%% $Id: pst-lsystem-doc.tex 820 2018-09-26 09:52:39Z herbert $
\documentclass[fontsize=11pt,english,BCOR=10mm,DIV=12,bibliography=totoc,parskip=false,
  headings=small, headinclude=false,footinclude=false,oneside,abstract=on]{pst-doc}
\usepackage{pst-lsystem}
\let\pstFV\fileversion
\usepackage{dtk-logos}
\usepackage{xltabular}
\renewcommand\bgImage{%
\begin{pspicture}(-2,-0.5)(3,6)
\pslsystem[
 Start=Y,
 X={X[-FFF][+FFF]FX},
 Y={YFX[+Y][-Y]},
 Angle=25,
 N=6,
 Ftype=1,
 BaseLength=2.5pt,
 usecolor=2](0,0)
\psdot(0,0)
\end{pspicture}
}

\addbibresource{\jobname.bib}


\lstset{language=PSTricks,
   morekeywords={pslsystem},basicstyle=\footnotesize\ttfamily,
 literate=%
   {Ö}{{\"O}}1
   {Ä}{{\"A}}1
   {Ü}{{\"U}}1
   {ß}{{\ss}}1
   {ü}{{\"u}}1
   {ä}{{\"a}}1
   {ö}{{\"o}}1
   {~}{{\textasciitilde}}1
}
\begin{document}

\title{\texttt{pst-lsystem}}
\subtitle{Creating images, based on the Lindenmayer-system; v.\pstFV}
\author{Herbert Voß}
\docauthor{}
\date{\today}
\maketitle

\tableofcontents

\begin{abstract}
\noindent
\LPack{pst-lsystem} loads by default the following packages:  \LPack{pst-xkey}, and, of course \LPack{pstricks}.
All should be already part of your local \TeX\ installation. If not, or in case
of having older versions, go to \url{http://www.CTAN.org/} and load the newest version.



\vfill\noindent
Thanks to \\
Michel Charpentier,
and last but not least
   \url{http://mathworld.wolfram.com}.

\end{abstract}


\clearpage


\section{Introduction}
A L-system or Lindenmayer system is a parallel rewriting system and a type of
formal grammar. An L-system consists of an alphabet of symbols that can be used
to make strings, a collection of production rules that expand each symbol into
some larger string of symbols, an initial »axiom« string from which to begin construction,
and a mechanism for translating the generated strings into geometric structures.
L-systems were introduced and developed in 1968 by Aristid Lindenmayer,
a Hungarian theoretical biologist and botanist at the University of Utrecht.~\cite{wikipedia}


\section{Usage}
There are no optional arguments for the package:
\begin{verbatim}
\usepackage{pst-lsystem}
\end{verbatim}

There is only one command:

\begin{BDef}
\Lcs{pslsystem}\OptArgs\Largr{x,y}
\end{BDef}

If the coordinates for the origin are missing, then $(0,0)$ is assumed. The L-System ist
defined by the three functions $F$, $X$, and $Y$. At least one function must be given.

\subsection{Optional arguments}

The following optional arguments for the macro are possible:

\begin{xltabular}{\linewidth}{@{} l l X @{}}\toprule
\emph{name} & \emph{default} & \emph{menaing}\\\midrule
\Lkeyword{F} & & Rule $F\rightarrow(F)$\\
\Lkeyword{X} & & Rule $X\rightarrow(F,X,Y)$\\
\Lkeyword{Y} & & Rule $Y\rightarrow(F,X,Y)$\\
\Lkeyword{Start} & & Startrule $S\rightarrow(F,X,Y)$\\
\Lkeyword{Angle} & 45 & Angle for the drection change\\
\Lkeyword{N} & 5 & Number of the recursive calls\\
\Lkeyword{Ftype} & 4 & How the F-rule should be handled\\
\Lkeyword{BaseLength} & 1mm & The length of a base line, created by the ruke F (Forward)\\
\Lkeyword{usecolor} & 0 & Which color should be used for the lines.\\
%\define@key[psset]{pst-lsystem}{order}[5]{\pst@getint{#1}\psk@lsystem@order}
%\define@key[psset]{pst-lsystem}{factor}[2]{\pst@checknum{#1}\psk@lsystem@factor}
% Size (the smaller, the bigger), no need to be changed, normally
%\define@key[psset]{pst-lsystem}{size}[4]{\pst@getint{#1}\psk@lsystem@size}
%\define@key[psset]{pst-lsystem}{type}[0]{\pst@getint{#1}\psk@lsystem@type}
\bottomrule
\end{xltabular}

\bigskip
If the rules contain square brackets then it must be enclosed by braces:
\verb|X=F[-X]| is wrong and \verb|X={F[-X]}| is correct.

\subsection{Different types for the F-rule}

It depends to the given rule(s) what kind of the F-type must be used.
There are five possibilities:

\begin{xltabular}{\linewidth}{@{} >{\ttfamily}l X @{}}
0 & $F\rightarrow \textrm{draw line element}$ \\
 & in PostScript: \verb|/F { D } def|\\
1 & $F\rightarrow \textrm{If loop variable }=0 \textrm{ then draw line element}$\\
 & in PostScript: \verb|/F { 0 eq { D } if } def|\\
2 & $F\rightarrow \textrm{If loop variable }=0 \textrm{ then draw line element and keep variable}$\\
 & in PostScript: \verb|/F { dup 0 eq { D } if } def|\\
3 & $F\rightarrow \textrm{draw line element and delete current loop variable}$\\
 & in PostScript: \verb|/F { pop D } def|\\
4 & $F\rightarrow \textrm{If loop variable }=0 $ then draw line element! If not $=0$ decrease loop variable, duplicate it
   $n-1$ times (n is the number of functions in $F$) and put F-rule on stack\\
 & in PostScript: \verb|/F { dup 0 eq { D }{ 1 sub N 1 sub {dup} repeat F-rule } ifelse pop } def|
\end{xltabular}

\iffalse
\begin{verbatim}
\ifcase\psk@lsystem@Ftype
 /F { D } def    % type 0
\or % 1
 /F { 0 eq { D } if } def
\or % 2
 /F { dup 0 eq { D } if } def
\or % 3
 /F { pop D } def
\else % 4
 /F { dup 0 eq { D }{ 1 sub \psk@lsystem@Fnumber {dup} repeat \psk@lsystem@F } ifelse pop } def
\fi
\end{verbatim}
\fi

The function D does nothing else than drawing a line in the current direction.
Its length is given by the optional parameter BaseLength.

\subsection{Color}
There are four predefined color modes, where mode=0 is no color.


\psset{linewidth=0.1pt}

\section{Examples}
\subsection{Dragon}
\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-2,-1.5)(4,6)
\pslsystem[
 X=-FX++FY-,
 Y=+FX--FY+,
 Ftype=1,
 Start=X,
 Angle=45,
 N=9,
 BaseLength=2mm](0,0)
\psdot(0,0)
\end{pspicture}
\end{LTXexample}

\subsection{Hilbert}
\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-1,-0.5)(4,4)
\pslsystem[
 X=-YF+XFX+FY-,
 Y=+XF-YFY-FX+,
 Ftype=3,
 Start=X,
 Angle=90](0,0)
\psdot(0,0)
\end{pspicture}
\end{LTXexample}



\clearpage
\subsection{Kochflake}

If the rule for \Lkeyword{Start} has more than one function name, one has to repeat
the number of iterations, which is \Lkeyword{N}, before every following function, but not
for the first one. That is done already internally:

\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-2,-.5)(5,6)
\pslsystem[
 Start=F--NF--NF,%    repeat number of iterations N
 F=F+F--F+F,
 Angle=60,
 N=4,
 BaseLength=2pt,
 linecolor=red](0,0)
\psdot(0,0)
\end{pspicture}
\end{LTXexample}



\subsection{Plant 1}

\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-2,-2.3)(4,6)
\pslsystem[
 Start=F,
 F={FF-[-F+F+F]+[+F-F-F]},
 Angle=22.5,
 BaseLength=2pt,
 usecolor=4](0,-2)
\psdot(0,-2)
\end{pspicture}
\end{LTXexample}


\clearpage

\subsection{Plant 2}


\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-3,-2.3)(2,6)
\pslsystem[
 Start=X,
 X={F-[[X]+X]+F[+FX]-X},
 F=FF,
 Angle=22.5,
 N=6,
 BaseLength=1.25pt,
 usecolor=3](0,-2)
\psdot(0,-2)
\end{pspicture}
\end{LTXexample}



\subsection{Plant 3}

\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-2,-2.5)(2,5)
\psset{xunit=3}
\pslsystem[
 Start=F,
 F={F[+F]F[-F][F]},
 Angle=20,
 usecolor=3](0,-2)
\psdot(0,-2)
\end{pspicture}
\end{LTXexample}

\clearpage


\clearpage

\subsection{Plant 4}

\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-2,-0.5)(3,6)
\pslsystem[
 Start=Y,
 X={X[-FFF][+FFF]FX},
 Y={YFX[+Y][-Y]},
 Angle=25,
 N=6,
 Ftype=1,
 BaseLength=2.5pt,
 usecolor=2](0,0)
\psdot(0,0)
\end{pspicture}
\end{LTXexample}



\subsection{Plant 5}

\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-3,-.5)(3,9)
\pslsystem[
 Start=X,
 X={F[+X][-X]FX},
 F={FF},
 Angle=25,
 N=7,
 BaseLength=1pt,
 usecolor=2](0,0)
\psdot(0,0)
\end{pspicture}
\end{LTXexample}

\clearpage

\clearpage

\subsection{Plant 6}

\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-3,-.5)(3,9)
\pslsystem[
 Start=X,
 X={F[+X]F[-X]+X},
 F={FF},
 Angle=20,
 N=7,
 BaseLength=1pt,
 usecolor=2](0,0)
\psdot(0,0)
\end{pspicture}
\end{LTXexample}

\subsection{Plant 7}

\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-3,-.5)(3,9)
\pslsystem[
 Start=F,
 F={F[+F]F[-F]F},
 Angle=25,
 BaseLength=1pt,
 usecolor=2](0,0)
\psdot(0,0)
\end{pspicture}
\end{LTXexample}

\clearpage


\subsection{Plant 8}

\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-4,-.5)(5,9)
\pslsystem[
 Start=F,
 F={F[+F[+F][-F]F][-F[+F][-F]F]F[+F][-F]F},
 Angle=30,
 BaseLength=1pt,
 usecolor=4](0,0)
\psdot(0,0)
\end{pspicture}
\end{LTXexample}

\subsection{Special case}

\begin{LTXexample}[pos=r]
\begin{pspicture}[showgrid=true](-2,-0.5)(1,4)
\pslsystem[
 Start=X,
 F=FF,
 X=F+X-F-X+F,
 Angle=90,
 N=6,
 BaseLength=1pt](0,0)
\psdot(0,0)
\end{pspicture}
\end{LTXexample}



\clearpage
\section{List of all optional arguments for \nxLPack{pst-lsystem}}

\xkvview{family=pst-lsystem,columns={key,type,default}}


\bgroup
\raggedright
\nocite{*}
\printbibliography
\egroup

\printindex



\end{document}



%                 F=F+FF-FF-F-F+F+FF-F-F+F+FF+FF-F,

You are viewing proxied material from ftp.icm.edu.pl. The copyright of proxied material belongs to its original authors. Any comments or complaints in relation to proxied material should be directed to the original authors of the content concerned. Please see the disclaimer for more details.