montecarlopi.tex

\documentclass[beamer,tikz]{standalone}

% Define some custom colors
\definecolor{seaborncolorblind1}{RGB}{1,115,178}
\definecolor{seaborncolorblind2}{RGB}{222,143,5}
\definecolor{seaborncolorblind3}{RGB}{2,158,115}

\usetikzlibrary{overlay-beamer-styles}
\usetikzlibrary{calc,math}

\begin{document}
\newcount\ptctr
\begin{standaloneframe}{}{}{}
  \begin{tikzpicture}

    \draw[step=0.5, gray, very thin] (-1, -1) grid (1, 1);
    \draw[black, thick] (-1, -1) rectangle (1, 1);

    \draw[black, thick, fill=seaborncolorblind1,nearly transparent] (0, 0) circle [radius=1];

    \foreach \x in {-1, -0.5, 0, 0.5, 1} {
      \node[anchor=east,text=gray,font=\tiny] at (-1, \x) {\x};
      \node[anchor=north,text=gray,font=\tiny] at (\x, -1) {\x};
    }

    \node [anchor=south, visible on=<1>] at (0, 1.25) {\(\pi \approx 4\frac{|\mathrm{in}|}{|\mathrm{all}|}\)};

    \foreach  \i [evaluate=\i as \x using rand, evaluate=\i as \y using rand] in {1, 2, ..., 500} {
      \pgfmathsetmacro{\d}{sqrt(\x*\x + \y*\y)}
      \pgfmathparse{\d <= 1 ? int(1):int(0)}
      \ifnum\pgfmathresult>0\relax
        \node at (\x, \y) [circle, fill=seaborncolorblind3, seaborncolorblind3, inner sep=0.5pt, visible on=<2>] { };
        \global\advance\ptctr by 1\relax
      \else
        \node at (\x, \y) [circle, fill=seaborncolorblind2, seaborncolorblind2, inner sep=0.5pt, visible on=<2>] { };
      \fi
    }

    \pgfmathsetmacro{\n}{round(int(\the\ptctr) / 2)}
    \pgfmathsetmacro{\ourPi}{4 * (\n / 500)}

    \node [anchor=south, visible on=<2>] at (0, 1.25) {\(\pi \approx 4\frac{\n}{500} = \pgfmathprintnumber[precision=3]{\ourPi}\)};

  \end{tikzpicture}
\end{standaloneframe}
\end{document}

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