File:ArcTraMapT.jpg

Complex map of function ArcTra,

$u\!+\! \mathrm i v = \mathrm{ArcTra}(x\!+\! \mathrm i y)$

See Trappmann function for details.

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 complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"
//#include "fsexp.cin"
//#include "fslog.cin"
//z_type zex(z_type z){ return z*exp(z);} 
//z_type tra(z_type z){ return z+exp(z);} 

#include "Tania.cin"
//#include "LambertW.cin"

z_type tra(z_type z){ return z+exp(z);} 
//z_type ArcTra(z_type z){ return z-LambertW(exp(z));} 

main(){ int j,k,m,n; DB x1,x,y, p,q, t; z_type z,c,d, cu,cd;
int M=601,M1=M+1;
int N=1201,N1=N+1;
DB X[M1],Y[N1];
DB *g, *f, *w; // w is working array.
g=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
f=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
w=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
char v[M1*N1]; // v is working array
FILE *o;o=fopen("ArcTraMap.eps","w");  ado(o,1202,1202);
fprintf(o,"601 601 translate\n 100 100 scale\n");
fprintf(o,"1 setlinejoin 2 setlinecap\n");
DO(m,M1) X[m]=-6.+.02*(m-.5);
DO(n,N1) Y[n]=-6.+.01*(n-.5); 
//for(n=0;n<N1;n++) { Y[n]=0.6*sinh((3./200.)*(n-200.5)); printf("%3d %9.6f\n",n,Y[n]); }
for(m=-6;m<7;m++) {M(m,-6)L(m,6)}
for(n=-6;n<7;n++) {M(  -6,n)L(6,n)} fprintf(o,".006 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){      g[m*N1+n]=999;
                       f[m*N1+n]=999;}
DO(m,M1){x=X[m]; if(m/10*10==m) printf("x=%6.3f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);  
// c=ArcTra(z);  
// c=Tania(z+1.); // WrightOmega(z);  
c=z-Tania(z-1.);   
p=Re(c); q=Im(c);
//        if(p>-19 && p<19 &&  fabs(q)>1.e-12 && fabs(p)>1.e-12) 
g[m*N1+n]=p;
//        if(p>-19 && p<19 &&  fabs(q)>1.e-12 && fabs(p)>1.e-12) 
f[m*N1+n]=q;
       }}
fprintf(o,"1 setlinejoin 1 setlinecap\n");  p=.1;q=.1;
for(m=-8;m<8;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q,q);fprintf(o,".007 W 0 .6 0 RGB S\n");
for(m=0;m<8;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);fprintf(o,".007 W .9 0 0 RGB S\n");
for(m=0;m<8;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);fprintf(o,".007 W 0 0 .9 RGB S\n");
for(m= 1;m<17;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);fprintf(o,".02 W .8 0 0 RGB S\n");
for(m= 1;m<17;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);fprintf(o,".02 W 0 0 .8 RGB S\n");
               conto(o,f,w,v,X,Y,M,N, (0.  ),-p,p); fprintf(o,".02 W .5 0 .5 RGB S\n");
for(m=-16;m<17;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".02 W 0 0 0 RGB S\n");
M(-6, M_PI)L(-1, M_PI)
M(-6,-M_PI)L(-1,-M_PI)
fprintf(o,".01 W 1 1 1 RGB S\n");
 fprintf(o,"showpage\n");  fprintf(o,"%c%cTrailer\n",'%','%');
fclose(o);  free(f); free(g); free(w);
      system("epstopdf ArcTraMap.eps"); 
      system(    "open ArcTraMap.pdf"); //for macintosh
      getchar(); system("killall Preview"); // For macintosh
}

Latex generator of labels

% %<br> \documentclass[12pt]{article} % <br> \paperheight 1228px % <br> \paperwidth 1236px % <br> \textwidth 1394px % <br> \textheight 1300px % <br> \topmargin -104px % <br> \oddsidemargin -78px % <br> \usepackage{graphics} % <br> \usepackage{rotating} % <br> \newcommand \sx {\scalebox} % <br> \newcommand \rot {\begin{rotate}} % <br> \newcommand \ero {\end{rotate}} % <br> \newcommand \ing {\includegraphics} % <br> \newcommand \rmi {\mathrm{i}} % <br> \begin{document} % <br> \newcommand \zoomax { % <br> \put(18,1206){\sx{3.3}{$y$}} % <br> \put(18,1113){\sx{3}{$5$}} % <br> \put(18,1013){\sx{3}{$4$}} % <br> \put(18, 913){\sx{3}{$3$}} % <br> \put(18, 813){\sx{3}{$2$}} % <br> \put(18, 713){\sx{3}{$1$}} % <br> \put(18, 613){\sx{3}{$0$}} % <br> \put(-6, 513){\sx{3}{$-1$}} % <br> \put(-6, 413){\sx{3}{$-2$}} % <br> \put(-6, 313){\sx{3}{$-3$}} % <br> \put(-6, 213){\sx{3}{$-4$}} % <br> \put(-6, 113){\sx{3}{$-5$}} % <br> \put(-6, 013){\sx{3}{$-6$}} % <br> \put(014, -5){\sx{3}{$-6$}} % <br> \put(114, -5){\sx{3}{$-5$}} % <br> \put(214, -5){\sx{3}{$-4$}} % <br> \put(314, -5){\sx{3}{$-3$}} % <br> \put(414, -5){\sx{3}{$-2$}} % <br> \put(514, -5){\sx{3}{$-1$}} % <br> \put(635, -5){\sx{3}{$0$}} % <br> \put(735, -5){\sx{3}{$1$}} % <br> \put(835, -5){\sx{3}{$2$}} % <br> \put(935, -5){\sx{3}{$3$}} % <br> \put(1035, -5){\sx{3}{$4$}} % <br> \put(1135, -5){\sx{3}{$5$}} % <br> \put(1227,-4){\sx{3}{$x$}} % <br> } % <br> \parindent 0pt % <br> \sx{1}{\begin{picture}(1252,1220) % <br> %\put(40,20){\ing{b271tMap3}} % <br> %\put(40,20){\ing{ExpMap}} % <br> %\put(40,20){\ing{suzexD1map}} % <br> \put(40,20){\ing{ArcTraMap}} % <br> \zoomax % <br> \put(80,898){\sx{5}{$v\!=\!3$}} % <br> \put(80,810){\sx{5}{$v\!=\!2$}} % <br> \put(80,710){\sx{5}{$v\!=\!1$}} % <br> \put(80,608){\sx{5}{$v\!=\!0$}} % <br> \put(80,504){\sx{5}{$v\!=\!-1$}} % <br> \put(80,409){\sx{5}{$v\!=\!-2$}} % <br> \put(80,312){\sx{5}{$v\!=\!-3$}} % <br> \put(261,555){\sx{5}{\rot{90}$u\!=\!-4$\ero}} % <br> \put(365,555){\sx{5}{\rot{90}$u\!=\!-3$\ero}} % <br> \put(474,555){\sx{5}{\rot{90}$u\!=\!-2$\ero}} % <br> \put(597,555){\sx{5}{\rot{90}$u\!=\!-1$\ero}} % <br> \put(760,562){\sx{5}{\rot{90}$u\!=\!0$\ero}} % <br> \put(1032,564){\sx{5}{\rot{90}$u\!=\!1$\ero}} % <br> % <br> \end{picture}} % <br> \end{document} % <br>