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\listfiles
\documentclass[11pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{geometry,lmodern}
\usepackage{pstricks}
\usepackage{showexpl}
%\lstset{wide=true}
\usepackage{pst-fractal}
\let\myFV\fileversion
\usepackage{url}
\usepackage[bottom]{footmisc}
\usepackage{fancyhdr}
\usepackage{abstract}
\pagestyle{fancy}
\usepackage{url}
\def\UrlFont{\small\ttfamily}
\makeatletter
\def\verbatim@font{\small\normalfont\ttfamily}
\makeatother
\lfoot{\small\ttfamily\jobname.tex}
\cfoot{}
\rfoot{\thepage}
\renewcommand{\headrulewidth}{0pt}
\renewcommand{\footrulewidth}{0pt}
\let\myPart\part
\renewcommand{\part}[1]{\clearpage\myPart{#1}}
\newcommand{\PS}{PostScript}
\newcommand\CMD[1]{\texttt{\textbackslash#1}}
\psset{subgriddiv=0,gridlabels=7pt,gridcolor=black!15}
\usepackage[pdfauthor={Herbert Voss},pdftitle={Fractals},linktocpage,colorlinks]{hyperref}
%
%
\begin{document}
\author{Herbert Voß\thanks{voss@perce.de}}
\date{\today}
\title{Fractals: pst-fractal v\myFV\\Documentation}
\maketitle%
\begin{abstract}
The well known \verb+pstricks+ package offers excellent macros to insert more or less complex
graphics into a document. \verb+pstricks+ itself is the base for several other additional packages,
which are mostly named \verb+pst-xxxx+, like \verb+pst-fractal+.
This version uses the extended keyval package \verb+xkeyval+, so be sure that you have installed
this package together with the spcecial one \verb+pst-xkey+ for PSTricks. The \verb+xkeyval+
package is available at \href{ftp://ftp.dante.de/pub/tex/macros/latex/contrib/xkeyval/}{CTAN:/macros/latex/contrib/xkeyval/}.
It is also important that after \verb+pst-fractal+ no package is loaded, which uses the old keyval interface.
The fractals are really big, which is the reason why this document is about 15 MByte.
\vspace*{2cm}
\end{abstract}%
\tableofcontents
\section{Julia and Mandelbrot sets}
The syntax of the \verb+psfractal+ macro is simple
\begin{verbatim}
\psfractal[settings](x0,y0)(x1,y1)
\end{verbatim}
All Arguments are optional, \verb+psfractal+ is the same as \verb+\psfractal(-1,-1)(1,1)+.
The Julia and Mandelbrot sets are a graphical representation of the following sequence
$x$ is the real and $y$ the imaginary part of the complex number $z$. $C(x,y)$ is a complex constant
and preset by $(0,0)$.
\begin{align}
z_{n+1}(x,y) &= (z_n(x,y))^2 +C(x,y)\\
\end{align}
\subsection{Julia sets}
A Julia set is given with
\begin{align}
z_{n+1}(x,y) &= (z_n(x,y))^2 +C(x,y)\\
z_0 &= (x_0;y_0)
\end{align}
$(x_0;y_0)$ is the starting value.
\begin{LTXexample}[width=3cm]
\psfractal
\end{LTXexample}
\begin{LTXexample}[width=5cm]
\psfractal[xWidth=5cm,yWidth=5cm,
baseColor=white,
dIter=20](-2,-2)(2,2)
\end{LTXexample}
\subsection{Mandelbrot sets}
A Mandelbrot set is given with
\begin{align}
z_{n+1}(x,y) &= (z_n(x,y))^2 +C(x,y)\\
z_0 &= (0;0)\\
C(x,y) &= (x_0;y_0)
\end{align}
$(x_0;y_0)$ is the starting value.
\begin{LTXexample}[width=3cm]
\psfractal[type=Mandel]
\end{LTXexample}
\begin{LTXexample}[width=6.5cm]
\psfractal[type=Mandel,
xWidth=6cm,yWidth=4.8cm,
baseColor=white,
dIter=10](-2,-1.2)(1,1.2)
\end{LTXexample}
\subsection{Sierpinski triangle}
The triangle must be given by three mandatory arguments:
\begin{verbatim}
\psSier[settings](x0,y0)(x1,y1)(x2,y2)
\end{verbatim}
In difference to \verb|psfractal| it doesn't reserve any space, this is the
reason why it should be part of a \verb|pspicture| environment.
\begin{LTXexample}[width=6.5cm]
\begin{pspicture}(5,5)
\psSier(0,0)(2,5)(5,0)
\end{pspicture}
\end{LTXexample}
\section{The options}
\subsection{\texttt{type}}
Can be of "`Julia"' (default) or "`Mandel"'.
\begin{LTXexample}[width=4.5cm]
\psfractal\quad \psfractal[type=Mandel]
\end{LTXexample}
\subsection{\texttt{baseColor}}
The color for the convergent part.
\begin{LTXexample}[pos=t]
\psfractal[xWidth=5cm,yWidth=5cm,dIter=10](-2,-2)(2,2)\quad
\psfractal[xWidth=5cm,yWidth=5cm,baseColor=white,dIter=10](-2,-2)(2,2)
\end{LTXexample}
\subsection{\texttt{xWidth} and \texttt{yWidth}}
These values define the physical width of the fractal.
\begin{LTXexample}[pos=t]
\psfractal[type=Mandel,xWidth=12.8cm,yWidth=10.8cm,dIter=5](-2.5,-1.3)(0.7,1.3)
\end{LTXexample}
\subsection{\texttt{cx} and \texttt{cy}}
Define the starting value for the complex constant number $C$.
\begin{LTXexample}[pos=t]
\psset{xWidth=5cm,yWidth=5cm}
\psfractal[dIter=2](-2,-2)(2,2)\quad \psfractal[dIter=2,cx=-1.3,cy=0](-2,-2)(2,2)
\end{LTXexample}
\subsection{\texttt{dIter}}
The color is set by wavelength to RGB conversion of the iteration number, where
\verb+dIter+ is the step, predefined by 1. The wavelength is given by
the value of iter added by 400.
\begin{LTXexample}[pos=t]
\psset{xWidth=5cm,yWidth=5cm}
\psfractal[dIter=30](-2,-2)(2,2)\quad \psfractal[dIter=10,cx=-1.3,cy=0](-2,-2)(2,2)
\end{LTXexample}
\subsection{\texttt{maxIter}}
\verb+maxIter+ is the number of the maximum iteration until it leaves the loop.
It is predefined by 255, but internally multiplied by \texttt{dIter}.
\begin{LTXexample}[pos=t]
\psset{xWidth=5cm,yWidth=5cm}
\psfractal[maxIter=50,dIter=3](-2,-2)(2,2)\quad
\psfractal[maxIter=30,cx=-1.3,cy=0](-2,-2)(2,2)
\end{LTXexample}
\subsection{\texttt{maxRadius}}
if the square of distance of $z_n$ to the origin of the complex coordinate system
is greater as \texttt{maxRadius} then the algorithm leaves the loop
and sets the point. \texttt{maxRadius} should always be the square of the "`real"'
value, it is preset by 100.
\begin{LTXexample}[pos=t]
\psset{xWidth=5cm,yWidth=5cm}
\psfractal[maxRadius=30,dIter=10](-2,-2)(2,2)\quad
\psfractal[maxRadius=30,dIter=30,cx=-1.3,cy=0](-2,-2)(2,2)
\end{LTXexample}
\subsection{\texttt{plotpoints}}
This option is only valid for the Sierpinski triangle and preset by 2000.
\begin{LTXexample}[pos=t]
\begin{pspicture}(5,5)
\psSier(0,0)(2.5,5)(5,0)
\end{pspicture}\quad
\begin{pspicture}(5,5)
\psSier[plotpoints=10000](0,0)(2.5,5)(5,0)
\end{pspicture}
\end{LTXexample}
\section{PDF output}
\verb|pst-fractal| is based on the popular \verb|pstricks| package and writes pure \PS code\cite{PostScript}, so it is not possible to run \TeX{} files with pdf\LaTeX{} when there are pstricks macros in the document. If you still need a PDF output use one of the following possibilities:
\begin{itemize}
\item package \verb|pdftricks.sty|\cite{pdftricks}
\item the for Linux free available program VTeX/Lnx\footnote{\url{http://www.micropress-inc.com/linux/}}
\item build the PDF with \verb|ps2pdf| (\verb|dvi|$\rightarrow$\verb|ps|$\rightarrow$\verb|pdf|)
\item use the \verb|pst-pdf| package.\footnote{\url{http://www.ctan.org/CTAN/macros/latex/contrib/pst-pdf/}}
\end{itemize}
You do not need to load \verb|pstricks.sty|, it will be done by \verb|pst-fractal| by default.
\section{FAQ}
\begin{itemize}
\item The fractal is not correct placed.
Be sure that you view your output with a dvi viewer which can show PostScript code, like
kdvi but not xdvi. It is better to run \verb|dvips| and then view the ps-file with \verb|gv|.
\item Unknown PostScript command:
Be sure that you have the ''newest`` \verb|pstricks-add.tex| file
\begin{verbatim}
\def\fileversion{2.85}
\def\filedate{2007/04/01}
\end{verbatim}
\end{itemize}
\section{Credits}
\nocite{*}
\bibliographystyle{plain}
\bibliography{pst-fractal-doc}
\end{document}
|
