File:Paradoxical decomposition F2.png
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![File:Paradoxical decomposition F2.png](http://upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Paradoxical_decomposition_F2.png/623px-Paradoxical_decomposition_F2.png)
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Summary
DescriptionParadoxical decomposition F2.png |
English: Illustration for the paradoxical decomposition of |
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Source | Own work, made using MetaPost program. | ||||||||
Author | David Benbennick | ||||||||
Permission (Reusing this file) |
I, the copyright holder of this work, hereby publish it under the following licenses:
![]() ![]() ![]() This file is licensed under the Creative Commons Attribution-Share Alike 2.0 Generic license.
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Linethickness = 1pt; beginfig(1); recursion_depth := 6; const := 2.2; numeric length; length := 1.3in / (const**recursion_depth); pickup pencircle scaled Linethickness; picture p, q, r; for i = 1 upto recursion_depth - 2: draw (0,0) -- (length,0); draw (0,-length) -- (0,length); length := length * const; currentpicture := currentpicture shifted (length,0); p := currentpicture rotated 90; q := p yscaled -1; addto currentpicture also p; addto currentpicture also q; endfor; draw (0,0) -- (length,0); draw (0,-length) -- (0,length); length := length * const; currentpicture := currentpicture shifted (length,0); p := currentpicture rotated 90; q := p yscaled -1; r := currentpicture xscaled -1; addto currentpicture also p; addto currentpicture also q; addto currentpicture also r; draw (-length,0) -- (length,0); draw (0,-length) -- (0,length); dotlabel.urt(btex$e$etex, (0,0)); dotlabel.ulft(btex$a$etex, (length,0)); dotlabel.lrt(btex$b$etex, (0,length)); pair P, Q, R; P := (-0.5length, 0.5length); Q := (-length, 0.9length); draw P .. Q .. (-2length,0) .. Q yscaled -1 .. P yscaled -1 .. cycle withcolor red; label.top(btex$S(a^{-1})$etex, (-1.2length, 0.9length)) withcolor red; Q := (length, length); R := (0, 2length); draw P xscaled -1 --- Q .. R .. (-2.2length, 0) .. R yscaled -1 .. Q yscaled -1 --- P scaled -1 .. cycle withcolor blue; label.rt(btex$aS(a^{-1})$etex, (1.1length,1.1length)) withcolor blue; currentpicture := currentpicture shifted (10cm,10cm); endfig; end;
I saved the above as Paradoxical_decomposition_F2.mp, and the following LaTeX program as Paradoxical_decomposition_F2.tex:
%&latex \documentclass[12pt]{article} \usepackage{graphicx} \pagestyle{empty} \begin{document} \includegraphics{Paradoxical_decomposition_F2.1} \end{document}
I then ran the following commands:
mpost Paradoxical_decomposition_F2 tex Paradoxical_decomposition_F2 dvips -mode ljfzzz -D 1200 Paradoxical_decomposition_F2 -o convert -density 1200 Paradoxical_decomposition_F2.ps Paradoxical_decomposition_F2.pnm pnmcrop Paradoxical_decomposition_F2.pnm | pnmtopng > Paradoxical_decomposition_F2.png advpng -z4 Paradoxical_decomposition_F2.png
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 07:22, 27 January 2011 | ![]() | 2,977 × 2,864 (104 KB) | ChrstphrChvz | ImageOptim with PNGOUT |
06:54, 12 June 2005 | ![]() | 2,977 × 2,864 (121 KB) | Dbenbenn | higher resolution version, 2977x2864 | |
04:30, 13 December 2004 | ![]() | 514 × 494 (9 KB) | Dbenbenn | Illustration for the paradoxical decomposition of F_2 |
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