Difference between revisions of "File:TraItT.jpg"

Revision as of 09:44, 21 June 2013

Iterates of the Trappmann function, $~\mathrm{tra}(z)=x+\mathrm e^z$.

$y=\mathrm{tra}^n(x)=\mathrm{hen}\Big(n+\mathrm{ahe}(x)\Big)$

versus $x$ for various values of $n$.

The Henryk function hen and the ArcHenryk ahe are superfunction and Abel function of the Trappmann function. They can be expressed through superfunction and Abel function of function zex.

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

% % % file PowPlo.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 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}{$3$}} % \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}} % % \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} % %

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