Lindenmayer 系统案例

Question

显然，制作这样的作品的最佳方式

是 TikZ 中的 Lindenmayer 系统。

以下是我的一些尝试，根据评论中的建议进行保留。

\documentclass[tikz]{standalone}
\usetikzlibrary{lindenmayersystems}

\begin{document}
\pgfdeclarelindenmayersystem{try}{
  \symbol{S}{\pgflsystemstep=.6\pgflsystemstep}
  \rule{X -> FS[S-Y]YF}
  \rule{Y -> FS[SX-]XF}
}

\begin{tikzpicture}
    \draw [rotate=45]
    [l-system={try, axiom=X, order=10, step=124pt, angle=90}]
    lindenmayer system;
\end{tikzpicture}
\end{document} 

\documentclass[tikz]{standalone}
\usetikzlibrary{lindenmayersystems}

\begin{document}
\pgfdeclarelindenmayersystem{try}{
  \symbol{S}{\pgflsystemstep=.8\pgflsystemstep}
  \rule{X -> FX[-SFY]FX}
  \rule{Y -> FY[+FX]FY}
}

\begin{tikzpicture}
    \draw [rotate=-45]
    [l-system={try, axiom=X, order=7, step=1.2pt, angle=90}]
    lindenmayer system;
\end{tikzpicture}
\end{document} 

\documentclass[tikz]{standalone}
\usetikzlibrary{lindenmayersystems}

\begin{document}
\pgfdeclarelindenmayersystem{try}{
  \symbol{S}{\pgflsystemstep=.67\pgflsystemstep}
  \symbol{p}{\draw circle (.01\pgflsystemstep);}
  \rule{X -> FS[+S[p]Y]X}
  \rule{Y -> FS[S[p]X]Y}
}

\begin{tikzpicture}
    \draw [rotate=135]
    [l-system={try, axiom=X, order=12, step=140pt, angle=90}]
    lindenmayer system;
\end{tikzpicture}
\end{document} 

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{lindenmayersystems}

\begin{document}
\pgfdeclarelindenmayersystem{try}{
  \symbol{S}{\pgflsystemstep=.67\pgflsystemstep}
  \symbol{p}{\draw circle (.01\pgflsystemstep);}
  \rule{X -> [p]FS[-ff++SY]X}
  \rule{Y -> [p]FS[+ff--SX]Y}
}

\begin{tikzpicture}
    \draw [rotate=45]
    [l-system={try, axiom=X, order=12, step=160pt, angle=90}]
    lindenmayer system;
\end{tikzpicture}
\end{document} 

Answer 1

这还不是一个完整的答案，但由于 OP 的输入，我们可能已经接近目标。这个答案的作用是定义一个减小幅度的锯齿形的规则，以及将它们组合起来的方法。

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{lindenmayersystems}
\def\pgflsystemturnr{%
    \pgftransformrotate{-90}}%
\def\pgflsystemturnl{%
    \pgftransformrotate{90}}%

\begin{document}
\begin{tikzpicture}[l-system={step=10pt, order=7,angle=165}] 
\pgfdeclarelindenmayersystem{pft}{
    \symbol{D}{\pgflsystemdrawforward}
    \symbol{M}{\pgflsystemmoveforward}
    \symbol{S}{\pgflsystemstep=0.9\pgflsystemstep}
    \symbol{I}{\pgflsystemstep=1.1\pgflsystemstep}
    \symbol{L}{\pgflsystemstep=3\pgflsystemstep}
    \symbol{l}{\pgflsystemturnl}
    \symbol{r}{\pgflsystemturnr}
    \rule{Z -> [Y]-DDDDDSS+Z} % line up zigzag
    \rule{Y -> -DI+DI-DI+DI-DI+DI-DI+DI-DI+DI-DI+DI-DI+DI-DI+DI} % zigzag
  }
  \draw [red,rotate=-60] (0,0) l-system [l-system={pft, axiom=Z, anchor=south west}]; 
\end{tikzpicture}
\end{document}

使用这个可以获得类似于您的屏幕截图的东西。

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{lindenmayersystems}
\def\pgflsystemturnr{%
    \pgftransformrotate{-90}}%
\def\pgflsystemturnl{%
    \pgftransformrotate{90}}%
\newcounter{lmn}
\begin{document}
\begin{tikzpicture}[l-system={step=10pt, order=8,angle=165},line join=bevel,
pics/linden row/.style={code={\draw[shorten >=-#1*0.05cm] (0,0) -- (-142.5:2*#1)
foreach \XX in {1,...,#1} {coordinate[pos={pow(0.75,\XX-1)}] (p-#1-\XX)
node[circle,fill,pos={1.02*pow(0.75,\XX-1)},scale={pow(0.75,\XX-1)}]{}};
\foreach \XX in {1,...,#1}
{\draw[rotate=-57.5] (p-#1-\XX)
l-system [l-system={pft,step={pow(0.8,-#1+2*\XX+5)*4pt}, axiom=Z, anchor=west}];}}}] 
\pgfdeclarelindenmayersystem{pft}{
    \symbol{D}{\pgflsystemdrawforward}
    \symbol{M}{\pgflsystemmoveforward}
    \symbol{S}{\pgflsystemstep=0.9\pgflsystemstep}
    \symbol{I}{\pgflsystemstep=1.1\pgflsystemstep}
    \symbol{L}{\pgflsystemstep=3\pgflsystemstep}
    \symbol{l}{\pgflsystemturnl}
    \symbol{r}{\pgflsystemturnr}
    \symbol{o}{\stepcounter{lmn}%
    \pgfnode{coordinate}{center}{\pgfpointorigin}{X\number\value{lmn}}{}}%
    \symbol{c}{\pgfpathlineto{\pgfpointanchor{X\number\value{lmn}}{center}}}
    \rule{Z -> [Y]-DDDDDSS+Z} % line up zigzag
    \rule{Y -> rMl-Do[rD]I+DI-DI+DI-DI+DI-DI+DI-DI+DI-DI+DI-DI+DI-DI[c]+DI} % zigzag
  }
  \path foreach \X in {4,5,...,8} {(-30:{pow(1.2,\X)*6cm}) pic{linden row=\X}};
\end{tikzpicture}
\end{document}

Answer 2

下面是一个相当接近它的代码。

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{lindenmayersystems}

\begin{document}
\pgfdeclarelindenmayersystem{try}{
  \symbol{S}{\pgflsystemstep=.67\pgflsystemstep}
  \symbol{p}{\draw circle (.01\pgflsystemstep);}
  \rule{X -> [p]S[-FF++SY]Xf}
  \rule{Y -> [p]S[+FF--SX]Yf}
}

\begin{tikzpicture}
    \draw [rotate=45]
    [l-system={try, axiom=X, order=12, step=280pt, angle=90}]
    lindenmayer system;
\end{tikzpicture}
\end{document} 

是否可以做得更好，我不知道，欢迎大家进一步改进