File:TraItT.jpg: Difference between revisions

Latest revision as of 18:53, 11 March 2022

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current	18:53, 11 March 2022		1,258 × 1,258 (604 KB)	Maintenance script (talk \| contribs)	== Summary == Importing file

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Iteration of function

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 == Summary ==
-{{Image_Details|user
+Importing file
-|description  = [[Iteration of function|iterate]]s of the [[Trappmann function]], [[tra]]<math>(z)=z+\exp(z)~</math>. For various number <math>n</math> of iteration, <math>~y\!=\~\mathrm{tra}^n(x)~</math> is plottecd versus <math>x</math>.
-|author       = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
-|date-created = 2012.11.11
-|pub-country  = Japan
-|notes        =
-|versions     = http://tori.ils.uec.ac.jp/TORI/index.php/File:TraItT.jpg
-}}
-== Licensing ==
-{{CC|by|3.0}}
-==[[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"
- 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("TraIt.eps","w");  ado(o,604,604);
- fprintf(o,"302 302 translate\n 100 100 scale\n");
- fprintf(o,"1 setlinejoin 2 setlinecap\n");
- for(n=-3;n<4;n++) {M(-3,n)L(3,n)}
- for(m=-3;m<4;m++) {M(m,-3)L(m,3)}
- // 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=-3.02+.02*m; y=Re(tra(x));                                   if(m==0) M(x,y) else L(x,y) if(x>3.03||y>10.03) break;}
- DO(m,700){x=-3.02+.02*m; y=Re(tra(tra(x)));                              if(m==0) M(x,y) else L(x,y) if(x>3.03||y>10.03) break;}
- DO(m,700){x=-3.02+.02*m; y=Re(tra(tra(tra(x))));                         if(m==0) M(x,y) else L(x,y) if(x>3.03||y>10.03) break;}
- DO(m,700){x=-3.02+.02*m; y=Re(tra(tra(tra(tra(x)))));                    if(m==0) M(x,y) else L(x,y) if(x>3.03||y>10.03) break;}
- DO(m,700){x=-3.02+.02*m; y=Re(tra(tra(tra(tra(tra(x))))));               if(m==0) M(x,y) else L(x,y) if(x>3.03||y>10.03) break;}
- DO(m,700){x=-3.02+.02*m; y=Re(tra(tra(tra(tra(tra(tra(x)))))));          if(m==0) M(x,y) else L(x,y) if(x>3.03||y>10.03) break;}
- DO(m,700){x=-3.02+.02*m; y=Re(tra(tra(tra(tra(tra(tra(tra(x))))))));     if(m==0) M(x,y) else L(x,y) if(x>3.03||y>10.03) break;}
- DO(m,700){x=-3.02+.02*m; y=Re(tra(tra(tra(tra(tra(tra(tra(tra(x)))))))));if(m==0) M(x,y) else L(x,y) if(x>3.03||y>10.03) break;}
- fprintf(o,".022 W 0 1 0 RGB S\n");
- DO(m,700){y=-3.02+.02*m; x=Re(tra(y));                                   if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.03) break;}
- DO(m,700){y=-3.02+.02*m; x=Re(tra(tra(y)));                              if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.03) break;}
- DO(m,700){y=-3.02+.02*m; x=Re(tra(tra(tra(y))));                         if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.03) break;}
- DO(m,700){y=-3.02+.02*m; x=Re(tra(tra(tra(tra(y)))));                    if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.03) break;}
- DO(m,700){y=-3.02+.02*m; x=Re(tra(tra(tra(tra(tra(y))))));               if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.03) break;}
- DO(m,700){y=-3.02+.02*m; x=Re(tra(tra(tra(tra(tra(tra(y)))))));          if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.03) break;}
- DO(m,700){y=-3.02+.02*m; x=Re(tra(tra(tra(tra(tra(tra(tra(y))))))));     if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.03) break;}
- DO(m,700){y=-3.02+.02*m; x=Re(tra(tra(tra(tra(tra(tra(tra(tra(y)))))))));if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.03) break;}
- fprintf(o,".022 W 1 0 1 RGB S\n");
- for(n=-20;n<21;n+=1){
-   DO(m,700){x=-3.01 +.02*m; y=Re(G(x)); y=Re(F(.1*n+y)); if(m==0) M(x,y) else L(x,y) if(x>3.03||y>3.03) break;}
-   fprintf(o,".01 W 0 0 0 RGB S\n");
-                    }
- fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%');  fclose(o);
-       system("epstopdf TraIt.eps");
-       system(    "open TraIt.pdf"); //for macintosh
-       getchar(); system("killall Preview"); // For macintosh
- }
-==[[Latex]] Generator of labels==
-%<nowiki> %<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 606pt % <br>
-\paperheight 606pt % <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}(602,602) % <br>
-%\put(10,10){\ing{PowPlo}} % <br>
-\put(0,0){\ing{TraIt}} % <br>
-\put(311,590){\sx{2.5}{$y$}} % <br>
-\put(311,495){\sx{2.4}{$3$}} % <br>
-\put(311,395){\sx{2.4}{$1$}} % <br>
-\put(311,295){\sx{2.4}{$0$}} % <br>
-\put(307,194){\sx{2.4}{$-1$}} % <br>
-\put(307,093.4){\sx{2.4}{$-2$}} % <br>
- % <br>
-\put(083,308){\sx{2.4}{$-2$}} % <br>
-\put(183,308){\sx{2.4}{$-1$}} % <br>
-\put(297,308){\sx{2.4}{$0$}} % <br>
-\put(397,308){\sx{2.4}{$1$}} % <br>
-\put(497,308){\sx{2.4}{$2$}} % <br>
-\put(590,308){\sx{2.5}{$x$}} % <br>
- % <br>
-\put(117,532){\sx{2.4}{\rot{87}$n\!=\!8$\ero}} % <br>
-\put(137,532){\sx{2.4}{\rot{86}$n\!=\!7$\ero}} % <br>
-\put(156,532){\sx{2.4}{\rot{85}$n\!=\!6$\ero}} % <br>
-\put(177,532){\sx{2.4}{\rot{84}$n\!=\!5$\ero}} % <br>
-\put(204,532){\sx{2.4}{\rot{83}$n\!=\!4$\ero}} % <br>
-\put(238,532){\sx{2.4}{\rot{82}$n\!=\!3$\ero}} % <br>
-\put(278,532){\sx{2.4}{\rot{79}$n\!=\!2$\ero}} % <br>
-\put(366,532){\sx{2.4}{\rot{71}$n\!=\!1$\ero}} % <br>
-%\put(264,350){\sx{3.1}{\rot{61}$y\!=\!x\!+\!\mathrm e^x$\ero}} % <br>
-%\put(427,528){\sx{2.3}{\rot{62}$c\!=\!0.6$\ero}} % <br>
-\put(448,528){\sx{2.4}{\rot{60}$n\!=\!0.4$\ero}} % <br>
-\put(469,530){\sx{2.4}{\rot{57}$n\!=\!0.3$\ero}} % <br>
-\put(491,532){\sx{2.4}{\rot{53}$n\!=\!0.2$\ero}} % <br>
-\put(517,534){\sx{2.4}{\rot{49}$n\!=\!0.1$\ero}} % <br>
- % <br>
-\put(541,531){\sx{2.4}{\rot{45}$n\!=\!0$\ero}} % <br>
-% <br>
-\put(521,462){\sx{2.4}{\rot{37}$n\!=\!-0.2$\ero}} % <br>
-\put(517,423){\sx{2.4}{\rot{30}$n\!=\!-0.4$\ero}} % <br>
-\put(527,349){\sx{2.4}{\rot{17}$n\!=\!-1$\ero}} % <br>
-\put(524,261){\sx{2.4}{\rot{8}$n\!=\!-2$\ero}} % <br>
-\put(523,222){\sx{2.4}{\rot{6}$n\!=\!-3$\ero}} % <br>
-\put(523,188){\sx{2.4}{\rot{4}$n\!=\!-4$\ero}} % <br>
-\put(523,161){\sx{2.4}{\rot{3}$n\!=\!-5$\ero}} % <br>
-\put(523,141){\sx{2.4}{\rot{2}$n\!=\!-6$\ero}} % <br>
-\put(523,122){\sx{2.4}{\rot{1}$n\!=\!-7$\ero}} % <br>
-\put(523,104){\sx{2.4}{\rot{1}$n\!=\!-8$\ero}} % <br>
-\end{picture} % <br>
-\end{document} % <br>
-%</nowiki>
-[[Category:Trappmann function]]
-[[Category:Iteration]]
-[[Category:Superfunction]]
-[[Category:Abel function]]
-[[Category:Transfer function]]
-[[Category:Explicit plot]]
-[[Category:C++]]
-[[Category:Latex]]