%% Copyright 2013 Kevin Ryde
%%
%% This file is part of Math-PlanePath.
%%
%% Math-PlanePath is free software; you can redistribute it and/or modify it
%% under the terms of the GNU General Public License as published by the Free
%% Software Foundation; either version 3, or (at your option) any later
%% version.
%%
%% Math-PlanePath is distributed in the hope that it will be useful, but
%% WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
%% or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
%% for more details.
%%
%% You should have received a copy of the GNU General Public License along
%% with Math-PlanePath. If not, see .
%% Usage: latex dragon-pgf-latex.tex
%% xdvi dragon-pgf-latex.dvi
%% See dragon-pgf-plain.tex for more comments. The F,S here behave
%% the same as there.
%%
%% The rule here is a 45-degree variation which keeps the net
%% direction unchanged after expansion. This means the curve endpoint
%% remains in a fixed direction horizontal no matter what expansion
%% level is applied.
%%
%% Does Mandelbrot's book ``Fractal Geometry of Nature'' have an
%% expansion like this, but maybe with just a single drawing symbol?
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{lindenmayersystems}
\begin{document}
\pgfdeclarelindenmayersystem{Dragon curve}{
\symbol{S}{\pgflsystemdrawforward}
\rule{F -> -F++S-}
\rule{S -> +F--S+}
}
\foreach \i in {1,...,8} {
\hbox{
order=\i
\hspace{.5em}
\begin{tikzpicture}[baseline=0pt]
\draw
[lindenmayer system={Dragon curve, step=10pt,angle=45, axiom=F, order=\i}]
lindenmayer system;
\end{tikzpicture}
\hspace{1em}
}
\vspace{.5ex}
}
\end{document}