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
//Files ado.cin, conto.cin, Tania.cin should be loaded to the working directory in order to compile the code below

using namespace std; typedef complex z_type; //#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);}
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 1) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)
 * 4) include "conto.cin"

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