Graphics, Figures & Tables ⇒ How to create two copies of the Sierpinski triangle?

[moitetajni]

Hello. I am trying to create two copies of the Sierpinski triangle like this:


For this I borrowed some code I found online and tried to modify it a little bit to meet my needs. Here's my edited version of the code:

Code: Select all

\documentclass[border=5mm]{standalone}
\usepackage{tikz}

\usetikzlibrary{lindenmayersystems}

\begin{document}%
\def\trianglewidth{2cm}%
\pgfdeclarelindenmayersystem{Sierpinski triangle}{
    \symbol{X}{\pgflsystemdrawforward}
    \symbol{Y}{\pgflsystemdrawforward}
    \rule{X -> X-Y+X+Y-X}
    \rule{Y -> YY}
}%

\tikzset
{
l-system={step=\trianglewidth/(2^6), order=6, angle=-120}
}

\begin{tikzpicture}[scale=2]
\fill [black] (0,0) -- ++(0:\trianglewidth) -- ++(120:\trianglewidth) -- cycle;
\draw [draw=none] (0,0) l-system [l-system={Sierpinski triangle, axiom=X},fill=white];
\end{tikzpicture}
\end{document}

However, I don't know how to create the second copy of the Sierpinski triangle in the same tikzpicture enviroment (minipage does not work for my purpose). I tried to create a copy of the code inside the tikzpicture environment and then modify some parameters but it didn't work. This is the code of that attempt:

Code: Select all

\documentclass[border=5mm]{standalone}
\usepackage{tikz}

\usetikzlibrary{lindenmayersystems}

\begin{document}%
\def\trianglewidth{2cm}%
\pgfdeclarelindenmayersystem{Sierpinski triangle}{
    \symbol{X}{\pgflsystemdrawforward}
    \symbol{Y}{\pgflsystemdrawforward}
    \rule{X -> X-Y+X+Y-X}
    \rule{Y -> YY}
}%

\tikzset
{
l-system={step=\trianglewidth/(2^6), order=6, angle=-120}
}

\begin{tikzpicture}[scale=2]
\fill [black] (0,0) -- ++(0:\trianglewidth) -- ++(120:\trianglewidth) -- cycle;
\draw [draw=none] (0,0) l-system [l-system={Sierpinski triangle, axiom=X},fill=white];

% It does not look like the Sierpinski triangle
\fill [black] (3,0) -- ++(0:\trianglewidth) -- ++(120:\trianglewidth) -- cycle;
\draw [draw=none] (3,0) l-system [l-system={Sierpinski triangle, axiom=X},fill=white];
\end{tikzpicture}
\end{document}

So my question would be: how can I modify the code to obtain the two copies of the Sierpinki triangles?

Note: The code was taken from https://www.overleaf.com/latex/examples ... zOB36GVvvx and was created by Jake on TeX SE.

[mas]

You can repeat the code inside a scope environment with a shift in the x-direction.

Code: Select all

\documentclass[border=5mm]{standalone}
\usepackage{tikz}

\usetikzlibrary{lindenmayersystems}

\begin{document}%
\def\trianglewidth{2cm}%
\pgfdeclarelindenmayersystem{Sierpinski triangle}{
    \symbol{X}{\pgflsystemdrawforward}
    \symbol{Y}{\pgflsystemdrawforward}
    \rule{X -> X-Y+X+Y-X}
    \rule{Y -> YY}
}%

\tikzset
{
l-system={step=\trianglewidth/(2^6), order=6, angle=-120}
}

\begin{tikzpicture}[scale=2]

  \fill [black] (0,0) -- ++(0:\trianglewidth) -- 
    ++(120:\trianglewidth) -- cycle;

  \draw [draw=none] (0,0) l-system 
    [l-system={Sierpinski triangle, axiom=X},fill=white];

  \begin{scope}[xshift=3cm]
  \fill [black] (0,0) -- ++(0:\trianglewidth) -- 
    ++(120:\trianglewidth) -- cycle;

  \draw [draw=none] (0,0) l-system 
    [l-system={Sierpinski triangle, axiom=X},fill=white];
    
  \end{scope}
\end{tikzpicture}
\end{document}

x.png (8.92 KiB) Viewed 4448 times

You can also use the pic method of repeating an object.

Code: Select all

\documentclass[border=5mm]{standalone}
\usepackage{tikz}

\usetikzlibrary{lindenmayersystems}

\begin{document}%
\def\trianglewidth{2cm}%
\pgfdeclarelindenmayersystem{Sierpinski triangle}{
    \symbol{X}{\pgflsystemdrawforward}
    \symbol{Y}{\pgflsystemdrawforward}
    \rule{X -> X-Y+X+Y-X}
    \rule{Y -> YY}
}%

\tikzset
{
l-system={step=\trianglewidth/(2^6), order=6, angle=-120}
}

\tikzset{
  sierp/.pic={
    \fill [black] (0,0) -- ++(0:\trianglewidth) -- 
      ++(120:\trianglewidth) -- cycle;

    \draw [draw=none] (0,0) l-system 
      [l-system={Sierpinski triangle, axiom=X},fill=white];
}}


\begin{tikzpicture}[scale=2]

  \pic at (0,0) {sierp} ;
  \pic at (1,1) {sierp} ;

\end{tikzpicture}
\end{document}

x2.png (16.43 KiB) Viewed 4446 times

[Johannes_B]

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