draw Sierpinski's triangle in Pascal's triangle in tikz (30 row or more)

Question

I want to draw Sierpinski's triangle in Pascal's triangle in tikz for 30 rows or more but my code only works for 13 rows.

\documentclass{article}
\usepackage{tikz}
\usepackage{pdfpages}
\begin{document}
\begin{center} 
\newdimen\R
\R=.4cm
\newcommand\mycolor{white}
\newcommand\thik{\pgflinewidth}
\begin{tikzpicture}[line width=.8pt]
\foreach \k in {0,...,13}{
\begin{scope}[shift={(-60:{sqrt(3)*\R*\k})}]
\pgfmathtruncatemacro\ystart{13-\k}
\foreach \n in {0,...,\ystart}{
\pgfmathtruncatemacro\newn{\n+\k}
%binomila ceeficients
\pgfmathsetmacro{\value}{1};
\ifthenelse{\k>0}{
\foreach \b in {1,...,\k}{
\pgfmathtruncatemacro{\value}{\value*(\newn-\b+1)/\b)};
\global\let\value=\value
}
}{};
\pgfmathtruncatemacro{\rest}{mod(\value,2)};
\ifthenelse{\rest=0}{\def\mycolor{green}}{}

\begin{scope}[shift={(-120:{sqrt(3)*\R*\n})}]
\draw[top color=\mycolor!20,bottom color=\mycolor!60] 
(30:\R) \foreach \x in {90,150,...,330} {
-- (\x:\R)}
--cycle (90:0) node {\tiny $\mathbf{\value}$};
\end{scope}
}
\end{scope}
}
\end{tikzpicture}
\end{center}
\end{document}

Answer 1

Welcome to SE! This was really fun.

I reacquainted myself with fp.sty. I have also formatted the code to be a little easier to follow (indentation is your friend!). I have tried this with as many as 35 rows -- more are certainly possible. Note, however, that as the number of rows increases, so does the time necessary to compile this. I've also made it into a macro for easy experimentation -- and entertainment!

UPDATE!

I got up early this morning to play with my new toy. I was greeted with a TeX error: Dimension too large. Odd because I have the output graphics to prove that the code worked just fine yesterday. Apparently, overnight, PGF decided that it would choke using mod. Not to be deterred, I found \modulo at How do I calculate n modulo 3 in LaTeX?, which I have employed here. Thank you @Werner! Long live StackExchange!!

The output was incorrect -- that has been corrected as well.

\documentclass[tikz,border=0.25in]{standalone}

\usepackage{fp}

\newlength{\R}
\setlength{\R}{.75cm}
\newcommand\mycolor{white}

%% https://tex.stackexchange.com/questions/34424/how-do-i-calculate-n-modulo-3-in-latex/34425#34425
\newcommand{\modulo}[2]{%
  \FPeval{\result}{trunc(#1-(#2*trunc(#1/#2,0)),0)}\result%
}

%%  #1 determines which hexagons are filled (default is 2); #2 is number of rows
\newcommand{\makesierp}[2][2]{%
    \begin{tikzpicture}[line width=.8pt]
        \foreach \k in {0,...,#2}{
            \begin{scope}[shift={(-60:{sqrt(3)*\R*\k})}]
                \pgfmathtruncatemacro\ystart{#2-\k}
                \foreach \n in {0,...,\ystart}{
                    \pgfmathtruncatemacro\newn{\n+\k}
                    \pgfmathsetmacro{\myvalue}{1}
                    \ifnum\k>0
                        \foreach \b in {1,...,\k}{
                            \FPeval\myvalue{trunc(\myvalue*(\newn-\b+1)/\b:0)}
                            \global\let\myvalue=\myvalue
                        }
                    \fi
                    \modulo{\myvalue}{#1}%
                    \ifnum\result=0 \def\mycolor{green}\fi%
                    \begin{scope}[shift={(-120:{sqrt(3)*\R*\n})}]
                        \draw[fill=\mycolor!20] 
                        (30:\R) \foreach \x in {90,150,...,330} {
                        -- (\x:\R)}
                        --cycle (90:0)node[font=\tiny] {$\mathbf{\myvalue}$};
                    \end{scope}
                }
            \end{scope}
        }
    \end{tikzpicture}
}

\begin{document}

\makesierp{20}

\end{document}

The second graphic was generated with \makesierp[5]{20}

Have fun!