# How to create equi-distant nodes on a spiral with TikZ?

I have borrowed the following code to draw a spiral using one of the existing posts in TEX.SE.

\begin{tikzpicture}
\draw [domain=0:25.1327,variable=\t,smooth,samples=55]
plot[mark=*,mark options={fill=white}] ({\t r}: {0.002*\t*\t});
\end{tikzpicture}


As seen, nodes in the resulting spiral get closer and closer as they approach the center. What I'd like to have is to specify a set of nodes on the spiral that are equally distant from their adjacent ones. That is, they do not get closer to each other towards the center as in the figure above. The resulting spiral can be assumed as an approximation of the existing one which of course would no longer be looking smooth.

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– Tom Bombadil Jun 24 '13 at 23:06
Which distance is meant? The one as in the TeXample linked by Tom Bombadil and Jake’s answer (direct straight line) or along the path? – Qrrbrbirlbel Jun 25 '13 at 1:41

If you don't need to reproduce your existing spiral exactly, you can use a path with a constant segment length and a corner angle that increases with the square root of the distance:

\documentclass[border=5mm]{standalone}

\usepackage{tikz}

\begin{document}
\begin{tikzpicture}

\draw  (0,0) \foreach \t in {0.1,0.2,...,3}{
-- ++({sqrt(\t)*700}:0.4cm)
};
\draw [fill=white] circle [radius=1pt] (0,0) \foreach \t in {0.1,0.2,...,3}{
};

\end{tikzpicture}

\end{document}

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Based on your statement "a corner angle that increases with the square root of the distance" and your defined \t variable, I think \t does not represent any geometrical distance. What do you think of it? – kiss my armpit Jun 25 '13 at 2:03
@mozartstraße: \t is proportional to the distance travelled along the path, since each segment has the same length (0.4cm). – Jake Jun 25 '13 at 2:06
Okey. Thank you. – kiss my armpit Jun 25 '13 at 2:11

With PSTricks. Just for fun!

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{multido,pst-node}
\begin{document}
\begin{pspicture}[showgrid](-5,-5)(5,5)
\def\points{}%
\multido{\r=0.0+0.1}{90}{\xdef\points{\points(!1 \r\space sqrt 700 mul PtoC)}}
\psset{showpoints,dotstyle=o,dotscale=2}
\rput(-1,0){\expandafter\psrline\points}
\end{pspicture}
\end{document}


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it's funny that you're going to have the tikz gold badge before the one for pstricks :) +1 – cmhughes Jun 25 '13 at 3:05
@cmhughes: You are a good analyst. Thank you! – kiss my armpit Jun 25 '13 at 4:08