# Example: Fibonacci spiral

Published 2009-08-03 | Author: Andrew Mertz

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% Fibonacci spiral
% Author: Andrew Mertz
\documentclass{minimal}
\usepackage{amsmath,tikz}
\usetikzlibrary{backgrounds,calc}
\begin{document}
% I have seen many beautiful depictions of Fibonacci spirals and
% golden spirals. So I thought it would be nice to make a Fibonacci
% spiral in TikZ. I like the look of white on black so here I define a
% black background rectangle.
\begin{tikzpicture}[background rectangle/.style={fill=black},
show background rectangle]
% Create some counters for holding the Fibonacci numbers
\newcounter{a}
\newcounter{b}
\newcounter{temp}

% Initialize the counters
\setcounter{a}{0}
\setcounter{b}{1}

% The spiral will start at the origin
\coordinate (0) at (0,0);

% This loop defines the number of turns in the spiral. Note that we
% will have to be careful not to overflow our counters or make the
% spiral too large for TeX to handle. This is easy to do as the
% Fibonacci sequence grows exponentially.
\foreach \i in {1,...,18}
{
% Get the "name" of the last point on the spiral
\pgfmathsetmacro{\lastpoint}{\i-1}

% Compute the angle for this turn of the spiral
\pgfmathsetmacro{\startangle}{mod(\i-1,4) * 90}

% Draw this turn of the spiral and remember the point where we end
\draw[white] (\lastpoint) arc
(\startangle : \startangle + 90 : \value{b}/10.0pt) coordinate (\i);

% Compute the next Fibonacci number
\setcounter{temp}{\value{b}}
\setcounter{a}{\value{temp}}
}

% Add some framing for the spiral while at the same time not "boxing"
% it in. Note that to put a square around each turn of the spiral we
% could have just used the command \draw[white] (\lastpoint)
% rectangle (\i); after drawing each turn in the loop above.
\foreach \i in {1,3,...,17}
{
\pgfmathsetmacro{\lastpoint}{\i-1}
\draw[white] (\lastpoint) -| (\i);
}

\foreach \i in {2,4,...,16}
{
\pgfmathsetmacro{\lastpoint}{\i-1}
\draw[white] (\lastpoint) |- (\i);
}

\draw[white] (17) -- (17 |- 18);

% Add some text displaying the formula for the Fibonacci numbers
\node(eq) at ($(18) + (2.5,1)$)
[white,text width = 2cm,font=\fontsize{8}{8}\selectfont] {
\begin{displaymath}
f(n) = \left\{
\begin{array}{lr}
0 & \text{~~if } n = 0\\
1 & \text{~~if } n = 1\\
f(n-1) + f(n-2) & \text{~~if } n \geq 2\\
\end{array}
\right.
\end{displaymath}
};
\end{tikzpicture}
\end{document}
% LocalWords:  tikzpicture eq lr TikZ


• #1 Nilay, August 4, 2009 at 11:25 a.m.

hi,

i tried to compile this code on my machine. And i get following error message . Can you pl. help me ?

(/usr/share/texmf/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex
! Undefined control sequence.
\pgfsetplottension ...ttension {\pgf@sys@tonumber
\pgf@x }
l.104 \pgfsetplottension{0.5}

• #2 Kjell Magne Fauske, August 4, 2009 at 2:20 p.m.

What version of PGF are you using Nilay? I assume it works with PGF 2.0 or later, but I have only tested it using a recent CVS build of PGF

• #3 Andrew Mertz, August 4, 2009 at 8:30 p.m.

I have tested it with TeX Live 2008 using PGF 2.0.

• #4 Vinny, June 6, 2010 at 8:16 a.m.

I have the same error message. I have a clean installation of teTeX in CentOS 5.5 and I'm using the latest build of pgf/tikz. Can anyone help? 