File:ExpIte4T.jpg

Summary

Title / Description	iteration of exponential, ${\displaystyle ~y=\exp ^{n}(x)~}$ for various values of number ${\displaystyle n}$ of iteration.
Citizendium author & Copyright holder	Copyright © Dmitrii Kouznetsov. See below for licence/re-use information.
Date created	2012.11.11
Country of first publication	Japan
Notes	Copied from TORI
Other versions	http://tori.ils.uec.ac.jp/TORI/index.php/File:ExpIte4T.jpg
Using this image on CZ	Please click here to add the credit line, then copy the code below to add this image to a Citizendium article, changing the size, alignment, and caption as necessary. {{Image|ExpIte4T.jpg|right|350px|Add image caption here.}}

C++ generator of curves

// Files ado.cin, fsexp.cin, fslog.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 "fsexp.cin"
#include "fslog.cin"

// z_type tra(z_type z){ return exp(z)+z;}
// z_type F(z_type z){ return log(suzex(z));}
// z_type G(z_type z){ return auzex(exp(z));}

#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("ExpIte4.eps","w");  ado(o,804,804);
fprintf(o,"402 402 translate\n 100 100 scale\n");
fprintf(o,"1 setlinejoin 2 setlinecap\n");
for(n=-4;n<5;n++) {M(-4,n)L(4,n)}
for(m=-4;m<5;m++) {M(m,-4)L(m,4)}
// M(M_E,0)L(M_E,1) M(0,M_E)L(1,M_E)  
fprintf(o,".004 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 0 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 .5 0 RGB S\n");
// M(0,0) L(12.03,12.03) fprintf(o,".04 W 0 1 0 RGB S\n");
DO(m,700){x=-4.02+.02*m; y=exp(x);          if(m==0) M(x,y) else L(x,y) if(x>4.03||y>4.03) break;} fprintf(o,".032 W 0 1 0 RGB S\n");
DO(m,700){x=-4.02+.02*m; y=exp(exp(x));     if(m==0) M(x,y) else L(x,y) if(x>4.03||y>4.03) break;} fprintf(o,".032 W 0 1 0 RGB S\n");
DO(m,700){x=-4.02+.02*m; y=exp(exp(exp(x)));if(m==0) M(x,y) else L(x,y) if(x>4.03||y>4.03) break;} fprintf(o,".032 W 0 1 0 RGB S\n");
DO(m,700){y=-4.02+.02*m; x=exp(y);          if(m==0) M(x,y) else L(x,y) if(x>4.03||y>4.03) break;} fprintf(o,".032 W 1 0 1 RGB S\n");
DO(m,700){y=-4.02+.02*m; x=exp(exp(y));     if(m==0) M(x,y) else L(x,y) if(x>4.03||y>4.03) break;} fprintf(o,".032 W 1 0 1 RGB S\n");
DO(m,700){y=-4.02+.02*m; x=exp(exp(exp(y)));if(m==0) M(x,y) else L(x,y) if(x>4.03||y>4.03) break;} fprintf(o,".032 W 1 0 1 RGB S\n");
for(n=0;n<34;n+=1) {DO(m,700){x=-4.01 +.02*m; y=Re(FSLOG(x)); y=Re(FSEXP(.1*n+y)); if(m==0) M(x,y) else L(x,y) if(x>4.03||y>4.03) break;}}
for(n=-33;n<0;n+=1){t=Re(FSEXP( FSLOG(-4.)-.1*n));
                    DO(m,700){x=t +.02*m; y=Re(FSLOG(x)); y=Re(FSEXP(.1*n+y)); if(m==0) M(x,y) else L(x,y) if(x>4.03||y>4.03) break;}}
  fprintf(o,".01 W 0 0 0 RGB S\n");
fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%');  fclose(o);
      system("epstopdf ExpIte4.eps"); 
      system(    "open ExpIte4.pdf"); //for macintosh
      getchar(); system("killall Preview"); // For macintosh
}

Latex generator of labels

% %<br> % file PowPlo.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 806pt % <br> \paperheight 806pt % <br> \topmargin -105pt % <br> \oddsidemargin -73pt % <br> \textwidth 1100pt % <br> \textheight 1100pt % <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}(802,802) % <br> %\put(10,10){\ing{PowPlo}} % <br> %\put(0,0){\ing{TraItu3}} % <br> \put(0,0){\ing{ExpIte4}} % <br> \put(411,788){\sx{3}{$y$}} % <br> \put(411,693.6){\sx{2.9}{$3$}} % <br> \put(411,593.4){\sx{2.9}{$2$}} % <br> \put(411,493.2){\sx{2.9}{$1$}} % <br> \put(411,393){\sx{2.9}{$0$}} % <br> \put(407,292.8){\sx{2.9}{$-1$}} % <br> \put(407,192.6){\sx{2.9}{$-2$}} % <br> \put(407,092.4){\sx{2.9}{$-3$}} % <br>  % <br> \put(081,408){\sx{2.9}{$-3$}} % <br> \put(181,408){\sx{2.9}{$-2$}} % <br> \put(281,408){\sx{2.9}{$-1$}} % <br> \put(396,408){\sx{2.9}{$0$}} % <br> \put(497,408){\sx{2.9}{$1$}} % <br> \put(597,408){\sx{2.9}{$2$}} % <br> \put(697,408){\sx{2.9}{$3$}} % <br> \put(787,408){\sx{3}{$x$}} % <br>  % <br> \put(6,748){\sx{3}{\rot{4}$n\!=\!3.2$\ero}} % <br> \put(6,708){\sx{3}{\rot{3}$n\!=\!3.1$\ero}} % <br> \put(6,675){\sx{3}{\rot{3}$n\!=\!3$\ero}} % <br> \put(5,643){\sx{3}{\rot{3}$n\!=\!2.9$\ero}} % <br> \put(6,345){\sx{3}{\rot{1}$n\!=\!0.6$\ero}} % <br> % \put(7,308){\sx{3}{\rot{4}$n\!=\!0.4$\ero}} % <br> \put(7,280){\sx{3}{\rot{5}$n\!=\!0.3$\ero}} % <br> \put(8,242){\sx{3}{\rot{9}$n\!=\!0.2$\ero}} % <br> \put(9,185){\sx{3}{\rot{11}$n\!=\!0.1$\ero}} % <br>  % <br> \put(50,36){\sx{3}{\rot{45}$n\!=\!0$\ero}} % <br> % <br> \put(202,5){\sx{3}{\rot{76}$n\!=\!-0.1$\ero}} % <br> \put(263,5){\sx{3}{\rot{82}$n\!=\!-0.2$\ero}} % <br> \put(299,5){\sx{3}{\rot{84}$n\!=\!-0.3$\ero}} % <br> \put(691,5){\sx{3}{\rot{84}$n\!=\!-3$\ero}} % <br> \put(724,5){\sx{3}{\rot{83}$n\!=\!-3.1$\ero}} % <br> \put(764,5){\sx{3}{\rot{82}$n\!=\!-3.2$\ero}} % <br>  % <br> \put(480,600){\sx{3.6}{\rot{69}$y\!=\!\exp(x)$\ero}} % <br> \put(641,630){\sx{3.4}{\rot{44}$y\!=\!x$\ero}} % <br> \put(650,484){\sx{3.6}{\rot{19}$y\!=\!\ln(x)$\ero}} % <br> \end{picture} % <br> \end{document} % <br> %

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