我画了一个卡尔金–威尔夫树没有“For”，但我想用循环来绘制这棵树。
\documentclass[10pt]{article}
\usepackage{mathtools}
\usepackage{pgf,tikz}
\begin{document}
\begin{tikzpicture}[x=1cm,y=1.2cm]
\begin{scope}[line width=1.5pt,draw=red,font=\Huge]
%%%%%سطر صفر و یک
\node (A11) at (0,0) {$\dfrac{1}{1}$};
\node (A12) at (-3,0) {$\frac{1}{2}$};
\node (A21) at (3,0) {$\frac{2}{1}$};
\draw (A12) -- (A11) -- (A21);
%%%
\end{scope}
\begin{scope}[line width=1.5pt,draw=red!90,font=\huge]
%%%سطر دو
\node (A31) at (3,3) {$\frac{3}{1}$};
\node (A23) at (3,-3) {$\frac{2}{3}$};
\draw (A31) -- (A21) -- (A23);
\node (A13) at (-3,3) {$\frac{1}{3}$};
\node (A32) at (-3,-3) {$\frac{3}{2}$};
\draw (A13) -- (A12) -- (A32);
%%%
%%%
\end{scope}
\begin{scope}[line width=1.5pt,draw=red!80,font=\LARGE]
%%%سطر سوم
\node (A43) at (-4.5,3) {$\frac{4}{3}$};
\node (A14) at (-1.5,3) {$\frac{1}{4}$};
\draw (A43) -- (A13) -- (A14);
%%%
%%%
\node (A35) at (-4.5,-3) {$\frac{3}{5}$};
\node (A52) at (-1.5,-3) {$\frac{5}{2}$};
\draw (A35) -- (A32) -- (A52);
%%%
%%%
\node (A41) at (1.5,3) {$\frac{4}{1}$};
\node (A34) at (4.5,3) {$\frac{3}{4}$};
\draw (A41) -- (A31) -- (A34);
%%%
%%%
\node (A53) at (4.5,-3) {$\frac{5}{3}$};
\node (A25) at (1.5,-3) {$\frac{2}{5}$};
\draw (A25) -- (A23) -- (A53);
%%%
%%%
\end{scope}
\begin{scope}[line width=1.5pt,draw=red!70,font=\Large]
%%%سطر چهارم
\node (A47) at (-4.5,4.5) {$\frac{4}{7}$};
\node (A73) at (-4.5,1.5) {$\frac{7}{3}$};
\draw (A47) -- (A43) -- (A73);
%%%
%%%
\node (A54) at (-1.5,4.5) {$\frac{5}{4}$};
\node (A15) at (-1.5,1.5) {$\frac{1}{5}$};
\draw (A15) -- (A14) -- (A54);
%%%
%%%
\node (A74) at (4.5,4.5) {$\frac{7}{4}$};
\node (A37) at (4.5,1.5) {$\frac{3}{7}$};
\draw (A74) -- (A34) -- (A37);
%%%
%%%
\node (A45) at (1.5,4.5) {$\frac{4}{5}$};
\node (A51) at (1.5,1.5) {$\frac{5}{1}$};
\draw (A51) -- (A41) -- (A45);
%%%
%%%
\node (A85) at (-4.5,-4.5) {$\frac{8}{5}$};
\node (A38) at (-4.5,-1.5) {$\frac{3}{8}$};
\draw (A85) -- (A35) -- (A38);
%%%
%%%
\node (A57) at (-1.5,-4.5) {$\frac{5}{7}$};
\node (A72) at (-1.5,-1.5) {$\frac{7}{2}$};
\draw (A57) -- (A52) -- (A72);
%%%
%%%
\node (A58) at (4.5,-4.5) {$\frac{5}{8}$};
\node (A83) at (4.5,-1.5) {$\frac{8}{3}$};
\draw (A58) -- (A53) -- (A83);
%%%
%%%
\node (A75) at (1.5,-4.5) {$\frac{7}{5}$};
\node (A27) at (1.5,-1.5) {$\frac{2}{7}$};
\draw (A75) -- (A25) -- (A27);
%%%
%%%
\end{scope}
\begin{scope}[line width=1.5pt,draw=red!60]
%%%سطر پنجم
%%%%%بالایی ها
\node (A710) at (-5.25,1.5) {$\frac{7}{10}$};
\node (A103) at (-3.75,1.5) {$\frac{10}{3}$};
\draw (A710) -- (A73) -- (A103);
%%%
%%%
\node (A117) at (-5.25,4.5) {$\frac{11}{7}$};
\node (A411) at (-3.75,4.5) {$\frac{4}{11}$};
\draw (A117) -- (A47) -- (A411);
%%%
%%%
\node (A16) at (-2.25,1.5) {$\frac{1}{6}$};
\node (A65) at (-.75,1.5) {$\frac{6}{5}$};
\draw (A16) -- (A15) -- (A65);
%%%
%%%
\node (A94) at (-2.25,4.5) {$\frac{9}{4}$};
\node (A59) at (-.75,4.5) {$\frac{5}{9}$};
\draw (A59) -- (A54) -- (A94);
%%%
%%%
\node (A107) at (5.25,1.5) {$\frac{10}{7}$};
\node (A310) at (3.75,1.5) {$\frac{3}{10}$};
\draw (A107) -- (A37) -- (A310);
%%%
%%%
\node (A711) at (5.25,4.5) {$\frac{7}{11}$};
\node (A114) at (3.75,4.5) {$\frac{11}{14}$};
\draw (A711) -- (A74) -- (A114);
%%%
%%%
\node (A61) at (2.25,1.5) {$\frac{6}{1}$};
\node (A56) at (.75,1.5) {$\frac{5}{6}$};
\draw (A61) -- (A51) -- (A56);
%%%
%%%
\node (A49) at (2.25,4.5) {$\frac{4}{9}$};
\node (A95) at (.75,4.5) {$\frac{9}{5}$};
\draw (A95) -- (A45) -- (A49);
%%%
%%%
%%%%%پایینی ها
\node (A811) at (5.25,-1.5) {$\frac{8}{11}$};
\node (A113) at (3.75,-1.5) {$\frac{11}{3}$};
\draw (A811) -- (A83) -- (A113);
%%%
%%%
\node (A138) at (5.25,-4.5) {$\frac{13}{8}$};
\node (A513) at (3.75,-4.5) {$\frac{5}{13}$};
\draw (A513) -- (A58) -- (A138);
%%%
%%%
\node (A29) at (2.25,-1.5) {$\frac{2}{9}$};
\node (A97) at (.75,-1.5) {$\frac{9}{7}$};
\draw (A29) -- (A27) -- (A97);
%%%
%%%
\node (A125) at (2.25,-4.5) {$\frac{12}{5}$};
\node (A712) at (.75,-4.5) {$\frac{7}{12}$};
\draw (A125) -- (A75) -- (A712);
%%%
%%%
\node (A118) at (-5.25,-1.5) {$\frac{11}{8}$};
\node (A311) at (-3.75,-1.5) {$\frac{3}{11}$};
\draw (A118) -- (A38) -- (A311);
%%%
%%%
\node (A813) at (-5.25,-4.5) {$\frac{8}{13}$};
\node (A135) at (-3.75,-4.5) {$\frac{13}{5}$};
\draw (A813) -- (A85) -- (A135);
%%%
%%%
\node (A92) at (-2.25,-1.5) {$\frac{9}{2}$};
\node (A79) at (-.75,-1.5) {$\frac{7}{9}$};
\draw (A92) -- (A72) -- (A79);
%%%
%%%
\node (A512) at (-2.25,-4.5) {$\frac{5}{12}$};
\node (A127) at (-.75,-4.5) {$\frac{12}{7}$};
\draw (A512) -- (A57) -- (A127);
%%%
%%%
\end{scope}
\begin{scope}[line width=1.5pt,draw=red!50]
%%%سطر ششم
%%%%بالا چپ
%%%%بالا چپ
\node (A1118) at (-5.25,5.25) {$\frac{11}{18}$};
\node (A187) at (-5.25,3.75) {$\frac{18}{7}$};
\draw (A1118) -- (A117) -- (A187);
%%%
%%%
\node (A1511) at (-3.75,5.25) {$\frac{15}{11}$};
\node (A415) at (-3.75,3.75) {$\frac{4}{15}$};
\draw (A1511) -- (A411) -- (A415);
%%%
%%%
%%%سطر ششم
%%%%بالا چپ
%%%%پایین چپ
\node (A717) at (-5.25,2.25) {$\frac{7}{17}$};
\node (A1710) at (-5.25,.75) {$\frac{17}{10}$};
\draw (A717) -- (A710) -- (A1710);
%%%
%%%
\node (A133) at (-3.75,2.25) {$\frac{13}{3}$};
\node (A1013) at (-3.75,.75) {$\frac{10}{13}$};
\draw (A133) -- (A103) -- (A1013);
%%%
%%%
%%%سطر ششم
%%%%بالا چپ
%%%%بالا راست
\node (A913) at (-2.25,5.25) {$\frac{9}{13}$};
\node (A134) at (-2.25,3.75) {$\frac{13}{4}$};
\draw (A913) -- (A94) -- (A134);
%%%
%%%
\node (A149) at (-.75,5.25) {$\frac{14}{9}$};
\node (A514) at (-.75,3.75) {$\frac{5}{14}$};
\draw (A149) -- (A59) -- (A514);
%%%
%%%
%%%سطر ششم
%%%%بالا چپ
%%%%پایین راست
\node (A17) at (-2.25,2.25) {$\frac{1}{7}$};
\node (A76) at (-2.25,.75) {$\frac{7}{6}$};
\draw (A17) -- (A16) -- (A76);
%%%
%%%
\node (A115) at (-.75,2.25) {$\frac{11}{5}$};
\node (A611) at (-.75,.75) {$\frac{6}{11}$};
\draw (A115) -- (A65) -- (A611);
%%%
%%%
%%%سطر ششم
%%%%بالا راست
%%%%بالا راست
\node (A1811) at (5.25,5.25) {$\frac{18}{11}$};
\node (A718) at (5.25,3.75) {$\frac{7}{18}$};
\draw (A1811) -- (A711) -- (A718);
%%%
%%%
\node (A1115) at (3.75,5.25) {$\frac{11}{15}$};
\node (A154) at (3.75,3.75) {$\frac{15}{4}$};
\draw (A1115) -- (A114) -- (A154);
%%%
%%%
%%%سطر ششم
%%%%بالا راست
%%%%پایین راست
\node (A177) at (5.25,2.25) {$\frac{17}{7}$};
\node (A1017) at (5.25,.75) {$\frac{10}{17}$};
\draw (A177) -- (A107) -- (A1017);
%%%
%%%
\node (A313) at (3.75,2.25) {$\frac{3}{13}$};
\node (A1310) at (3.75,.75) {$\frac{13}{10}$};
\draw (A313) -- (A310) -- (A1310);
%%%
%%%
%%%سطر ششم
%%%%بالا راست
%%%%بالا چپ
\node (A139) at (2.25,5.25) {$\frac{13}{9}$};
\node (A413) at (2.25,3.75) {$\frac{4}{13}$};
\draw (A139) -- (A49) -- (A413);
%%%
%%%
\node (A914) at (.75,5.25) {$\frac{9}{14}$};
\node (A145) at (.75,3.75) {$\frac{14}{5}$};
\draw (A914) -- (A95) -- (A145);
%%%
%%%
%%%سطر ششم
%%%%بالا راست
%%%%پایین چپ
\node (A71) at (2.25,2.25) {$\frac{7}{1}$};
\node (A67) at (2.25,.75) {$\frac{6}{7}$};
\draw (A71) -- (A61) -- (A67);
%%%
%%%
\node (A511) at (.75,2.25) {$\frac{5}{11}$};
\node (A116) at (.75,.75) {$\frac{11}{5}$};
\draw (A511) -- (A56) -- (A116);
%%%
%%%
%%%سطر ششم
%%%%پایین چپ
%%%%پایین چپ
\node (A2113) at (-5.25,-5.25) {$\frac{21}{13}$};
\node (A821) at (-5.25,-3.75) {$\frac{8}{21}$};
\draw (A2113) -- (A813) -- (A821);
%%%
%%%
\node (A1318) at (-3.75,-5.25) {$\frac{13}{18}$};
\node (A185) at (-3.75,-3.75) {$\frac{18}{5}$};
\draw (A1318) -- (A135) -- (A185);
%%%
%%%
%%%سطر ششم
%%%%پایین چپ
%%%%بالا چپ
\node (A198) at (-5.25,-2.25) {$\frac{19}{8}$};
\node (A1119) at (-5.25,-.75) {$\frac{11}{19}$};
\draw (A198) -- (A118) -- (A1119);
%%%
%%%
\node (A314) at (-3.75,-2.25) {$\frac{3}{14}$};
\node (A1411) at (-3.75,-.75) {$\frac{14}{11}$};
\draw (A314) -- (A311) -- (A1411);
%%%
%%%
%%%سطر ششم
%%%%پایین چپ
%%%%پایین راست
\node (A1712) at (-2.25,-5.25) {$\frac{17}{12}$};
\node (A517) at (-2.25,-3.75) {$\frac{5}{17}$};
\draw (A1712) -- (A512) -- (A517);
%%%
%%%
\node (A1219) at (-.75,-5.25) {$\frac{12}{19}$};
\node (A197) at (-.75,-3.75) {$\frac{19}{7}$};
\draw (A1219) -- (A127) -- (A197);
%%%
%%%
%%%سطر ششم
%%%%پایین چپ
%%%%بالا راست
\node (A112) at (-2.25,-2.25) {$\frac{11}{2}$};
\node (A911) at (-2.25,-.75) {$\frac{9}{11}$};
\draw (A112) -- (A92) -- (A911);
%%%
%%%
\node (A716) at (-.75,-2.25) {$\frac{7}{16}$};
\node (A169) at (-.75,-.75) {$\frac{16}{9}$};
\draw (A716) -- (A79) -- (A169);
%%%
%%%
%%%سطر ششم
%%%%پایین راست
%%%%پایین راست
\node (A1321) at (5.25,-5.25) {$\frac{13}{21}$};
\node (A218) at (5.25,-3.75) {$\frac{21}{8}$};
\draw (A1321) -- (A138) -- (A218);
%%%
%%%
\node (A1813) at (3.75,-5.25) {$\frac{18}{13}$};
\node (A518) at (3.75,-3.75) {$\frac{5}{18}$};
\draw (A1813) -- (A513) -- (A518);
%%%
%%%
%%%سطر ششم
%%%%پایین راست
%%%%بالا راست
\node (A819) at (5.25,-2.25) {$\frac{8}{19}$};
\node (A1911) at (5.25,-.75) {$\frac{19}{11}$};
\draw (A819) -- (A811) -- (A1911);
%%%
%%%
\node (A143) at (3.75,-2.25) {$\frac{14}{3}$};
\node (A1114) at (3.75,-.75) {$\frac{11}{14}$};
\draw (A143) -- (A113) -- (A1114);
%%%
%%%
%%%سطر ششم
%%%%پایین راست
%%%%پایین چپ
\node (A1217) at (2.25,-5.25) {$\frac{12}{17}$};
\node (A175) at (2.25,-3.75) {$\frac{17}{15}$};
\draw (A1217) -- (A125) -- (A175);
%%%
%%%
\node (A1912) at (.75,-5.25) {$\frac{19}{12}$};
\node (A719) at (.75,-3.75) {$\frac{7}{19}$};
\draw (A1912) -- (A712) -- (A719);
%%%
%%%
%%%سطر ششم
%%%%پایین راست
%%%%بالا چپ
\node (A211) at (2.25,-2.25) {$\frac{2}{11}$};
\node (A119) at (2.25,-.75) {$\frac{11}{9}$};
\draw (A211) -- (A29) -- (A119);
%%%
%%%
\node (A167) at (.75,-2.25) {$\frac{16}{7}$};
\node (A916) at (.75,-.75) {$\frac{9}{16}$};
\draw (A167) -- (A97) -- (A916);
%%%
%%%
\end{scope}
\end{tikzpicture}
\end{document}
答案1
这可能有一些变化吗？
\documentclass[tikz,border=5]{standalone}
\usetikzlibrary{lindenmayersystems}
\newcount\cwtcounta
\newcount\cwtcountb
\newcount\cwtlevel
\pgfdeclarelindenmayersystem{calkin-wilf tree}{
\symbol{I}{%
\cwtcounta=1
\cwtcountb=1
\cwtlevel=1
}
\symbol{F}{%
\path [every calkin-wilf tree branch/.try] (0,0) -- (\pgflsystemstep,0);
\pgflsystemdrawforward
\pgflsystemstep=0.707106\pgflsystemstep
\advance\cwtlevel by1
}
\symbol{P}{%
\advance\cwtcounta by\cwtcountb
}
\symbol{Q}{%
\advance\cwtcountb by\cwtcounta
}
\symbol{N}{%
\node [every calkin-wilf tree node/.try]
{$\frac{\the\cwtcounta}{\the\cwtcountb}$};
}
\symbol{+}{\pgflsystemturnright}
\symbol{-}{\pgflsystemturnleft}
\rule{S -> IN}
\rule{N -> [-FPN][+FQN]N}
}
\tikzset{
calkin-wilf tree/.style={
lindenmayer system={calkin-wilf tree, axiom=+S, angle=90, #1},
insert path={lindenmayer system}
},
every calkin-wilf tree node/.style={
fill=white, inner sep=0.25ex, scale=1/sqrt(\cwtlevel)
},
every calkin-wilf tree branch/.style={
draw=red
}
}
\begin{document}
\begin{tikzpicture}[xscale=0.75]
\path [calkin-wilf tree={order=7, step=2cm}];
\end{tikzpicture}
\end{document}
