# Tikz-drawing Brownian motion on the unit circle $S^{1}$

I'm trying to draw Brownian motion on the unit circle $S^{1}$ $({Z \in \mathbb{C} : |Z|=1})$ using the package TikZ. Here is the picture that I am trying to get:

I have just a simple example to circle :

    \begin{tikzpicture}[scale=3]
\draw[step=.5cm,gray,very thin] (-1.4,-1.4) grid (1.4,1.4);
\draw (-1.5,0) -- (1.5,0);
\draw (0,-1.5) -- (0,1.5);
\draw (0,0) circle (1cm);
\draw (3mm,0mm) arc (0:30:3mm);
\end{tikzpicture}

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## With PSTricks (version 1)

\documentclass[pstricks,border=12pt]{standalone}
\SpecialCoor
\everypsbox{\scriptsize}
\begin{document}
\begin{pspicture}(-2,-2)(2,2)
\pscircle[linecolor=blue]{1}
\qdisk(0,0){2pt}
\qdisk(1;30){2pt}
\psline(1;30)
\uput{4pt}[-100](1;30){$z$}
\rput{30}(1;30){%
\psline[linecolor=red]{<->}(0,1)(0,0)(1,0)%
\psarc[arcsep=\pslinewidth](0,0){6pt}{0}{90}%
\uput{2pt}[30]{*0}(0,1){$i_z$}%
\uput{2pt}[-45]{*0}(1,0){$z$}%
}
\end{pspicture}
\end{document}


## With PSTricks (version 2)

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-node}
\begin{document}
\begin{pspicture}[showgrid](-2,-2)(2,2)
\pnode(0,0){O}
\pnode(1;30){P}
\pnode([nodesep=-1]{O}P){X}
\pnode([offset=-1]{O}P){Y}
\pscircle[linecolor=blue](O){1}
\qdisk(O){2pt}
\qdisk(P){2pt}
\psline(P)
\psline[linecolor=red]{<->}(X)(P)(Y)
\psarc[arcsep=\pslinewidth,origin={P}](P){6pt}{(X)}{(Y)}
\psset{labelsep=3pt}
\uput[-20](P){$z$}
\uput[20](Y){$i_z$}
\uput[0](X){$z$}
\end{pspicture}
\end{document}


## Without PSTricks

\documentclass[tikz,border=12pt]{standalone}
\begin{document}
\Large
\begin{tikzpicture}[scale=3,>=stealth]
\draw[blue] (0,0) circle (1);
\fill (0,0) circle (1pt);
\fill (30:1) circle (1pt);
\draw (0,0) -- (30:1);
\node[anchor=150] at (30:1) {$z$};
\begin{scope}[shift={(30:1)},rotate=30]
\node[anchor=west] at (0,1) {$i_z$};
\node[anchor=north] at (1,0) {$z$};
\draw[red,<->] (0,1) -- (0,0) -- (1,0);
\draw (0:6pt) arc (0:90:6pt);
\end{scope}
\end{tikzpicture}
\end{document}


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hi Thanks Mr Mozartstrabe so much now it's work for me when i Compile it with xelatex or latex -> dvips -> ps2pdf in latex but please if you could to make it wit Tikz – Educ Jul 5 '13 at 10:45
Thanks so much Mr mozarstrabe it's work but i prefer in Tikz Thanks again – Educ Jul 5 '13 at 10:50
Thanks so much just on question how can i make it big in pdf because it plots small in my document – Educ Jul 5 '13 at 11:05
Thanks so much for ur time and ur help Please accept,Mr Mozarstrabe , the assurances of my highest consideration – Educ Jul 5 '13 at 11:12
sorry Mr Mozartstrasse – Educ Jul 5 '13 at 13:29