Difference between revisions of "File:ZexIteT.jpg"

Latest revision as of 10:31, 20 July 2020

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

%

% % 
% file ZexIte.pdf should be generated with the code above in order to compile the Latex document below. % 
% Copyleft 2012 by Dmitrii Kouznetsov %
\documentclass[12pt]{article} % 
\usepackage{geometry} % 
\usepackage{graphicx} % 
\usepackage{rotating} % 
\paperwidth 1208pt % 
\paperheight 1208pt % 
\topmargin -103pt % 
\oddsidemargin -73pt % 
\textwidth 1404pt % 
\textheight 1404pt % 
\pagestyle {empty} % 
\newcommand \sx {\scalebox} % 
\newcommand \rot {\begin{rotate}} % 
\newcommand \ero {\end{rotate}} % 
\newcommand \ing {\includegraphics} % 
\parindent 0pt% 
\pagestyle{empty} % 
\begin{document} % 
\begin{picture}(1202,1202) % 
%\put(10,10){\ing{IterPowPlot}} % 
%\put(10,10){\ing{IterEq2plot}} % 
\put(0,0){\ing{ZexIte}} % 
\put(11,1184){\sx{4.4}{$y$}} % 
\put(04,1090){\sx{4}{$11$}} % 
\put(04,990){\sx{4}{$10$}} % 
\put(11,890){\sx{4}{$9$}} % 
\put(11,790){\sx{4}{$8$}} % 
\put(11,690){\sx{4}{$7$}} % 
\put(11,590){\sx{4}{$6$}} % 
\put(11,490){\sx{4}{$5$}} % 
\put(11,390){\sx{4}{$4$}} % 
\put(11,290){\sx{4}{$3$}} % 
\put(11,190){\sx{4}{$2$}} % 
\put(11,090){\sx{4}{$1$}} % 
% 
\put(91,6){\sx{4}{$1$}} % 
\put(191,6){\sx{4}{$2$}} % 
\put(291,6){\sx{4}{$3$}} % 
\put(391,6){\sx{4}{$4$}} % 
\put(492,6){\sx{4}{$5$}} % 
\put(592,6){\sx{4}{$6$}} % 
\put(693,6){\sx{4}{$7$}} % 
\put(794,6){\sx{4}{$8$}} % 
\put(894,6){\sx{4}{$9$}} % 
\put(982,6){\sx{4}{$10$}} % 
\put(1082,6){\sx{4}{$11$}} % 
\put(1180,6){\sx{4.4}{$x$}} % 
% 

\put(116,1058){\sx{5}{\rot{88}$n\!=\!2$\ero}} % 
\put(182,1058){\sx{5}{\rot{88}$n\!=\!1$\ero}} % 
\put(141,706){\sx{4.5}{\rot{86}$y\!=\!\mathrm{zex}(x)$\ero}} % 
%
\put(512,1030){\sx{5}{\rot{72}$n\!=\!0.3$\ero}} % 
\put(629,1032){\sx{5}{\rot{64}$n\!=\!0.2$\ero}} % 
\put(804,1037){\sx{5}{\rot{56}$n\!=\!0.1$\ero}} % 
% 
\put(1072,1052){\sx{5}{\rot{44}$n\!=\!0$\ero}} % 
\put(772,752){\sx{5}{\rot{44}$y\!=\!x$\ero}} % 
% 
\put(1028,762){\sx{5}{\rot{32}$n\!=\!-0.1$\ero}} % 
\put(1014,590){\sx{5}{\rot{23}$n\!=\!-0.2$\ero}} % 
\put(1006,470){\sx{5}{\rot{17}$n\!=\!-0.3$\ero}} % 
%
\put(510,108){\sx{4.3}{\rot{3}$y\!=\!\mathrm{LambertW}(x)$\ero}} % 
\put(1010,142){\sx{5}{\rot{2}$n\!=\!-1$\ero}} % 
\put(1010,83){\sx{5}{\rot{1}$n\!=\!-2$\ero}} % 
% 
\end{picture} % 
\end{document} % 
%

File history

Click on a date/time to view the file as it appeared at that time.

	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

You cannot overwrite this file.

File usage

The following 2 pages use this file:

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Horizontal resolution	150 dpi
Vertical resolution	150 dpi