How to create a Sierpinski triangle in LaTeX with numbers in the triangles?

Question

I would need to create a Sierpinski triangle in LaTeX, with numbers in the triangles.

As follows:

I have tried to modify the following code:

\begin{figure}[h]
\centering
\begin{tikzpicture}[scale=2]
    \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}
    }


    \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}
\caption{Sierpiński Sieve.}
\label{fig:SierpinskiTriangle}
\end{figure}

But without success :( How can I write numbers in the triangles??

Related: How to create a Sierpinski triangle in LaTeX? – Werner Sep 05 '16 at 17:21 — Werner, Sep 05 '16 at 17:21
Please always post complete examples we can compile! – cfr Sep 05 '16 at 22:17 — cfr, Sep 05 '16 at 22:17

score 8 · Accepted Answer · edited Apr 13 '17 at 12:34

8

You could use Mark Wibrow's solution, but it employs lualatex and if you don't already use it, it might not be worth it to switch to a different engine. Besides, that solution uses hexagons instead of triangles and it doesn't color them.

So here's an alternative version based on that answer but that has all the necessary changes. Plus it works with regular pdflatex, since we use pgfmath to do the proper calculations.

Output

enter image description here

Code

\documentclass[tikz,margin=10pt]{standalone}
\usetikzlibrary{shapes.geometric}

\tikzset{
    tris/.style={#1,
    font=\ttfamily,
    regular polygon, regular polygon sides=3, 
    minimum size=2cm, inner sep=0pt,
}
}

\begin{document}
\begin{tikzpicture}[x=2cm*sin 60, y=3cm*cos 60]

\foreach \n in {0,...,7}{
    \foreach \k in {0,...,\n}{ 
        \pgfmathtruncatemacro\fact{factorial(\n)/(factorial(\n-\k)*factorial(\k))}
    \ifodd\fact
        \node[tris={draw,fill, text=white}] at (-\n/2+\k, -\n) {\fact};
    \else
        \node[tris] at (-\n/2+\k, -\n) {\fact};
    \fi
    }
}
\end{tikzpicture}
\end{document}

edited Apr 13 '17 at 12:34

Community

1

answered Sep 05 '16 at 19:34

Alenanno

37,338

Thank you very much!!. I could ask how to make the image smaller? – Darío A. Gutiérrez Sep 05 '16 at 20:03
@DarioGutierrez No problem! You can add scale=0.8, every node/.style={transform shape} to the tikzpicture options (next to x=2cm*sin 60, y=3cm*cos 60). – Alenanno Sep 05 '16 at 20:07
@DarioGutierrez But scaling fonts in diagrams is not recommended. – cfr Sep 05 '16 at 22:17
@cfr wouldn't that scale text properly as well? If not, he can simply modify the x and y values, along with the node sizes. – Alenanno Sep 05 '16 at 22:43
That's my point. It is better not to scale text in diagrams to arbitrary sizes unless you really are stuck with no choice. It is better to use one of the standard sizes to ensure consistency. – cfr Sep 05 '16 at 23:59

How to create a Sierpinski triangle in LaTeX with numbers in the triangles?

1 Answers1

Output

Code