File:ZexIteT.jpg
Explicit plot of iterations of function Zex
$ y=\mathrm{zex}^n(x)$
for various number $n$ of iterates. Here, $\mathrm{zex}(z)\!=\!z\exp(z)$. The non-integer iterates are implemented through the superfunction of zex and its abelfunction, named SuZex and AuZex, as follows:
$ \mathrm{zex}^n(x)=\mathrm{SuZex}\Big(n+\mathrm{AuZex}(x)\Big)$
C++ generator of curves
// Files ado.cin, Tania.cin, LambertW.cin, SuZex.cin, AuZex.cin should be loaded to the working directory in order to compile the code below.
#include <math.h> #include <stdio.h> #include <stdlib.h> #define DB double #define DO(x,y) for(x=0;x<y;x++) using namespace std; #include<complex> typedef complex<double> z_type; #define Re(x) x.real() #define Im(x) x.imag() #define I z_type(0.,1.)
#include "Tania.cin" // need for LambertW #include "LambertW.cin" // need for AuZex #include "SuZex.cin" #include "AuZex.cin" #include "ado.cin" #define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y); #define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("ZexIte.eps","w"); ado(o,1204,1204);
fprintf(o,"2 2 translate\n 100 100 scale\n");
fprintf(o,"1 setlinejoin 2 setlinecap\n");
for(n=0;n<13;n++) {M(0,n)L(12,n)}
for(m=0;m<13;m++) {M(m,0)L(m,12)}
M(M_E,0)L(M_E,1) M(0,M_E)L(1,M_E) fprintf(o,".01 W S\n");
DO(m,700){x=.01 +.02*m; y=Re(LambertW(LambertW(x)));if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;} fprintf(o,".033 W 1 0 1 RGB S\n");
DO(m,700){x=.01 +.02*m; y=Re(LambertW(x));if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;} fprintf(o,".04 W 1 0 1 RGB S\n");
M(0,0) L(12.03,12.03) fprintf(o,".03 W 0 1 0 RGB S\n");
DO(m,700){x=.01 +.02*m; y=Re(zex(x)); if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;} fprintf(o,".04 W 0 1 0 RGB S\n");
DO(m,700){x=.01 +.02*m; y=Re(zex(zex(x))); if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;} fprintf(o,".033 W 0 1 0 RGB S\n");
for(n=-10;n<11;n++){
DO(m,700){x=.01 +.02*m; y=Re(auzex(x)); y=Re(suzex(.1*n+y)); if(m==0) M(x,y) else L(x,y) if(x>12.03||y>12.03) break;}
fprintf(o,".023 W 0 0 0 RGB S\n");
}
fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o);
system("epstopdf ZexIte.eps");
system( "open ZexIte.pdf"); //for macintosh
getchar(); system("killall Preview"); // For macintosh
}
Latex generator of labels
%
% %<br>
% file ZexIte.pdf should be generated with the code above in order to compile the Latex document below. %<br>
% Copyleft 2012 by Dmitrii Kouznetsov <br> %
\documentclass[12pt]{article} % <br>
\usepackage{geometry} % <br>
\usepackage{graphicx} % <br>
\usepackage{rotating} % <br>
\paperwidth 1208pt % <br>
\paperheight 1208pt % <br>
\topmargin -103pt % <br>
\oddsidemargin -73pt % <br>
\textwidth 1404pt % <br>
\textheight 1404pt % <br>
\pagestyle {empty} % <br>
\newcommand \sx {\scalebox} % <br>
\newcommand \rot {\begin{rotate}} % <br>
\newcommand \ero {\end{rotate}} % <br>
\newcommand \ing {\includegraphics} % <br>
\parindent 0pt% <br>
\pagestyle{empty} % <br>
\begin{document} % <br>
\begin{picture}(1202,1202) % <br>
%\put(10,10){\ing{IterPowPlot}} % <br>
%\put(10,10){\ing{IterEq2plot}} % <br>
\put(0,0){\ing{ZexIte}} % <br>
\put(11,1184){\sx{4.4}{$y$}} % <br>
\put(04,1090){\sx{4}{$11$}} % <br>
\put(04,990){\sx{4}{$10$}} % <br>
\put(11,890){\sx{4}{$9$}} % <br>
\put(11,790){\sx{4}{$8$}} % <br>
\put(11,690){\sx{4}{$7$}} % <br>
\put(11,590){\sx{4}{$6$}} % <br>
\put(11,490){\sx{4}{$5$}} % <br>
\put(11,390){\sx{4}{$4$}} % <br>
\put(11,290){\sx{4}{$3$}} % <br>
\put(11,190){\sx{4}{$2$}} % <br>
\put(11,090){\sx{4}{$1$}} % <br>
% <br>
\put(91,6){\sx{4}{$1$}} % <br>
\put(191,6){\sx{4}{$2$}} % <br>
\put(291,6){\sx{4}{$3$}} % <br>
\put(391,6){\sx{4}{$4$}} % <br>
\put(492,6){\sx{4}{$5$}} % <br>
\put(592,6){\sx{4}{$6$}} % <br>
\put(693,6){\sx{4}{$7$}} % <br>
\put(794,6){\sx{4}{$8$}} % <br>
\put(894,6){\sx{4}{$9$}} % <br>
\put(982,6){\sx{4}{$10$}} % <br>
\put(1082,6){\sx{4}{$11$}} % <br>
\put(1180,6){\sx{4.4}{$x$}} % <br>
% <br>
\put(116,1058){\sx{5}{\rot{88}$n\!=\!2$\ero}} % <br>
\put(182,1058){\sx{5}{\rot{88}$n\!=\!1$\ero}} % <br>
\put(141,706){\sx{4.5}{\rot{86}$y\!=\!\mathrm{zex}(x)$\ero}} % <br>
%
\put(512,1030){\sx{5}{\rot{72}$n\!=\!0.3$\ero}} % <br>
\put(629,1032){\sx{5}{\rot{64}$n\!=\!0.2$\ero}} % <br>
\put(804,1037){\sx{5}{\rot{56}$n\!=\!0.1$\ero}} % <br>
% <br>
\put(1072,1052){\sx{5}{\rot{44}$n\!=\!0$\ero}} % <br>
\put(772,752){\sx{5}{\rot{44}$y\!=\!x$\ero}} % <br>
% <br>
\put(1028,762){\sx{5}{\rot{32}$n\!=\!-0.1$\ero}} % <br>
\put(1014,590){\sx{5}{\rot{23}$n\!=\!-0.2$\ero}} % <br>
\put(1006,470){\sx{5}{\rot{17}$n\!=\!-0.3$\ero}} % <br>
%
\put(510,108){\sx{4.3}{\rot{3}$y\!=\!\mathrm{LambertW}(x)$\ero}} % <br>
\put(1010,142){\sx{5}{\rot{2}$n\!=\!-1$\ero}} % <br>
\put(1010,83){\sx{5}{\rot{1}$n\!=\!-2$\ero}} % <br>
%<br>
\end{picture} % <br>
\end{document} % <br>
%
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:50, 20 June 2013 | | 2,508 × 2,508 (973 KB) | Maintenance script (talk | contribs) | Importing image file |
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