%% 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: tex dragon-pgf-latex.tex
%% xdvi dragon-pgf-latex.dvi
%%
%% This a dragon curve drawn with the PGF lindenmayersystems library.
%%
%% http://sourceforge.net/projects/pgf/
%%
%% The PGF manual includes examles of Koch snowflake, Hilbert curve and
%% Sierpinski arrowhead. In the ``spy'' library section there's some
%% magnifications of the Koch and of a quadric curve too.
%%
%% In the rule here \symbol{S} is a second drawing symbol. It draws a
%% line segment the same as F, but the two different symbols let the
%% rules distinguish odd and even position line segments.
%%
%% F and S are always in pairs, F first and S second, F_S_F_S_F_S_F_S.
%% At each even position F expands to a left bend, ie with a "+" turn.
%% At each odd position S expands to a right bend, ie with a "-".
%% This is the "successive approximation" method for generating the
%% curve where each line segment is replaced by a bend to the left or
%% right according as it's at an even or odd position.
%%
%% The sequence of + and - turns resulting in the expansion follows
%% the "bit above lowest 1-bit" rule. This works essentially because
%% the bit above obeys an expansion rule
%%
%% if k even
%% bitabovelowest1bit(2k) = bitabovelowest1bit(k)
%% bitabovelowest1bit(2k+1) = 0 # the "+" in F -> F+S
%%
%% if k odd
%% bitabovelowest1bit(2k) = bitabovelowest1bit(k)
%% bitabovelowest1bit(2k+1) = 1 # the "-" in S -> F-S
%%
\input tikz.tex
\usetikzlibrary{lindenmayersystems}
\pgfdeclarelindenmayersystem{Dragon curve}{
\symbol{S}{\pgflsystemdrawforward}
\rule{F -> F+S}
\rule{S -> F-S}
}
\tikzpicture
\draw
[lindenmayer system={Dragon curve, step=10pt, axiom=F, order=8}]
lindenmayer system;
\endtikzpicture
\bye