imported>John Stephenson |
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| == Summary == | | == Summary == |
| {{Image_Details|user
| | Importing file |
| |description = [[iteration of function|iteration]] of [[exponential]], <math>~ y=\exp^n(x)~</math> for various values of number <math>n</math> of iteration.
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| |author = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
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| |date-created = 2012.11.11
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| |pub-country = Japan
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| |notes = Copied from [[TORI]]
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| |versions = http://tori.ils.uec.ac.jp/TORI/index.php/File:ExpIte4T.jpg
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| }}
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| | |
| ==[[C++]] generator of curves==
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| | |
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| // Files [[ado.cin]], [[fsexp.cin]], [[fslog.cin]]
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| //should be loaded to the working directory in order to compile the code below.
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| | |
| #include <math.h>
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| #include <stdio.h>
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| #include <stdlib.h>
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| #define DB double
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| #define DO(x,y) for(x=0;x<y;x++)
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| using namespace std;
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| #include<complex>
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| typedef complex<double> z_type;
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| #define Re(x) x.real()
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| #define Im(x) x.imag()
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| #define I z_type(0.,1.)
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| | |
| //#include "Tania.cin" // need for LambertW
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| //#include "LambertW.cin" // need for AuZex
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| //#include "SuZex.cin"
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| //#include "AuZex.cin"
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| #include "fsexp.cin"
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| #include "fslog.cin"
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| | |
| // z_type tra(z_type z){ return exp(z)+z;}
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| // z_type F(z_type z){ return log(suzex(z));}
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| // z_type G(z_type z){ return auzex(exp(z));}
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| | |
| #include "ado.cin"
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| #define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
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| #define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
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| | |
| 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);
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| fprintf(o,"402 402 translate\n 100 100 scale\n");
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| fprintf(o,"1 setlinejoin 2 setlinecap\n");
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| for(n=-4;n<5;n++) {M(-4,n)L(4,n)}
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| for(m=-4;m<5;m++) {M(m,-4)L(m,4)}
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| // M(M_E,0)L(M_E,1) M(0,M_E)L(1,M_E)
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| fprintf(o,".004 W S\n");
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| // 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");
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| // 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");
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| // M(0,0) L(12.03,12.03) fprintf(o,".04 W 0 1 0 RGB S\n");
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| 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");
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| 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");
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| 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");
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| 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");
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| 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");
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| 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");
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| 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;}}
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| for(n=-33;n<0;n+=1){t=Re(FSEXP( FSLOG(-4.)-.1*n));
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| 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;}}
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| fprintf(o,".01 W 0 0 0 RGB S\n");
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| fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o);
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| system("epstopdf ExpIte4.eps");
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| system( "open ExpIte4.pdf"); //for macintosh
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| getchar(); system("killall Preview"); // For macintosh
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| }
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| | |
| ==[[Latex]] generator of labels==
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| %<nowiki> %<br>
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| % file PowPlo.pdf should be generated with the code above in order to compile the Latex document below. %<br>
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| % Copyleft 2012 by Dmitrii Kouznetsov <br> %
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| \documentclass[12pt]{article} % <br>
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| \usepackage{geometry} % <br>
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| \usepackage{graphicx} % <br>
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| \usepackage{rotating} % <br>
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| \paperwidth 806pt % <br>
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| \paperheight 806pt % <br>
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| \topmargin -105pt % <br>
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| \oddsidemargin -73pt % <br>
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| \textwidth 1100pt % <br>
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| \textheight 1100pt % <br>
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| \pagestyle {empty} % <br>
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| \newcommand \sx {\scalebox} % <br>
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| \newcommand \rot {\begin{rotate}} % <br>
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| \newcommand \ero {\end{rotate}} % <br>
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| \newcommand \ing {\includegraphics} % <br>
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| \parindent 0pt% <br>
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| \pagestyle{empty} % <br>
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| \begin{document} % <br>
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| \begin{picture}(802,802) % <br>
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| %\put(10,10){\ing{PowPlo}} % <br>
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| %\put(0,0){\ing{TraItu3}} % <br>
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| \put(0,0){\ing{ExpIte4}} % <br>
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| \put(411,788){\sx{3}{$y$}} % <br>
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| \put(411,693.6){\sx{2.9}{$3$}} % <br>
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| \put(411,593.4){\sx{2.9}{$2$}} % <br>
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| \put(411,493.2){\sx{2.9}{$1$}} % <br>
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| \put(411,393){\sx{2.9}{$0$}} % <br>
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| \put(407,292.8){\sx{2.9}{$-1$}} % <br>
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| \put(407,192.6){\sx{2.9}{$-2$}} % <br>
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| \put(407,092.4){\sx{2.9}{$-3$}} % <br>
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| % <br>
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| \put(081,408){\sx{2.9}{$-3$}} % <br>
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| \put(181,408){\sx{2.9}{$-2$}} % <br>
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| \put(281,408){\sx{2.9}{$-1$}} % <br>
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| \put(396,408){\sx{2.9}{$0$}} % <br>
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| \put(497,408){\sx{2.9}{$1$}} % <br>
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| \put(597,408){\sx{2.9}{$2$}} % <br>
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| \put(697,408){\sx{2.9}{$3$}} % <br>
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| \put(787,408){\sx{3}{$x$}} % <br>
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| % <br>
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| \put(6,748){\sx{3}{\rot{4}$n\!=\!3.2$\ero}} % <br>
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| \put(6,708){\sx{3}{\rot{3}$n\!=\!3.1$\ero}} % <br>
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| \put(6,675){\sx{3}{\rot{3}$n\!=\!3$\ero}} % <br>
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| \put(5,643){\sx{3}{\rot{3}$n\!=\!2.9$\ero}} % <br>
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| \put(6,345){\sx{3}{\rot{1}$n\!=\!0.6$\ero}} % <br>
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| %
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| \put(7,308){\sx{3}{\rot{4}$n\!=\!0.4$\ero}} % <br>
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| \put(7,280){\sx{3}{\rot{5}$n\!=\!0.3$\ero}} % <br>
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| \put(8,242){\sx{3}{\rot{9}$n\!=\!0.2$\ero}} % <br>
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| \put(9,185){\sx{3}{\rot{11}$n\!=\!0.1$\ero}} % <br>
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| % <br>
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| \put(50,36){\sx{3}{\rot{45}$n\!=\!0$\ero}} % <br>
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| % <br>
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| \put(202,5){\sx{3}{\rot{76}$n\!=\!-0.1$\ero}} % <br>
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| \put(263,5){\sx{3}{\rot{82}$n\!=\!-0.2$\ero}} % <br>
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| \put(299,5){\sx{3}{\rot{84}$n\!=\!-0.3$\ero}} % <br>
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| \put(691,5){\sx{3}{\rot{84}$n\!=\!-3$\ero}} % <br>
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| \put(724,5){\sx{3}{\rot{83}$n\!=\!-3.1$\ero}} % <br>
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| \put(764,5){\sx{3}{\rot{82}$n\!=\!-3.2$\ero}} % <br>
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| % <br>
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| \put(480,600){\sx{3.6}{\rot{69}$y\!=\!\exp(x)$\ero}} % <br>
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| \put(641,630){\sx{3.4}{\rot{44}$y\!=\!x$\ero}} % <br>
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| \put(650,484){\sx{3.6}{\rot{19}$y\!=\!\ln(x)$\ero}} % <br>
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| | |
| \end{picture} % <br>
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| \end{document} % <br>
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| %</nowiki>
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| == Licensing ==
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| {{CC|by|3.0}}
| |
