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diff --git a/Master/texmf-dist/doc/generic/pst-fractal/pst-fractal-doc.tex b/Master/texmf-dist/doc/generic/pst-fractal/pst-fractal-doc.tex new file mode 100644 index 00000000000..430f66d6eb5 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pst-fractal/pst-fractal-doc.tex @@ -0,0 +1,256 @@ +\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} |