %%BeginResource: procset Adobe_cmykcolor 1.1 0 %%Title: (CMYK Color Operators) %%Version: 1.1 %%CreationDate: (1/23/89) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_cmykcolor 4 dict dup begin put /initialize % - initialize - { /setcmykcolor where { pop } { userdict /Adobe_cmykcolor_vars 2 dict dup begin put /_setrgbcolor /setrgbcolor load def /_currentrgbcolor /currentrgbcolor load def Adobe_cmykcolor begin Adobe_cmykcolor { dup xcheck { bind } if pop pop } forall end end Adobe_cmykcolor begin } ifelse } def /terminate % - terminate - { currentdict Adobe_cmykcolor eq { end } if } def /setcmykcolor % cyan magenta yellow black setcmykcolor - { 1 sub 4 1 roll 3 { 3 index add neg dup 0 lt { pop 0 } if 3 1 roll } repeat Adobe_cmykcolor_vars /_setrgbcolor get exec pop } def /currentcmykcolor % - currentcmykcolor cyan magenta yellow black { Adobe_cmykcolor_vars /_currentrgbcolor get exec 3 { 1 sub neg 3 1 roll } repeat 0 } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_cshow 1.1 0 %%Title: (cshow Operator) %%Version: 1.1 %%CreationDate: (1/23/89) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_cshow 3 dict dup begin put /initialize % - initialize - { /cshow where { pop } { userdict /Adobe_cshow_vars 1 dict dup begin put /_cshow % - _cshow proc {} def Adobe_cshow begin Adobe_cshow { dup xcheck { bind } if userdict 3 1 roll put } forall end end } ifelse } def /terminate % - terminate - { } def /cshow % proc string cshow - { exch Adobe_cshow_vars exch /_cshow exch put { 0 0 Adobe_cshow_vars /_cshow get exec } forall } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_customcolor 1.0 0 %%Title: (Custom Color Operators) %%Version: 1.0 %%CreationDate: (5/9/88) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_customcolor 5 dict dup begin put /initialize % - initialize - { /setcustomcolor where { pop } { Adobe_customcolor begin Adobe_customcolor { dup xcheck { bind } if pop pop } forall end Adobe_customcolor begin } ifelse } def /terminate % - terminate - { currentdict Adobe_customcolor eq { end } if } def /findcmykcustomcolor % cyan magenta yellow black name findcmykcustomcolor object { 5 packedarray } def /setcustomcolor % object tint setcustomcolor - { exch aload pop pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } def /setoverprint % boolean setoverprint - { pop } def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_IllustratorA_AI3 1.0 1 %%Title: (Adobe Illustrator (R) Version 3.0 Abbreviated Prolog) %%Version: 1.0 %%CreationDate: (7/22/89) () %%Copyright: ((C) 1987-1990 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_IllustratorA_AI3 61 dict dup begin put % initialization /initialize % - initialize - { % 47 vars, but leave slack of 10 entries for custom Postscript fragments userdict /Adobe_IllustratorA_AI3_vars 57 dict dup begin put % paint operands /_lp /none def /_pf {} def /_ps {} def /_psf {} def /_pss {} def /_pjsf {} def /_pjss {} def /_pola 0 def /_doClip 0 def % paint operators /cf currentflat def % - cf flatness % typography operands /_tm matrix def /_renderStart [/e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0] def /_renderEnd [null null null null /i1 /i1 /i1 /i1] def /_render -1 def /_rise 0 def /_ax 0 def % x character spacing (_ax, _ay, _cx, _cy follows awidthshow naming convention) /_ay 0 def % y character spacing /_cx 0 def % x word spacing /_cy 0 def % y word spacing /_leading [0 0] def /_ctm matrix def /_mtx matrix def /_sp 16#020 def /_hyphen (-) def /_fScl 0 def /_cnt 0 def /_hs 1 def /_nativeEncoding 0 def /_useNativeEncoding 0 def /_tempEncode 0 def /_pntr 0 def /_tDict 2 dict def % typography operators /Tx {} def /Tj {} def % compound path operators /CRender {} def % printing /_AI3_savepage {} def % color operands /_gf null def /_cf 4 array def /_if null def /_of false def /_fc {} def /_gs null def /_cs 4 array def /_is null def /_os false def /_sc {} def /_i null def Adobe_IllustratorA_AI3 begin Adobe_IllustratorA_AI3 { dup xcheck { bind } if pop pop } forall end end Adobe_IllustratorA_AI3 begin Adobe_IllustratorA_AI3_vars begin newpath } def /terminate % - terminate - { end end } def % definition operators /_ % - _ null null def /ddef % key value ddef - { Adobe_IllustratorA_AI3_vars 3 1 roll put } def /xput % key value literal xput - { dup load dup length exch maxlength eq { dup dup load dup length 2 mul dict copy def } if load begin def end } def /npop % integer npop - { { pop } repeat } def % marking operators /sw % ax ay string sw x y { dup length exch stringwidth exch 5 -1 roll 3 index 1 sub mul add 4 1 roll 3 1 roll 1 sub mul add } def /swj % cx cy fillchar ax ay string swj x y { dup 4 1 roll dup length exch stringwidth exch 5 -1 roll 3 index 1 sub mul add 4 1 roll 3 1 roll 1 sub mul add 6 2 roll /_cnt 0 ddef {1 index eq {/_cnt _cnt 1 add ddef} if} forall pop exch _cnt mul exch _cnt mul 2 index add 4 1 roll 2 index add 4 1 roll pop pop } def /ss % ax ay string matrix ss - { 4 1 roll { % matrix ax ay char 0 0 {proc} - 2 npop (0) exch 2 copy 0 exch put pop gsave false charpath currentpoint 4 index setmatrix stroke grestore moveto 2 copy rmoveto } exch cshow 3 npop } def /jss % cx cy fillchar ax ay string matrix jss - { 4 1 roll { % cx cy fillchar matrix ax ay char 0 0 {proc} - 2 npop (0) exch 2 copy 0 exch put gsave _sp eq { exch 6 index 6 index 6 index 5 -1 roll widthshow currentpoint } { false charpath currentpoint 4 index setmatrix stroke }ifelse grestore moveto 2 copy rmoveto } exch cshow 6 npop } def % path operators /sp % ax ay string sp - { { 2 npop (0) exch 2 copy 0 exch put pop false charpath 2 copy rmoveto } exch cshow 2 npop } def /jsp % cx cy fillchar ax ay string jsp - { { % cx cy fillchar ax ay char 0 0 {proc} - 2 npop (0) exch 2 copy 0 exch put _sp eq { exch 5 index 5 index 5 index 5 -1 roll widthshow } { false charpath }ifelse 2 copy rmoveto } exch cshow 5 npop } def % path construction operators /pl % x y pl x y { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } def /setstrokeadjust where { pop true setstrokeadjust /c % x1 y1 x2 y2 x3 y3 c - { curveto } def /C /c load def /v % x2 y2 x3 y3 v - { currentpoint 6 2 roll curveto } def /V /v load def /y % x1 y1 x2 y2 y - { 2 copy curveto } def /Y /y load def /l % x y l - { lineto } def /L /l load def /m % x y m - { moveto } def } {%else /c { pl curveto } def /C /c load def /v { currentpoint 6 2 roll pl curveto } def /V /v load def /y { pl 2 copy curveto } def /Y /y load def /l { pl lineto } def /L /l load def /m { pl moveto } def }ifelse % graphic state operators /d % array phase d - { setdash } def /cf {} def % - cf flatness /i % flatness i - { dup 0 eq { pop cf } if setflat } def /j % linejoin j - { setlinejoin } def /J % linecap J - { setlinecap } def /M % miterlimit M - { setmiterlimit } def /w % linewidth w - { setlinewidth } def % path painting operators /H % - H - {} def /h % - h - { closepath } def /N % - N - { _pola 0 eq { _doClip 1 eq {clip /_doClip 0 ddef} if newpath } { /CRender {N} ddef }ifelse } def /n % - n - {N} def /F % - F - { _pola 0 eq { _doClip 1 eq { gsave _pf grestore clip newpath /_lp /none ddef _fc /_doClip 0 ddef } { _pf }ifelse } { /CRender {F} ddef }ifelse } def /f % - f - { closepath F } def /S % - S - { _pola 0 eq { _doClip 1 eq { gsave _ps grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { _ps }ifelse } { /CRender {S} ddef }ifelse } def /s % - s - { closepath S } def /B % - B - { _pola 0 eq { _doClip 1 eq % F clears _doClip gsave F grestore { gsave S grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { S }ifelse } { /CRender {B} ddef }ifelse } def /b % - b - { closepath B } def /W % - W - { /_doClip 1 ddef } def /* % - [string] * - { count 0 ne { dup type (stringtype) eq {pop} if } if _pola 0 eq {newpath} if } def % group operators /u % - u - {} def /U % - U - {} def /q % - q - { _pola 0 eq {gsave} if } def /Q % - Q - { _pola 0 eq {grestore} if } def /*u % - *u - { _pola 1 add /_pola exch ddef } def /*U % - *U - { _pola 1 sub /_pola exch ddef _pola 0 eq {CRender} if } def /D % polarized D - {pop} def /*w % - *w - {} def /*W % - *W - {} def % place operators /` % matrix llx lly urx ury string ` - { /_i save ddef 6 1 roll 4 npop concat userdict begin /showpage {} def false setoverprint pop } def /~ % - ~ - { end _i restore } def % color operators /O % flag O - { 0 ne /_of exch ddef /_lp /none ddef } def /R % flag R - { 0 ne /_os exch ddef /_lp /none ddef } def /g % gray g - { /_gf exch ddef /_fc { _lp /fill ne { _of setoverprint _gf setgray /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /G % gray G - { /_gs exch ddef /_sc { _lp /stroke ne { _os setoverprint _gs setgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /k % cyan magenta yellow black k - { _cf astore pop /_fc { _lp /fill ne { _of setoverprint _cf aload pop setcmykcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /K % cyan magenta yellow black K - { _cs astore pop /_sc { _lp /stroke ne { _os setoverprint _cs aload pop setcmykcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /x % cyan magenta yellow black name gray x - { /_gf exch ddef findcmykcustomcolor /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /X % cyan magenta yellow black name gray X - { /_gs exch ddef findcmykcustomcolor /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def % locked object operator /A % value A - { pop } def currentdict readonly pop end setpacking % annotate page operator /annotatepage { } def %%EndResource %AI3-Grid.0 18 18 3 0 0 0 3 %%EndProlog %%BeginSetup Adobe_cmykcolor /initialize get exec Adobe_cshow /initialize get exec Adobe_customcolor /initialize get exec Adobe_IllustratorA_AI3 /initialize get exec %%EndSetup 0 A u u u u 0 R 0 G 0 i 0 J 0 j 1 w 4 M []0 d %AI3_Note: 0 D 103.8711 412.8662 m 134.8572 390.3529 L 103.8706 367.8406 L 111.1857 390.3537 L 103.8706 412.8666 L 103.8711 412.8662 L s U u 65.5686 367.8405 m 34.5839 390.3542 L 22.7471 353.9286 L 46.4184 353.9279 L 65.5689 367.8411 L 65.5686 367.8405 L s U u 84.7177 308.9012 m 115.7044 331.4135 L 84.7182 353.9268 L 77.4031 331.4137 L 84.7181 308.9008 L 84.7177 308.9012 L s U u 84.7197 353.9272 m 115.7044 331.4135 L 127.5412 367.8391 L 103.8699 367.8398 L 84.7194 353.9266 L 84.7197 353.9272 L s U u 46.4183 353.9272 m 84.7197 353.9272 L 72.8838 390.3536 L 65.5686 367.8405 L 46.4178 353.9271 L 46.4183 353.9272 L s U u 111.1856 390.3527 m 72.8849 390.3538 L 84.7197 353.9272 L 103.8706 367.8406 L 111.1855 390.3533 L 111.1856 390.3527 L s U u 84.7197 353.9272 m 46.4189 353.9283 L 58.2537 317.5017 L 77.4046 331.4151 L 84.7196 353.9278 L 84.7197 353.9272 L s U u 103.8685 294.9884 m 65.5678 294.9895 L 77.4046 331.4151 L 84.7189 308.9021 L 103.8691 294.9883 L 103.8685 294.9884 L s U U u 3 w 65.5708 294.9904 m 34.5839 390.3542 l 134.8541 390.356 l 115.7062 331.4186 l 65.5708 294.9904 l s U U u u u 1 w 127.5397 367.8398 m 115.7026 331.4149 L 154.0028 331.4132 L 146.6889 353.926 L 127.5391 367.8399 L 127.5397 367.8398 L s U u 103.8682 367.8407 m 134.8548 390.3523 L 146.6889 353.926 L 127.5388 367.8401 L 103.8677 367.8404 L 103.8682 367.8407 L s U u 158.5257 390.3513 m 196.8266 390.3507 L 184.9913 426.7769 L 177.676 404.2642 L 158.5251 390.3512 L 158.5257 390.3513 L s U u 134.8548 390.3523 m 146.6889 353.926 L 177.6755 376.4375 L 158.5253 390.3517 L 134.8543 390.352 L 134.8548 390.3523 L s U u 177.6759 404.2634 m 146.692 426.7772 L 134.8548 390.3523 L 158.5257 390.3513 L 177.6762 404.264 L 177.6759 404.2634 L s U U u 3 w 115.7062 331.4186 m 196.8266 390.3507 l 115.7074 449.2898 l 134.8541 390.356 l 115.7062 331.4186 l s U U u u u 1 w 77.4019 258.5626 m 65.5666 294.989 L 103.8672 294.9884 L 84.7166 281.0748 L 77.402 258.562 L 77.4019 258.5626 L s U u 134.8538 272.4756 m 146.6877 236.0498 L 177.6739 258.561 L 158.524 272.475 L 134.8533 272.4753 L 134.8538 272.4756 L s U u 154.0052 331.4132 m 115.7046 331.4138 L 127.5398 294.9875 L 146.6905 308.9011 L 154.0051 331.4139 L 154.0052 331.4132 L s U u 127.5384 294.9881 m 115.7046 331.4138 L 84.7184 308.9027 L 103.8683 294.9887 L 127.539 294.9883 L 127.5384 294.9881 L s U u 158.5245 272.4755 m 127.5384 294.9881 L 115.7032 258.5619 L 134.8538 272.4756 L 158.525 272.4752 L 158.5245 272.4755 L s U u 84.7173 281.0756 m 115.7022 258.5624 L 127.5384 294.9881 L 103.8672 294.9884 L 84.717 281.0751 L 84.7173 281.0756 L s U u 127.5384 294.9881 m 158.5234 272.4749 L 170.3596 308.9005 L 146.6884 308.9009 L 127.5382 294.9875 L 127.5384 294.9881 L s U u 146.6896 353.9252 m 177.6745 331.4121 L 146.6884 308.9009 L 154.0037 331.4133 L 146.6892 353.9256 L 146.6896 353.9252 L s U U u 3 w 177.6716 331.4131 m 146.6877 236.0498 l 65.5673 294.9847 l 115.7001 331.4108 l 177.6716 331.4131 l s U U u u u 1 w 77.4017 213.5386 m 84.7163 191.0258 L S U u 108.388 236.0515 m 146.6877 236.0498 L 134.8538 272.4755 L 115.7032 258.5628 L 108.3881 236.0509 L 108.388 236.0515 L s U u 58.2536 272.4783 m 46.4173 236.0527 L 84.7179 236.0521 L 77.4033 258.565 L 58.2529 272.4785 L 58.2536 272.4783 L s U u 84.7169 236.051 m 46.4173 236.0527 L 58.2512 199.6269 L 77.4017 213.5397 L 84.7168 236.0516 L 84.7169 236.051 L s U u 115.7028 258.5634 m 84.7169 236.051 L 115.7027 213.5386 L 108.388 236.0515 L 115.7033 258.5638 L 115.7028 258.5634 L s U u 84.7157 191.0267 m 115.7019 213.5378 L 84.7169 236.051 L 77.4017 213.5386 L 84.7162 191.0263 L 84.7157 191.0267 L s U u 84.7169 236.051 m 115.7031 258.5622 L 84.7181 281.0753 L 77.4029 258.5629 L 84.7174 236.0506 L 84.7169 236.051 L s U u 34.5829 272.4776 m 65.569 294.9887 L 77.4029 258.5629 L 58.253 272.4769 L 34.5823 272.4772 L 34.5829 272.4776 L s U U u 3 w 46.4188 236.0475 m 65.5671 294.9862 l 146.6877 236.0498 l S U U u u u 1 w 34.5837 317.4952 m 65.5698 294.9819 L 34.5832 272.4696 L 41.8983 294.9827 L 34.5832 317.4956 L 34.5837 317.4952 L s U u 15.4303 213.5302 m 46.417 236.0425 L 15.4308 258.5558 L 8.1157 236.0427 L 15.4307 213.5298 L 15.4303 213.5302 L s U u 15.4323 258.5561 m 46.417 236.0425 L 58.2538 272.468 L 34.5825 272.4687 L 15.432 258.5556 L 15.4323 258.5561 L s U u -22.8691 258.5561 m 15.4323 258.5561 L 3.5963 294.9826 L -3.7188 272.4695 L -22.8697 258.5561 L -22.8691 258.5561 L s U u 41.8982 294.9817 m 3.5975 294.9828 L 15.4323 258.5561 L 34.5832 272.4696 L 41.8981 294.9822 L 41.8982 294.9817 L s U u 15.4323 258.5561 m -22.8685 258.5573 L -11.0337 222.1306 L 8.1172 236.0441 L 15.4322 258.5567 L 15.4323 258.5561 L s U u 34.5811 199.6174 m -3.7196 199.6185 L 8.1172 236.0441 L 15.4315 213.5311 L 34.5817 199.6173 L 34.5811 199.6174 L s U U u 3 w -3.7166 199.6194 m -34.7035 294.9831 l 65.5667 294.985 l 46.4188 236.0475 l -3.7166 199.6194 l s U U u u u 1 w -3.7193 317.4988 m -34.7058 294.9879 L -3.7211 272.4744 L 3.5944 294.9867 L -3.7198 317.4992 L -3.7193 317.4988 L s U u -22.8695 331.4133 m 15.4312 331.4122 L 3.5944 294.9867 L -3.7199 317.4996 L -22.8701 331.4134 L -22.8695 331.4133 L s U u 34.5809 317.498 m 65.5667 294.985 L 77.4025 331.4111 L 58.2516 317.4977 L 34.5804 317.4983 L 34.5809 317.498 L s U u 15.4312 331.4122 m 3.5944 294.9867 L 41.8952 294.9856 L 34.5808 317.4986 L 15.4306 331.4123 L 15.4312 331.4122 L s U u 58.2511 317.4971 m 46.4177 353.9231 L 15.4312 331.4122 L 34.5809 317.498 L 58.2517 317.4974 L 58.2511 317.4971 L s U U u 3 w -34.7007 294.9889 m 65.5667 294.985 l 34.583 390.3485 l 15.4328 331.4156 l -34.7007 294.9889 l s U U u u u 1 w 3.5987 367.8332 m 15.4341 331.4065 L -22.867 331.4071 L -3.7161 345.3209 L 3.5985 367.8338 L 3.5987 367.8332 L s U U u 3 w 15.4334 331.4108 m -34.7 294.9843 l S U U u u u 1 w 58.2529 199.6267 m 46.4195 236.0527 L 15.433 213.5419 L 34.5827 199.6276 L 58.2535 199.627 L 58.2529 199.6267 L s U u 34.5827 199.6276 m 58.2539 199.627 L 77.4044 213.5401 L 77.4042 213.5396 L S U u 34.5827 199.6276 m S U U u 3 w 46.4188 236.0475 m S U U U u u u u u 1 w 34.5812 463.2072 m 65.5678 485.7195 L 77.4026 449.2929 L 58.252 463.207 L 34.5807 463.2069 L 34.5812 463.2072 L s U u 65.5666 412.8658 m 34.5801 390.355 L 65.5648 367.8414 L 72.8804 390.3537 L 65.5662 412.8662 L 65.5666 412.8658 L s U u 127.5383 412.8641 m 115.7035 449.2907 L 84.7168 426.7784 L 103.8674 412.8643 L 127.5388 412.8643 L 127.5383 412.8641 L s U u 84.717 426.7799 m 115.7035 449.2907 L 84.7188 471.8044 L 77.4032 449.292 L 84.7174 426.7795 L 84.717 426.7799 L s U u 72.881 390.3534 m 84.717 426.7799 L 46.416 426.7799 L 65.5666 412.8658 L 72.8809 390.3528 L 72.881 390.3534 L s U u 58.253 463.2066 m 46.4162 426.781 L 84.717 426.7799 L 77.4026 449.2929 L 58.2524 463.2067 L 58.253 463.2066 L s U u 84.717 426.7799 m 72.8802 390.3543 L 111.1809 390.3532 L 103.8666 412.8662 L 84.7164 426.78 L 84.717 426.7799 L s U u 146.6881 426.7781 m 134.8513 390.3525 L 103.8666 412.8662 L 127.5378 412.8655 L 146.6883 426.7786 L 146.6881 426.7781 L s U U u 3 w 65.5678 485.7195 m 34.5801 390.355 l 134.8513 390.3525 l 115.7035 449.2907 l 65.5678 485.7195 l s U U u u u 1 w 189.5108 485.7145 m 177.6749 449.2882 L 146.6893 471.8011 L 170.3608 471.8011 L 189.511 485.715 L 189.5108 485.7145 L s U u 134.8531 508.2279 m 146.6898 544.653 L 108.3896 544.6541 L 115.7038 522.1414 L 134.8537 508.2279 L 134.8531 508.2279 L s U u 84.7166 471.803 m 115.7023 449.29 L 127.5382 485.7163 L 103.8667 485.7163 L 84.7164 471.8024 L 84.7166 471.803 L s U u 127.539 485.715 m 115.7023 449.29 L 154.0025 449.2889 L 146.6882 471.8015 L 127.5384 485.7151 L 127.539 485.715 L s U u 115.7031 522.1412 m 127.539 485.715 L 158.5246 508.228 L 134.8531 508.2279 L 115.7029 522.1418 L 115.7031 522.1412 L s U u 170.3597 471.8009 m 158.5251 508.2269 L 127.539 485.715 L 146.6893 471.8011 L 170.3602 471.8011 L 170.3597 471.8009 L s U u 127.539 485.715 m 115.7044 522.1411 L 84.7182 499.6291 L 103.8685 485.7153 L 127.5395 485.7153 L 127.539 485.715 L s U u 77.4029 449.2903 m 65.5683 485.7164 L 103.8685 485.7153 L 84.7179 471.8021 L 77.4031 449.2898 L 77.4029 449.2903 L s U U u 3 w 65.5701 485.7138 m 146.6898 544.653 l 177.6769 449.2921 l 115.7077 449.2898 l 65.5701 485.7138 l s U U u u u 1 w 103.8679 485.7153 m 65.5671 485.716 L 77.4034 522.1417 L 84.718 499.6288 L 103.8685 485.7153 L 103.8679 485.7153 L s U u 108.3899 544.6547 m 146.6898 544.653 L 134.8558 581.0789 L 115.7051 567.1661 L 108.39 544.6541 L 108.3899 544.6547 L s U u 58.2552 581.0817 m 46.4188 544.6559 L 84.7196 544.6554 L 77.405 567.1683 L 58.2545 581.0818 L 58.2552 581.0817 L s U u 84.7187 544.6542 m 46.4188 544.6559 L 58.2528 508.23 L 77.4034 522.1428 L 84.7186 544.6548 L 84.7187 544.6542 L s U u 115.7048 567.1668 m 84.7187 544.6542 L 115.7046 522.1418 L 108.3899 544.6547 L 115.7052 567.1672 L 115.7048 567.1668 L s U u 84.7175 499.6297 m 115.7038 522.141 L 84.7187 544.6542 L 77.4034 522.1417 L 84.7179 499.6293 L 84.7175 499.6297 L s U u 84.7187 544.6542 m 115.7049 567.1655 L 84.7199 589.6788 L 77.4046 567.1663 L 84.7191 544.6538 L 84.7187 544.6542 L s U u 34.5844 581.081 m 65.5706 603.5922 L 77.4046 567.1663 L 58.2547 581.0803 L 34.5839 581.0806 L 34.5844 581.081 L s U U u 3 w 65.5688 603.5897 m 146.6898 544.653 l 65.5714 485.7152 l 46.4203 544.6508 l 65.5688 603.5897 l s U U u u u 1 w -34.702 558.5673 m -3.7153 581.0796 L 8.1195 544.653 L -11.0311 558.567 L -34.7025 558.567 L -34.702 558.5673 L s U u -3.7165 508.2259 m -34.7031 485.7151 L -3.7183 463.2014 L 3.5972 485.7138 L -3.717 508.2263 L -3.7165 508.2259 L s U u 58.2551 508.2241 m 46.4203 544.6508 L 15.4337 522.1385 L 34.5843 508.2244 L 58.2556 508.2244 L 58.2551 508.2241 L s U u 15.4338 522.14 m 46.4203 544.6508 L 15.4356 567.1644 L 8.1201 544.6521 L 15.4342 522.1396 L 15.4338 522.14 L s U u 3.5979 485.7135 m 15.4338 522.14 L -22.8671 522.14 L -3.7165 508.2259 L 3.5978 485.7129 L 3.5979 485.7135 L s U u -11.0301 558.5666 m -22.8669 522.1411 L 15.4338 522.14 L 8.1195 544.653 L -11.0307 558.5667 L -11.0301 558.5666 L s U u 15.4338 522.14 m 3.597 485.7144 L 41.8977 485.7133 L 34.5834 508.2263 L 15.4332 522.1401 L 15.4338 522.14 L s U u 77.4049 522.1382 m 65.5681 485.7126 L 34.5834 508.2263 L 58.2546 508.2256 L 77.4051 522.1387 L 77.4049 522.1382 L s U U u 3 w -3.7153 581.0796 m -34.7031 485.7151 l 65.5681 485.7126 l 46.4203 544.6508 l -3.7153 581.0796 l s U U u u u 1 w 22.7455 426.7754 m 34.5789 390.3493 L 65.5654 412.8601 L 46.4157 426.7744 L 22.745 426.7751 L 22.7455 426.7754 L s U u 3.5943 412.8624 m 15.431 449.288 L 46.4158 426.7744 L 22.7445 426.7751 L 3.5941 412.8619 L 3.5943 412.8624 L s U u 34.5818 463.2005 m 65.5681 485.7126 L 34.5826 508.2254 L 41.8969 485.7125 L 34.5814 463.2001 L 34.5818 463.2005 L s U u 15.431 449.288 m 46.4157 426.7744 L 58.2525 463.2 L 34.5812 463.2006 L 15.4308 449.2875 L 15.431 449.288 L s U u 41.8973 485.7118 m 3.5976 485.714 L 15.431 449.288 L 34.5818 463.2005 L 41.8972 485.7124 L 41.8973 485.7118 L s U U u 3 w 34.5797 390.3545 m 65.5681 485.7126 l -34.7019 485.7149 l 15.4283 449.2906 l 34.5797 390.3545 l s U U u u u 1 w -22.8693 449.2857 m 15.4322 449.2852 L 3.5956 412.8587 L -3.7191 435.3721 L -22.8699 449.2858 L -22.8693 449.2857 L s U u 22.7442 353.9178 m 34.5807 390.3442 L -3.7207 390.3448 L 3.5941 367.8315 L 22.7448 353.9177 L 22.7442 353.9178 L s U u -3.7197 390.3459 m 34.5807 390.3442 L 22.7466 426.7707 L 3.5956 412.8577 L -3.7196 390.3453 L -3.7197 390.3459 L s U u -34.7063 367.833 m -3.7197 390.3459 L -34.7061 412.8587 L -27.3913 390.3454 L -34.7067 367.8326 L -34.7063 367.833 L s U u -3.7185 435.3712 m -34.7053 412.8595 L -3.7197 390.3459 L 3.5956 412.8587 L -3.719 435.3716 L -3.7185 435.3712 L s U u -3.7197 390.3459 m -34.7065 367.8343 L -3.7209 345.3206 L 3.5945 367.8335 L -3.7201 390.3463 L -3.7197 390.3459 L s U u 46.4154 353.9186 m 15.4286 331.4069 L 3.5945 367.8335 L 22.7447 353.9193 L 46.4159 353.9189 L 46.4154 353.9186 L s U U u 3 w 15.4278 449.2858 m 34.5792 390.3493 l 15.4305 331.4094 l S U U u u u 1 w 15.4384 567.1596 m 46.4228 544.6462 L 58.2594 581.0714 L 34.5884 581.072 L 15.4381 567.159 L 15.4384 567.1596 L s U u 8.1228 544.6469 m -3.7119 581.0731 L 34.5884 581.072 L 15.4377 567.1587 L 8.1229 544.6463 L 8.1228 544.6469 L s 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Adobe_packedarray /terminate get exec %%EOF EndOfTheIncludedPostscriptMagicCookie \closepsdump % Finally, here is text11.tex: \magnification 1200 \let\nd\noindent % NOINDENT \def\NL{\hfill\break}% NEWLINE \def\qed{\hbox{\hskip 6pt\vrule width6pt height7pt depth1pt \hskip1pt}} \def\natural{{\rm I\kern-.18em N}} \def\N{{\bf N}} \def\integer{{\rm Z\kern-.32em Z}} \def\A{{\cal A}} \def\Z{{\bf Z}} \def\real{{\rm I\kern-.2em R}} \def\R{{\bf R}} \def\complex{\kern.1em{\raise.47ex\hbox{ $\scriptscriptstyle |$}}\kern-.40em{\rm C}} \def\C{{\bf C}} \def\vs#1 {\vskip#1truein} \def\hs#1 {\hskip#1truein} \def\signed{\vskip1truein\hskip 2.5truein{Charles Radin}} \def\Sinc{\vskip .5truein\hskip 2.5truein} \def\Indent{\vskip 0truein\hskip 2.5truein} \def\Month{\ifcase\number\month \relax\or January \or February \or March \or April \or May \or June \or July \or August \or September \or October \or November \or December \else \relax\fi } \def\date{\Month \the\day, \the\year} \def\lett{\nopagenumbers\hbox{}\vskip 1truein \hskip 2.5truein{\date}\vskip.5truein} \hsize=6truein \hoffset=.25truein %was \hoffset=1.2truein \vsize=8.8truein %\voffset=1truein \pageno=1 \baselineskip=12pt \parskip=0 pt \parindent=20pt \overfullrule=0pt \lineskip=0pt \lineskiplimit=0pt \hbadness=10000 \vbadness=10000 % REPORT ONLY BEYOND THIS BADNESS %\lett %\nd \pageno=0 \vskip -.9truein \rightline{Notices Amer. Math. Soc. 42 (1995), 26-31.} \footline{\ifnum\pageno=0\hss\else\hss\tenrm\folio\hss\fi} \hbox{}\vs2 \centerline{{SYMMETRY AND TILINGS} \footnote{*}{Research supported in part by NSF Grant No. DMS-9304269 and \vs0 Texas ARP Grant 003658-113\hfil}} \vs.3 \centerline{Charles Radin} \vs.05 \centerline{University of Texas} \vs.05 \centerline{Austin, TX\ \ 78712} \vs.1 \centerline{radin@math.utexas.edu} \vfill\eject A ``pinwheel'' tiling of the plane (as in Figure 1) does not have any translational or rotational symmetry in the usual sense. But in a tantalizing, unconventional way it is {\it highly} symmetric, and this unusual form of symmetry has significant applications, for instance in classifying the internal structures of solids. Tilings, which are decompositions of space into finite-size subsets called tiles, are a traditional medium for exhibiting symmetries. Usually, a pattern in space exhibits a symmetry by being invariant under the corresponding rigid motion of space. As an example consider an infinite length ``necklace'', a mixture of equidistant cubic and spherical beads embedded along a line. Such an object has a translational symmetry if the pattern is periodic, for instance if the bead-shapes alternate. A very different example is a paraboloid of revolution, which has as symmetries the rotations about its axis. By decomposing space into tiles, a tiling can be thought of as a ``multidimensional necklace'', with the ``beads'' fitting smoothly together like a jigsaw puzzle. As a link between continuous surfaces such as paraboloids and discrete sequences such as necklaces, tilings can exhibit an unusual richness of symmetries. The pinwheel and Penrose tilings of the plane (see Figure 2 for a portion of a Penrose tiling) belong to a special class of tilings in which symmetries are not exhibited in the above traditional sense, but in a more subtle manner, only recently understood. We will sketch the main ideas involved in the analysis of such tilings and their symmetries. This will prove to be an interdisciplinary endeavor, employing intuition from logic and condensed matter physics as well as mathematics. There are two features which together define the class of tilings, called hierarchical tilings, that we will consider. First, each tiling is made of polyhedral tiles congruent to those in some fixed finite set $S$. For the Penrose tilings $S$ contains just two such tiles, called the kite and the dart, shown in Figure 3. (The graphics of Figures 1 and 2 are convenient oversimplifications: they do not show the small bumps and dents that are more properly part of the tiles, as shown in Figure 3.) Second we require that {\it every} tiling that can be made with tiles from $S$ display a certain type of hierarchical structure. The hierarchical structure of the pinwheel and Penrose tilings is suggested by Figures 4 and 5. The structural fact which is suggested is that each such tiling ``displays'', in a {\it unique} way, another such tiling of space by the original tiles but enlarged by some factor:\ $(\sqrt 5 +1)/2$ for the Penrose tilings and $\sqrt 5 $ for the pinwheels. Furthermore, this larger scale tiling displays another unique tiling at the next larger scale, {\it etc.,} so each tiling displays an infinite hierarchy of tilings at larger and larger scales. (We note that the bumps and dents of Figure 3 are needed to ensure that the tiles can {\it only} fit together to form tilings with the desired hierarchical structure. With quadrilateral tiles the tiling of Figure 2 still displays a hierarchical structure, but only if the bumps and dents are added does it become a hierarchical tiling.) Think of tilings as fixed in space, and let $X$ be the set of all (hierarchical) tilings made from some finite set $S$ of polyhedral tiles. We now use $X$ to carry a representation of the special Euclidean group $G$ of rigid motions, ``special'' meaning without reflections. For $g$ in $G$, and thinking of a tiling $x$ as a set of tiles $P$ fixed in space, $x=\{P\}$, we define $T^g(x)=\{g(P)\}$; that is, we let $g$ move each of the tiles in $x$. We now note something much less obvious, using the hierarchical structure of the tilings. Given a tiling $x$, consider the collection of ``large tiles'' associated with the next higher level of the hierarchical structure of $x$ (such as that drawn with thick lines in Figure 4), and let $y(x)$ be the tiling made by shrinking these large tiles about the origin by the appropriate factor $\lambda$. This defines a map $T^s$ on $X$, by $T^s(x)=y(x)$. From the assumed uniqueness of the hierarchy, $T^s$ is invertible. It is important to note that $T^s$ can and should be thought of as a representation of that {\it similarity}, $s,$ of space which shrinks space linearly about the origin by the factor $\lambda$; in particular, $T^s$ has the correct group relations with all $T^g$, $g \in G$, such as $T^sT^t{T^{s}}^{-1}=T^{\lambda t}$ for any translation $t$. One use of this group representation is the following simple argument showing that no hierarchical tiling can be invariant under any nonzero translation. For assume $T^t(x) = x$ for some translation $t$. It is easy to show that $T^{s^n}(x)$ is then invariant under translation by $T^{\lambda^nt}$. But taking $n$ large enough this would imply invariance under a translation by less than the size of any tile, which is only possible if $t=0$. The above group representations on $X$ are also useful in understanding the rotational symmetries of these tilings. There are two ways of understanding these symmetries: as geometric features of the tilings and in terms of the mathematical structures of analysis. We will note both points of view, as they give different insight. As you might guess from Figure 2, kites and darts each appear in precisely ten different orientations in a Penrose tiling, and in fact they appear ``equally often'' in each of these ten orientations in the following sense. Take any large circle in any Penrose tiling, and divide the number of times a kite appears, in a certain orientation, within that circle by the area of the circle. This fraction has a limit, as the circle grows to the full plane, which is independent of the choice of tiling; furthermore this limit is {\it the same} for each of the ten orientations. Intuitively, we are saying that the Penrose tilings exhibit ten-fold {\it statistical} rotational symmetry; not just single kites and darts, but any finite collection of tiles will appear in every tiling in ten, and only ten, orientations (if it appears at all), and with the {\it same frequency} in each orientation. The symmetry of the pinwheel tilings is more surprising. Such tilings exhibit complete statistical rotational symmetry: given any two equal-size intervals $I_1$ and $I_2$ of orientations, and any finite collection of tiles, then in any tiling the collection will appear having an orientation in $I_1$ with the same frequency as with an orientation in $I_2$. This statistical type of symmetry can be put in the usual form of the invariance of something with respect to a group of rotations, but this requires some analysis. First we put a metric $\rho$ on $X$ such that two tilings are close if, within some large ball centered at the origin, wherever one tiling has a tile the other also has one, which almost coincides. Then we lift the action of the rotations and translations from the space $X$ of tilings to the space $B(X) $ of Borel probability measures on $X$, and define the subspace $B_T(X)$ of those measures which are {\it translation invariant}. With this notation, the above statistical symmetry is precisely the invariance of each element of $B_T(X)$ under the appropriate group of rotations -- the group of rotations by multiples of $2\pi/10$ for the Penrose tilings, and the group of all rotations for the pinwheel tilings. So ``statistical symmetry'' is a weakening of the usual notion of symmetry of a pattern, replacing the invariance of the pattern by the invariance of all invariant measures associated with the pattern. We now discuss the origins of hierarchical tilings and their statistical symmetries. The subject began 30 years ago when the philosopher Hao Wang was working on a decidability problem in propositional calculus. He reformulated his problem into the following one. Assume we are interested in arbitrary (not necessarily hierarchical) tilings of the plane by tiles which are all basically unit squares, but have different patterns of bumps and dents on their edges. Furthermore, assume as above that all the tiles are congruent to those from some finite set $S$. The question Wang asked is: Can there be an {\it algorithm} by which, given as input any such finite set $S$, we can determine whether or not we can actually tile the plane with such tiles? Now imagine there exists a set $S$ from which we can tile the plane but {\it only} in complicated ways, in particular only without any translation symmetry; Wang showed that an algorithm for tiling exists if and only if there does not exist such a set $S$. His student Robert Berger then constructed an example of such a set $S$ (producing hierarchical tilings which, as we saw above, cannot be invariant under a nonzero translation), thereby creating the subject. Logicians extended the result by constructing sets $S$ from which one could tile the plane but only by tilings which were each themselves not the output of any algorithm. (The connection between such ``square-ish'' tilings and algorithms is obtained by thinking of consecutive rows of a tiling as the tape of a Turing machine at consecutive time steps.) So the subject began in an attempt to make ``complex'' tilings, in the technical sense referring to complexity theory and algorithms. There was a different motivation in condensed matter physics. There, tilings like those of Penrose have been used to model the structure of unusual solids. For practical reasons, the relevant feature of the material which is of interest is the X-ray (or electron) scattering patterns produced by the materials. A chunk of a solid produces scattering patterns when illuminated by beams of waves (photons or electrons) of appropriate wavelength; in general one is interested in the family of patterns obtained for a range of wavelengths, and when viewed from a range of angles relative to that of the incoming beam. The pattern is produced by the constructive and destructive interference of the individual scatterings of the beam from each of the large number (order $10^{24}$) of constituent atoms. For an ordinary crystal, the atoms are roughly in a periodic configuration, and it can be proven (the so-called ``classification of crystallographic groups'') that the scattering patterns from any such configuration can only have certain rotational symmetries. Alan Mackay showed if we associate ``scatterers'' with each tile of a Penrose tiling, then such a configuration would produce a scattering pattern with a ten-fold rotational symmetry {\it unobtainable by any crystal}. And this became of much greater interest when real materials (``quasicrystals'') were found which actually produce such patterns. It is still not known if there is a good reason to model such real materials by means of (3-dimensional versions of) Penrose-like tilings, but much is being written on the subject. The point to be emphasized is that the symmetries of the scattering patterns associated with a tiling are precisely the statistical symmetries of the tilings, as discussed above; scattering patterns are not sensitive to the positions of every scatterer, but only sensitive to statistical properties of the positions. In summary, condensed matter physicists are interested in hierarchical tilings precisely for the statistical symmetries associated with them. The information flow from tilings to condensed matter physics is not just one-way. Once the above connection was made, it became interesting to ask for instance whether there was an analog in tilings to the phenomena associated with the temperature dependence of crystals, such as phase transitions. For solids it is believed (not proven) that solids melt, as temperature is raised, ``because'' with increasing temperature the periodic structure of the crystal contains more and more defects, which destroy the structure at some fixed temperature. It is then natural to investigate ``imperfect tilings'', in which defects are allowed. There is not yet much progress in this direction. (There is precious little proven in physics models either; phase transitions is a difficult subject. There is an interesting discussion of the value of this subject to mathematics in the 1988 Gibbs Lecture of David Ruelle.) Mathematically, we are studying the class of tilings generated by some family $S$ of polyhedra. In a way this is like solving a differential equation, where a (global) function is determined by the local constraints represented by the differential equation; for tilings by some $S$, the global tiling is determined by the local restrictions dictating how the tiles can fit together. And just as initial or boundary conditions play the role of reducing to a singleton the set of solutions of a differential equation, for tilings the hierarchical assumption plays such a role. From the hierarchical assumption it follows that all the tilings associated with an $S$ must be locally indistinguishable, and this is the appropriate notion of uniqueness for tilings. We will illustrate the general argument with the pinwheel tilings. We begin by encoding the information of the hierarchical structure into matrices, in such a way that the different levels of the hierarchy correspond to powers of the matrices. We will say that a composite object making up a large scale tile, congruent to some tile $P$ but larger by a power $k$ of the scale factor, is the tile $P$ ``at level $k$''. For the pinwheel we label the two tiles in $S$ as ``type 1'' and ``type 2'', as in Figure 6a; note they are just reflections of one another. Then we define a one parameter family of matrices, $A[m]$, with parameter $m\in \Z$, by $$A[m]_{jk} = \sum_ne^{ima_n(j,k)} \eqno 1)$$ \nd where $a_n(j,k)$ is the angle of rotation, of the $n^{th}$ copy of the tile of type $j$ which appears in a tile at level 1 of type $k$, the angle being with respect to some standard orientation. (See Figure 6b; note for instance that in a tile at level 1 of type 2 there are three tiles of type 1, and two tiles of type 2.) For the pinwheel tilings the matrices are: $$\pmatrix{e^{-ims}+e^{-im(s+\pi)}& 2e^{-im(s+\pi)}+e^{-im(s+3\pi/2)}\cr 2e^{im(s+\pi)}+e^{im(s+3\pi/2)}& e^{ims}+e^{im(s+\pi)}\cr}$$ Setting $m=0$, it is easy to see that ${A[0]^N}_{jk}$ is the number of copies of tiles of type $j$ in a large tile of type $k$ corresponding to level $N$ of the hierarchy. Setting $m=1$, we see that ${A[1]^N}_{jk}$ keeps track of all the angles of all the tiles in such a large tile. Since every tiling is hierarchical, to show that all tilings associated with some $S$ are statistically the same (ignoring angles for the moment) all one needs to show is that all large scale tiles are statistically the same. But that follows from the above matrix analysis using a theorem of Perron and Frobenius, which shows for instance that $${{A[0]^N}_{jk}\over {A[0]^N}_{j'k}}\longrightarrow_{N\to\infty} f(j,j')\ne 0$$ And finally we can apply the ``Weyl criterion'', used for proving that a sequence of numbers is uniformly distributed on an interval, to the sequence (labelled by $N$) of angles in the matrix element ${A[1]^N}_{jk}$, obtaining a simple geometric criterion, satisfied for the pinwheel, for uniform distribution. In the above analysis of the pinwheel we treated the system as if, like the Penrose system, there were only two tiles in $S$, a right triangle and its reflection, with some pattern of bumps and dents on them. This was mildly misleading, as in fact $S$ is a very large (but finite) set, with many different patterns of bumps and dents on each of those two triangles. And this is a story in itself. The way one creates a set $S$ as in Figure 3 is to start with an appropriate given tiling with simple shapes, like that shown in Figure 2 for the Penrose system. Of course the quadrilaterals in Figure 2 are not in themselves satisfactory for $S$ since not {\it all} tilings with such tiles would have the hierarchical structure. So one needs to alter them, by adding bumps and dents on the edges, so that the {\it only} way the tiles can tile space is like the given tiling with the original simpler shapes. For the Penrose system it is easy to see that the bumps and dents of Figure 3 do the job. For the pinwheel system it is much harder to determine {\it if and how} we can make such alterations to the basic triangle so the tiles only tile as in Figure 1. However, the case of ``square-ish'' tiles, discussed above with regard to Wang's thesis, has been well studied and it has been shown rather generally, by Shahar Mozes, how to make appropriate alterations for a given ``square-ish'' hierarchical structure. To be more specific assume we have a set $\A$ of four unit square ``colored'' tiles, $\{$A, B, C, D$\}$, and the hierarchical rule of Figure 7 (analogous to Figure 6b for the pinwheel), which associates an array of four unit square colored tiles to each element of $\A$. This rule determines a family of tilings of the plane with the four colored tiles, as follows. Using the convention adopted earlier we refer to each of the four composite objects in Figure 7 as tiles of level 1, and extend the notion to tiles at all levels by repeating the rule. We can then consider the special class of tilings, by the tiles of $\A$, which displays associated tilings at all levels; Figure 8 shows parts of levels 0 and 1 of such a tiling. What we want to do next is alter the edges of the four squares in $\A$ so that the altered tiles can {\it only} tile the plane in this hierarchical way. This is harder than for the Penrose system, and rests on the pioneering work of Berger, Raphael Robinson and others. Unfortunately we do have to enlarge the set $\A$ greatly in this process, having many different ``versions'' of each of the original four elements, each with various bumps and dents on each of their four sides. The above method does not seem to generalize directly to non-square hierarchical structures; the first test case was the pinwheel, and the method used for it was much more complicated. But it is hoped that now that the pinwheel is ``solved'' a truely broad method can be produced. Effectively this would give us a general way to realize hierarchical structures as produced from local rules, which could be useful, for example, in applied areas where at present hierarchical structures are mostly put into models in an {\it ad hoc} manner, without any attempt to show how they could arise from (local) physical laws. In conclusion, we have used tilings of space to illustrate a nontraditional, statistical form of symmetry, motivated in part by ideas from logic and physics. This mathematics has been slow to develop over the past thirty years, but seems at present to fit comfortably as a geometric extension (geometric in its use of rotations and similarities) of parts of ergodic theory, a rich extension which should prove fruitful to all the overlapping subjects. \vs1.3 \centerline{FURTHER READING} \vs.2 \nd {\bf Notes.} The Penrose and pinwheel tilings are presented in [2] and [6] respectively. Square-ish tilings are introduced {\it beautifully} in [8], together with their connection with certain decidability problems. Chapters 10 and 11 in [3] are a general introduction to the literature on the sort of tilings used in this article, comprehensive until the mid-1980's. The above works are mainly combinatorial geometry, and require little background. After Penrose found his tilings, conceptual progress required the use of tools from analysis, chiefly ergodic theory. In particular [4] gives a general method for creating hierarchical tilings (that is, finding the bumps and dents) for appropriate given square-ish tilings; and [7] gives a general method to determine the statistical symmetry of hierarchical tilings. A connection with statistical mechanics appears to be intrinsic to the subject. There is a fine introduction to the use of statistical mechanics in mathematics in [9], and a more specialized study of the connection between statistical mechanics and tilings in [5]. They both require a range of tools from analysis. [1] gives the connection between the way a beam of waves scatters off a configuration of scatterers, and the dynamical spectrum associated with the configuration. It is written in the language of physics. \vs.2 \nd [1]\ S.\ Dworkin, `Spectral theory and x-ray diffraction', {\it J.\ Math.\ Phys.} {\bf 34} (1993), 2965-2967. \vs.15 \nd [2]\ M.\ Gardner, `Extraordinary nonperiodic tiling that enriches the theory of tiles', {\it Sci.\ Am.\ (USA)} {\bf 236} (1977), 110-119. \vs.15 \nd [3]\ B.\ Gr\"unbaum and G.C.\ Shephard, {\it Tilings and Patterns}, Freeman, New York, 1986. \vs.15 \nd [4]\ S.\ Mozes, `Tilings, substitution systems and dynamical systems generated by them', {\it J.\ d'Analyse Math.}\ {\bf 53} (1989), 139-186. \vs.15 \nd [5]\ C.\ Radin, `Global Order from Local Sources', {\it Bull. Amer. Math. Soc.} {\bf 25} (1991), 335-364. \vs.15 \nd [6]\ C.\ Radin, `The pinwheel tilings of the plane', {\it Annals of Math.} {\bf 139} (1994), 661-702. \vs.15 \nd [7]\ C.\ Radin, `Space tilings and substitutions', {\it Geometriae Dedicata}. To appear. \vs.15 \nd [8] R.M.\ Robinson, `Undecidability and nonperiodicity for tilings of the plane', {\it Invent.\ Math.} {\bf 12} (1971), 177-209. \vs.15 \nd [9]\ D.\ Ruelle, `Is our mathematics natural? The case of equilibrium statistical mechanics', {\it Bull.\ Amer.\ Math.\ Soc.} {\bf 19} (1988), 259-268. \vfill\eject \global\let\figures\relax % % ??/epsf.tex (written by Radical Eye Software and copied below) % defines the macro \epsfbox with one argument, % the encapsulated PostScript file to include. % Invoking it causes a \vbox with the natural size of the drawing % to be inserted at the point of invocation. % Usually figures are meant to be centered and set off, and possibly % to have a title and/or a figure number. The macros below do that. % You should assign values that please you to the variables % \abovefigskip, \belowfigskip, figtitleskip, figtitlefont,... % AFTER \inputting the present file: \input /u2/kbi/tex/epsfig % and BEFORE the first invocation of any of the macros below. % RESET AT YOUR PLEASURE THE VARIABLES AT THE VERY BOTTOM! % % For convenience we make a dimension for figures: \newdimen\FigSize \FigSize=.9\hsize % alter at your convenience % % For a SCALED HORIZONTALLY CENTERED FIGURE use \epsfig. % First argument is the horizontal width of the figure, given % in any way TeX can understand. % The second argument is an encapsulated PostScript file name (filnam.eps). % Note the mandatory semicolons between arguments in this example!: % \epsfig .8\hsize; example.ps; % will put a centered scaled \vbox of width .8\hsize suitably offset % at the point of invocation \newskip\abovefigskip \newskip\belowfigskip \gdef\epsfig#1;#2;{\par\vskip\abovefigskip\penalty -500 {\everypar={}\epsfxsize=#1\noindent \centerline{\epsfbox{#2}}}% \vskip\belowfigskip}% % % SCALED TITLED EPSFIG HORIZONTALLY CENTERED: \tepsfig. % First argument is the horizontal width of the figure, % second an encapsulated PostScript file name, % third a title for the figure. % Note the mandatory semicolons between arguments! % example: \tepsfig5truein; example.ps;{This is a figure} \newskip\figtitleskip \gdef\tepsfig#1;#2;#3{\par\vskip\abovefigskip\penalty -500 {\everypar={}\epsfxsize=#1\noindent \vbox {\centerline{\epsfbox{#2}}\vskip\figtitleskip \centerline{\figtitlefont#3}}}% \vskip\belowfigskip}% % % SCALED NUMBERED TITLED EPSFIG HORIZONTALLY CENTERED: \nepsfig % The figure number is automatically increased for every % invocation of \nepsfig or \nipsfig. \newcount\FigNr \global\FigNr=0 \gdef\nepsfig#1;#2;#3{\global\advance\FigNr by 1 \tepsfig#1;#2;{Figure\space\the\FigNr.\space#3}}% % % % Often you would rather have TeX decide where to put the figure % by using \midinsert. Here are macros that do that % (mnemonics ``ipsfig'' is for ``midInsert PS FIGure'') % % TeX-PLACED SCALED EPSFIG HORIZONTALLY CENTERED: \ipsfig \gdef\ipsfig#1;#2;{%\goodbreak ?? \midinsert{\everypar={}\epsfxsize=#1\noindent \centerline{\epsfbox{#2}}}% \endinsert}% % % TeX-PLACED SCALED TITLED EPSFIG HORIZONTALLY CENTERED: \tipsfig \gdef\tipsfig#1;#2;#3{\midinsert {\everypar={}\epsfxsize=#1\noindent \vbox{\centerline{\epsfbox{#2}}% \vskip\figtitleskip \centerline{\figtitlefont#3}}}\endinsert}% % % TeX-PLACED SCALED NUMBERED TITLED EPSFIG HORIZONTALLY CENTERED: \nipsfig % example: \nipsfigd.9\hsize;example.ps;{This is an example figure} \gdef\nipsfig#1;#2;#3{\global\advance\FigNr by1% \tipsfig#1;#2;{Figure\space\the\FigNr.\space#3}}% % % ================================================================ % old: % \ifx\Input\undefined\let\next\input\else\let\next\Input\fi % \next /usr/local/lib/tex/inputs/epsf.tex %On Suns %% \next /usr/lib/tex/inputs/epsf.tex %On NexTs % % to make sure no new version of epsf.tex corrupts the above, % I copy here that file in toto: % % EPSF.TEX macro file: % Written by Tomas Rokicki of Radical Eye Software, 29 Mar 1989. % Revised by Don Knuth, 3 Jan 1990. % Revised by Tomas Rokicki to accept bounding boxes with no % space after the colon, 18 Jul 1990. % % TeX macros to include an Encapsulated PostScript graphic. % Works by finding the bounding box comment, % calculating the correct scale values, and inserting a vbox % of the appropriate size at the current position in the TeX document. % % To use with the center environment of LaTeX, preface the \epsffile % call with a \leavevmode. (LaTeX should probably supply this itself % for the center environment.) % % To use, simply say % \input epsf % somewhere early on in your TeX file % \epsfbox{filename.ps} % where you want to insert a vbox for a figure % % Alternatively, you can type % % \epsfbox[0 0 30 50]{filename.ps} % to supply your own BB % % which will not read in the file, and will instead use the bounding % box you specify. % % The effect will be to typeset the figure as a TeX box, at the % point of your \epsfbox command. By default, the graphic will have its % `natural' width (namely the width of its bounding box, as described % in filename.ps). The TeX box will have depth zero. % % You can enlarge or reduce the figure by saying % \epsfxsize= \epsfbox{filename.ps} % (or % \epsfysize= \epsfbox{filename.ps}) % instead. Then the width of the TeX box will be \epsfxsize and its % height will be scaled proportionately (or the height will be % \epsfysize and its width will be scaled proportiontally). The % width (and height) is restored to zero after each use. % % A more general facility for sizing is available by defining the % \epsfsize macro. Normally you can redefine this macro % to do almost anything. The first parameter is the natural x size of % the PostScript graphic, the second parameter is the natural y size % of the PostScript graphic. It must return the xsize to use, or 0 if % natural scaling is to be used. Common uses include: % % \epsfxsize % just leave the old value alone % 0pt % use the natural sizes % #1 % use the natural sizes % \hsize % scale to full width % 0.5#1 % scale to 50% of natural size % \ifnum#1>\hsize\hsize\else#1\fi % smaller of natural, hsize % % If you want TeX to report the size of the figure (as a message % on your terminal when it processes each figure), say `\epsfverbosetrue'. % \newread\epsffilein % file to \read \newif\ifepsffileok % continue looking for the bounding box? \newif\ifepsfbbfound % success? \newif\ifepsfverbose % report what you're making? \newdimen\epsfxsize % horizontal size after scaling \newdimen\epsfysize % vertical size after scaling \newdimen\epsftsize % horizontal size before scaling \newdimen\epsfrsize % vertical size before scaling \newdimen\epsftmp % register for arithmetic manipulation \newdimen\pspoints % conversion factor % \pspoints=1bp % Adobe points are `big' \epsfxsize=0pt % Default value, means `use natural size' \epsfysize=0pt % ditto % \def\epsfbox#1{\global\def\epsfllx{72}\global\def\epsflly{72}% \global\def\epsfurx{540}\global\def\epsfury{720}% \def\lbracket{[}\def\testit{#1}\ifx\testit\lbracket \let\next=\epsfgetlitbb\else\let\next=\epsfnormal\fi\next{#1}}% % \def\epsfgetlitbb#1#2 #3 #4 #5]#6{\epsfgrab #2 #3 #4 #5 .\\% \epsfsetgraph{#6}}% % \def\epsfnormal#1{\epsfgetbb{#1}\epsfsetgraph{#1}}% % \def\epsfgetbb#1{% % % The first thing we need to do is to open the % PostScript file, if possible. % \openin\epsffilein=#1 \ifeof\epsffilein\errmessage{I couldn't open #1, will ignore it}\else % % Okay, we got it. Now we'll scan lines until we find one that doesn't % start with %. We're looking for the bounding box comment. % {\epsffileoktrue \chardef\other=12 \def\do##1{\catcode`##1=\other}\dospecials \catcode`\ =10 \loop \read\epsffilein to \epsffileline \ifeof\epsffilein\epsffileokfalse\else % % We check to see if the first character is a % sign; % if not, we stop reading (unless the line was entirely blank); % if so, we look further and stop only if the line begins with % `%%BoundingBox:'. % \expandafter\epsfaux\epsffileline:. \\% \fi \ifepsffileok\repeat \ifepsfbbfound\else \ifepsfverbose\message{No bounding box comment in #1; using defaults}\fi\fi }\closein\epsffilein\fi}% % % Now we have to calculate the scale and offset values to use. % First we compute the natural sizes. % \def\epsfsetgraph#1{% \epsfrsize=\epsfury\pspoints \advance\epsfrsize by-\epsflly\pspoints \epsftsize=\epsfurx\pspoints \advance\epsftsize by-\epsfllx\pspoints % % If `epsfxsize' is 0, we default to the natural size of the picture. % Otherwise we scale the graph to be \epsfxsize wide. % \epsfxsize\epsfsize\epsftsize\epsfrsize \ifnum\epsfxsize=0 \ifnum\epsfysize=0 \epsfxsize=\epsftsize \epsfysize=\epsfrsize % % We have a sticky problem here: TeX doesn't do floating point arithmetic! % Our goal is to compute y = rx/t. The following loop does this reasonably % fast, with an error of at most about 16 sp (about 1/4000 pt). % \else\epsftmp=\epsftsize \divide\epsftmp\epsfrsize \epsfxsize=\epsfysize \multiply\epsfxsize\epsftmp \multiply\epsftmp\epsfrsize \advance\epsftsize-\epsftmp \epsftmp=\epsfysize \loop \advance\epsftsize\epsftsize \divide\epsftmp 2 \ifnum\epsftmp>0 \ifnum\epsftsize<\epsfrsize\else \advance\epsftsize-\epsfrsize \advance\epsfxsize\epsftmp \fi \repeat \fi \else\epsftmp=\epsfrsize \divide\epsftmp\epsftsize \epsfysize=\epsfxsize \multiply\epsfysize\epsftmp \multiply\epsftmp\epsftsize \advance\epsfrsize-\epsftmp \epsftmp=\epsfxsize \loop \advance\epsfrsize\epsfrsize \divide\epsftmp 2 \ifnum\epsftmp>0 \ifnum\epsfrsize<\epsftsize\else \advance\epsfrsize-\epsftsize \advance\epsfysize\epsftmp \fi \repeat \fi % % Finally, we make the vbox and stick in a \special that dvips can parse. % \ifepsfverbose\message{#1: width=\the\epsfxsize, height=\the\epsfysize}\fi \epsftmp=10\epsfxsize \divide\epsftmp\pspoints \vbox to\epsfysize{\vfil\hbox to\epsfxsize{% \special{PSfile=#1 llx=\epsfllx\space lly=\epsflly\space urx=\epsfurx\space ury=\epsfury\space rwi=\number\epsftmp}% \hfil}}% \epsfxsize=0pt\epsfysize=0pt}% % % We still need to define the tricky \epsfaux macro. This requires % a couple of magic constants for comparison purposes. % {\catcode`\%=12 \global\let\epsfpercent=%\global\def\epsfbblit{%BoundingBox}}% % % So we're ready to check for `%BoundingBox:' and to grab the % values if they are found. % \long\def\epsfaux#1#2:#3\\{\ifx#1\epsfpercent \def\testit{#2}\ifx\testit\epsfbblit \epsfgrab #3 . . . \\% \epsffileokfalse \global\epsfbbfoundtrue \fi\else\ifx#1\par\else\epsffileokfalse\fi\fi}% % % Here we grab the values and stuff them in the appropriate definitions. % \def\epsfgrab #1 #2 #3 #4 #5\\{% \global\def\epsfllx{#1}\ifx\epsfllx\empty \epsfgrab #2 #3 #4 #5 .\\\else \global\def\epsflly{#2}% \global\def\epsfurx{#3}\global\def\epsfury{#4}\fi}% % % We default the epsfsize macro. % \def\epsfsize#1#2{\epsfxsize}% % % Finally, another definition for compatibility with older macros. % \let\epsffile=\epsfbox % ================================================================ % execution: why not set \epsfverbosetrue % reset at your pleasure \abovefigskip=\baselineskip % reset at your pleasure \belowfigskip=\baselineskip % reset at your pleasure \global\let\figtitlefont\bf % reset at your pleasure \global\figtitleskip=.5\baselineskip % reset at your pleasure \let\nd\noindent % NOINDENT \def\NL{\hfill\break}% NEWLINE \def\qed{\hbox{\hskip 6pt\vrule width6pt height7pt depth1pt \hskip1pt}} \def\natural{{\rm I\kern-.18em N}} \def\N{{\bf N}} \def\integer{{\rm Z\kern-.32em Z}} \def\B{{\cal B}} \def\A{{\cal A}} \def\EE{{\mit E}} \def\GG{{\mit G}} \def\HH{{\mit H}} \def\jj{{\mit j}} \def\kk{{\mit k}} \def\mm{{\mit m}} \def\nn{{\mit n}} \def\Z{{\bf Z}} \def\real{{\rm I\kern-.2em R}} \def\R{{\bf R}} \def\complex{\kern.1em{\raise.47ex\hbox{ $\scriptscriptstyle |$}}\kern-.40em{\rm C}} \def\C{{\bf C}} \def\vs#1 {\vskip#1truein} \def\hs#1 {\hskip#1truein} \def\signed{\vskip1truein\hskip 2.5truein{Charles Radin}} \def\Sinc{\vskip .5truein\hskip 2.5truein} \def\Indent{\vskip 0truein\hskip 2.5truein} \def\Month{\ifcase\number\month \relax\or January \or February \or March \or April \or May \or June \or July \or August \or September \or October \or November \or December \else \relax\fi } \def\date{\Month \the\day, \the\year} \def\lett{\nopagenumbers\hbox{}\vskip 1truein \hskip 2.5truein{\date}\vskip.5truein} \hsize=6truein \hoffset=.25truein %was \hoffset=1.2truein \vsize=8.8truein %\voffset=1truein \pageno=1 \baselineskip=12pt \parskip=0 pt \parindent=20pt \overfullrule=0pt \lineskip=0pt \lineskiplimit=0pt \hbadness=10000 \vbadness=10000 % REPORT ONLY BEYOND THIS BADNESS \nopagenumbers %\lett %\nd \hbox{} \vs.1 \hbox{}\hs-1.5 \vbox{\epsfxsize=7.5truein\epsfbox{jfig1.ps}} \vs.1 \centerline{Figure 1} \vfill \eject \hbox{} \epsfig 1.15\hsize; jfig2.ps; \vs-.5 \centerline{Figure 2} \vfill \eject \hbox{} \vs2 \nd \hs.2 \vbox{\epsfxsize=4.5truein\epsfbox{jfig7new.ps}} \vs.3 \nd \hs1.2 \hbox{kite}\hs2 \hbox{dart}\hfil \vs.4 \centerline{\hs-.75 Figure 3} \vfill\eject \hbox{} \vbox{\epsfxsize=6truein\epsfbox{pinwheel3.ps}} \vs.1 \centerline{Figure 4} \vfill\eject \hbox{} \epsfig 1.15\hsize; Penrose6.ai; \vs-.5 \centerline{Figure 5} \vfill \eject \hbox{}\vs1 \epsfig .8\hsize; fig6-1.eps; \hs1.75 type 1\hs2 type 2\vs.1 \nd \centerline{a)} \hbox{}\vs1 \epsfig .8\hsize; fig6-2.eps; \vs.1 \nd \centerline{b)} \vs1 \nd \centerline{Figure 6} \vfill\eject \hbox{}\vs2 \nd \epsfig .8\hsize; square.eps; \vs.1 \nd \centerline{Figure 7} \vfill\eject \hbox{}\vs2 \nd \epsfig .8\hsize; squares2.ps; \vs.1 \nd \centerline{Figure 8} \vfill\eject \bye