Monte Carlo Method Drawing

Question

I would like to produce a Monte-Carlo-Plot with tikz and pgfplots, similar to this:

enter image description here

I've already tried to adapt from this thread:

Filling specified area by random dots in TikZ

I've tried defining the quarter-circle as a function (y=sqrt(1-x^2). Looks kind of ugly.

So I've tried the method submitted by Claudio Fiandrino.

\begin{tikzpicture}

\draw [-latex, thick] (0, 0) -- (0, 6) node  [above] {\Large{$y$}};
\draw [-latex, thick] (0, 0) -- (6, 0) node  [right] {\Large{$x$}};
\draw [thick] (0, 5) -- (5, 5);
\draw [thick] (5, 0) -- (5, 5);

\draw [thick] (5,0 ) arc (0:90:5);

\clip (5, 0) arc (0:90:5)--++(5,0) arc(160:320:0); 
\drawdiagram[
 num points=600,
 use points equal width,
 point width=0.5pt,
 point fill color=blue,
 random point diagram] at (0, 0){};
 \end{tikzpicture}

This is as far as I got. How do I get red dot in the other area? I just want a plain plot, no animation.

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score 5 · Answer 1 · edited May 12 '15 at 14:33

You can also generate points and evaluate them with pgfmathparse.

\documentclass{article}
\usepackage[natural, table, fixpdftex, hyperref]{xcolor}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows,positioning,matrix,calc}

%%%<
\usepackage{verbatim}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{2pt}%
%%%>

\def\x{0}
\def\y{0}
\def\k{0}
\def\radius{5}

\begin{document}
\begin{tikzpicture}
    \draw[fill=gray, opacity=0.1] (\radius,0) arc(0:90:\radius) -- (0,0) -- cycle;
    \draw[gray, opacity=0.25] (0,0) rectangle (\radius,\radius);
    \draw[->] (0,0) -- (1.1*\radius,0);
    \draw[->] (0,0) -- (0,1.1*\radius);
    \foreach \i in {1,2,...,1000}{%
        \typeout{Point \i}%
        \pgfmathsetmacro\x{\radius*rnd}%
        \typeout{X \x}%
        \pgfmathsetmacro\y{\radius*rnd}%
        \typeout{Y \y}%
        \pgfmathsetmacro\k{(pow(\x,2)+pow(\y,2)) <pow(\radius,2)}%
        \typeout{im Kreis?: \k}%
        \pgfmathparse{ifthenelse(\k==1,"red","blue")}%
        \fill[\pgfmathresult] (\x,\y)circle(0.5pt);%
    }
\end{tikzpicture}
\end{document}

Result

cheers!

Welcome to TeX.SX! You can have a look at our starter guide to familiarize yourself further with our format. — Martin Schröder, May 12 '15 at 14:09

score 2 · Answer 2 · answered May 12 '15 at 09:10

You can use two different clipping with the help of scopes:

\begin{tikzpicture}

\draw [-latex, thick] (0, 0) -- (0, 6) node  [above] {\Large{$y$}};
\draw [-latex, thick] (0, 0) -- (6, 0) node  [right] {\Large{$x$}};
\draw [thick] (0, 5) -- (5, 5);
\draw [thick] (5, 0) -- (5, 5);

\draw [thick] (5,0 ) arc (0:90:5);

\begin{scope}
    \clip (5, 0) arc (0:90:5)--++(5,0) arc(160:320:0); 
    \node[
         num points=600,
         use points equal width,
         point width=0.5pt,
         point fill color=blue,
         random point diagram] at (0, 0){};
\end{scope}
\begin{scope}
    \clip (5, 0) arc (0:90:5)  -- (0,0) -- cycle; 
    \node[
         num points=600,
         use points equal width,
         point width=0.5pt,
         point fill color=red,
         random point diagram] at (0, 0){};
\end{scope}
\end{tikzpicture}

Please complete the snippet to a full document example. – Heiko Oberdiek May 12 '15 at 14:39 — Heiko Oberdiek, May 12 '15 at 14:39

Monte Carlo Method Drawing

2 Answers2

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