File:TraMapT.jpg

Complex map of the Trappmann function $\mathrm{tra}(z)=z+\mathrm e^z$.

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

C++ generator of curves
using namespace std; typedef complex z_type; //#include "fsexp.cin" //#include "fslog.cin"
 * 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"

//z_type zex(z_type z){ return z*exp(z);} z_type tra(z_type z){ return z+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=601,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("TraMap.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.+.02*(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=24.;q=.2; 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"); fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o); free(f); free(g); free(w); system("epstopdf TraMap.eps"); system(   "open TraMap.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{tramap}} \zoomax \put(90,1116){\sx{4}{$v\!=\!5$}} \put(90,1015){\sx{4}{$v\!=\!4$}} \put(90,914){\sx{4}{$v\!=\!3$}} \put(90,813){\sx{4}{$v\!=\!2$}} \put(90,712){\sx{4}{$v\!=\!1$}} \put(90,611){\sx{4}{$v\!=\!0$}} \put(90,510){\sx{4}{$v\!=\!-1$}} \put(90,409){\sx{4}{$v\!=\!-2$}} \put(90,308){\sx{4}{$v\!=\!-3$}} \put(90,207){\sx{4}{$v\!=\!-4$}} \put(90,106){\sx{4}{$v\!=\!-5$}} \put(257,555){\sx{4}{\rot{90}$u\!=\!-4$\ero}} \put(355,555){\sx{4}{\rot{90}$u\!=\!-3$\ero}} \put(447,555){\sx{4}{\rot{90}$u\!=\!-2$\ero}} \put(534,555){\sx{4}{\rot{90}$u\!=\!-1$\ero}} \put(600,572){\sx{4}{\rot{90}$u\!=\!0$\ero}} \put(656,574){\sx{4}{\rot{90}$u\!=\!1$\ero}}

\put(990,678){\sx{4}{\rot{-15}$v\!=\!16$\ero}} \put(990,550){\sx{4}{\rot{9}$v\!=\!-16$\ero}} \put(998,507){\sx{4}{\rot{-11}$u\!=\!16$\ero}} \put(996,380){\sx{4}{\rot{13}$u\!=\!-16$\ero}}

\end{picture}} \end{document}