Difference between revisions of "File:TraItT.jpg"

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[[Iterate]]s of the [[Trappmann function]]
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Importing image file
  
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  +
$y=\mathrm{tra}^n(x)$ for various $n$.
  +
  +
==[[C++]] generator of curves==
  +
<poem><nomathjax><nowiki>
  +
#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 std::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 "doya.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);
  +
int 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");
  +
M(-3,-3)L(3,3) fprintf(o,".022 W 0 .6 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
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of labels==
  +
<poem><nomathjax><nowiki>
  +
\documentclass[12pt]{article}
  +
\usepackage{geometry}
  +
\usepackage{graphicx}
  +
\usepackage{rotating}
  +
\paperwidth 606pt
  +
\paperheight 606pt
  +
\topmargin -105pt
  +
\oddsidemargin -73pt
  +
\textwidth 1100pt
  +
\textheight 1100pt
  +
\pagestyle {empty}
  +
\newcommand \sx {\scalebox}
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
\newcommand \ing {\includegraphics}
  +
\parindent 0pt
  +
\pagestyle{empty}
  +
\begin{document}
  +
\begin{picture}(602,602)
  +
%\put(10,10){\ing{PowPlo}}
  +
\put(0,0){\ing{TraIt}}
  +
\put(311,590){\sx{2.5}{$y$}}
  +
\put(311,495){\sx{2.4}{$2$}}
  +
\put(311,395){\sx{2.4}{$1$}}
  +
\put(311,295){\sx{2.4}{$0$}}
  +
\put(307,194){\sx{2.4}{$-1$}}
  +
\put(307,093.4){\sx{2.4}{$-2$}}
  +
  +
\put(083,308){\sx{2.4}{$-2$}}
  +
\put(183,308){\sx{2.4}{$-1$}}
  +
\put(297,308){\sx{2.4}{$0$}}
  +
\put(397,308){\sx{2.4}{$1$}}
  +
\put(497,308){\sx{2.4}{$2$}}
  +
\put(590,308){\sx{2.5}{$x$}}
  +
  +
\put(117,532){\sx{2.4}{\rot{87}$n\!=\!8$\ero}}
  +
\put(137,532){\sx{2.4}{\rot{86}$n\!=\!7$\ero}}
  +
\put(156,532){\sx{2.4}{\rot{85}$n\!=\!6$\ero}}
  +
\put(177,532){\sx{2.4}{\rot{84}$n\!=\!5$\ero}}
  +
\put(204,532){\sx{2.4}{\rot{83}$n\!=\!4$\ero}}
  +
\put(238,532){\sx{2.4}{\rot{82}$n\!=\!3$\ero}}
  +
\put(278,532){\sx{2.4}{\rot{79}$n\!=\!2$\ero}}
  +
\put(366,532){\sx{2.4}{\rot{71}$n\!=\!1$\ero}}
  +
%\put(264,350){\sx{3.1}{\rot{61}$y\!=\!x\!+\!\mathrm e^x$\ero}}
  +
%\put(427,528){\sx{2.3}{\rot{62}$c\!=\!0.6$\ero}}
  +
\put(448,528){\sx{2.4}{\rot{60}$n\!=\!0.4$\ero}}
  +
\put(469,530){\sx{2.4}{\rot{57}$n\!=\!0.3$\ero}}
  +
\put(491,532){\sx{2.4}{\rot{53}$n\!=\!0.2$\ero}}
  +
\put(517,534){\sx{2.4}{\rot{49}$n\!=\!0.1$\ero}}
  +
  +
\put(541,531){\sx{2.4}{\rot{45}$n\!=\!0$\ero}}
  +
% <br>
  +
\put(521,462){\sx{2.4}{\rot{37}$n\!=\!-0.2$\ero}}
  +
\put(517,423){\sx{2.4}{\rot{30}$n\!=\!-0.4$\ero}}
  +
\put(527,349){\sx{2.4}{\rot{17}$n\!=\!-1$\ero}}
  +
\put(524,261){\sx{2.4}{\rot{8}$n\!=\!-2$\ero}}
  +
\put(523,222){\sx{2.4}{\rot{6}$n\!=\!-3$\ero}}
  +
\put(523,188){\sx{2.4}{\rot{4}$n\!=\!-4$\ero}}
  +
\put(523,161){\sx{2.4}{\rot{3}$n\!=\!-5$\ero}}
  +
\put(523,141){\sx{2.4}{\rot{2}$n\!=\!-6$\ero}}
  +
\put(523,122){\sx{2.4}{\rot{1}$n\!=\!-7$\ero}}
  +
\put(523,104){\sx{2.4}{\rot{1}$n\!=\!-8$\ero}}
  +
\end{picture}
  +
\end{document}
  +
</nowiki></nomathjax></poem>
  +
  +
  +
==References==
  +
<references/>
  +
  +
[[Category:Abel function]]
  +
[[Category:Book]]
  +
[[Category:BookPlot]]
  +
[[Category:Superfunction]]
  +
[[Category:Tra]]
  +
[[Category:SuTra]]
  +
[[Category:Autra]]
  +
[[Category:Trappmann function]]
  +
[[Category:Iterate]]
  +
[[Category:Explicit plot]]
  +
[[Category:Test]]
  +
[[Category:Tra]]
  +
[[Category:C++]]
  +
[[Category:Latex]]

Latest revision as of 08:54, 1 December 2018

Iterates of the Trappmann function

$y=\mathrm{tra}^n(x)$ for various $n$.

C++ generator of curves


#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 std::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 "doya.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);
int 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");
M(-3,-3)L(3,3) fprintf(o,".022 W 0 .6 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


\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{graphicx}
\usepackage{rotating}
\paperwidth 606pt
\paperheight 606pt
\topmargin -105pt
\oddsidemargin -73pt
\textwidth 1100pt
\textheight 1100pt
\pagestyle {empty}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\parindent 0pt
\pagestyle{empty}
\begin{document}
\begin{picture}(602,602)
%\put(10,10){\ing{PowPlo}}
\put(0,0){\ing{TraIt}}
\put(311,590){\sx{2.5}{$y$}}
\put(311,495){\sx{2.4}{$2$}}
\put(311,395){\sx{2.4}{$1$}}
\put(311,295){\sx{2.4}{$0$}}
\put(307,194){\sx{2.4}{$-1$}}
\put(307,093.4){\sx{2.4}{$-2$}}

\put(083,308){\sx{2.4}{$-2$}}
\put(183,308){\sx{2.4}{$-1$}}
\put(297,308){\sx{2.4}{$0$}}
\put(397,308){\sx{2.4}{$1$}}
\put(497,308){\sx{2.4}{$2$}}
\put(590,308){\sx{2.5}{$x$}}

\put(117,532){\sx{2.4}{\rot{87}$n\!=\!8$\ero}}
\put(137,532){\sx{2.4}{\rot{86}$n\!=\!7$\ero}}
\put(156,532){\sx{2.4}{\rot{85}$n\!=\!6$\ero}}
\put(177,532){\sx{2.4}{\rot{84}$n\!=\!5$\ero}}
\put(204,532){\sx{2.4}{\rot{83}$n\!=\!4$\ero}}
\put(238,532){\sx{2.4}{\rot{82}$n\!=\!3$\ero}}
\put(278,532){\sx{2.4}{\rot{79}$n\!=\!2$\ero}}
\put(366,532){\sx{2.4}{\rot{71}$n\!=\!1$\ero}}
%\put(264,350){\sx{3.1}{\rot{61}$y\!=\!x\!+\!\mathrm e^x$\ero}}
%\put(427,528){\sx{2.3}{\rot{62}$c\!=\!0.6$\ero}}
\put(448,528){\sx{2.4}{\rot{60}$n\!=\!0.4$\ero}}
\put(469,530){\sx{2.4}{\rot{57}$n\!=\!0.3$\ero}}
\put(491,532){\sx{2.4}{\rot{53}$n\!=\!0.2$\ero}}
\put(517,534){\sx{2.4}{\rot{49}$n\!=\!0.1$\ero}}

\put(541,531){\sx{2.4}{\rot{45}$n\!=\!0$\ero}}
% <br>
\put(521,462){\sx{2.4}{\rot{37}$n\!=\!-0.2$\ero}}
\put(517,423){\sx{2.4}{\rot{30}$n\!=\!-0.4$\ero}}
\put(527,349){\sx{2.4}{\rot{17}$n\!=\!-1$\ero}}
\put(524,261){\sx{2.4}{\rot{8}$n\!=\!-2$\ero}}
\put(523,222){\sx{2.4}{\rot{6}$n\!=\!-3$\ero}}
\put(523,188){\sx{2.4}{\rot{4}$n\!=\!-4$\ero}}
\put(523,161){\sx{2.4}{\rot{3}$n\!=\!-5$\ero}}
\put(523,141){\sx{2.4}{\rot{2}$n\!=\!-6$\ero}}
\put(523,122){\sx{2.4}{\rot{1}$n\!=\!-7$\ero}}
\put(523,104){\sx{2.4}{\rot{1}$n\!=\!-8$\ero}}
\end{picture}
\end{document}


References

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