File:Z2itmapT.jpg

Complex map of function $T(z)=z^2$.

$\mu+\mathrm i \nu=T(x+\mathrm i y)$

C++ generator of curves
// #include  //using namespace std; typedef std::complex z_type;
 * 1) include 
 * 2) include 
 * 3) define DB double
 * 4) 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"

DB c=2.; // z_type F(z_type z) {return (c-1.)/(pow(2.,z)-c);} z_type F(z_type z) {return pow(z,c);}

int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; int M=501,M1=M+1; int N=501,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("z2itmap.eps","w"); ado(o,1002,1002); fprintf(o,"501 501 translate\n 100 100 scale\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n"); DO(m,M1) X[m]=-5+.02*(m-.5); DO(n,N1) Y[n]=-5+.02*(n-.5); //for(n=0;n.019) c=F(z); // p=abs(c-z)/(abs(c)+abs(z)); p=-log(p)/log(10.); if(p>0 && p<17) g[m*N1+n]=p; p=Re(c); q=Im(c); if(p>-99 && p<99 ){ g[m*N1+n]=p;f[m*N1+n]=q;} }} fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.2;q=.4;

for(m=-5;m<5;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q,q);fprintf(o,".01 W 0 .6 0 RGB S\n"); for(m=0;m<5;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);fprintf(o,".01 W .8 0 0 RGB S\n"); for(m=0;m<5;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);fprintf(o,".01 W 0 0 .8 RGB S\n"); for(m= 1;m<11;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<11;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. ),-2*p,2*p); fprintf(o,".02 W .5 0 .5 RGB S\n"); for(m=-10;m<11;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,"0 setlinejoin 0 setlinecap\n"); // M(-10,0)L(0,0) fprintf(o,"1 1 1 RGB .02 W S\n"); //#include "plofu.cin" fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o); free(f); free(g); free(w); system("epstopdf z2itmap.eps"); system(   "open z2itmap.pdf"); //for macintosh getchar; system("killall Preview"); // For macintosh } //

Latex generator of labels
% \documentclass[12pt]{article} \paperwidth 1044px \paperheight 1036px \textwidth 1204px \textheight 1200px \topmargin -86px \oddsidemargin -72px \usepackage{graphics} \usepackage{rotating} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \ing {\includegraphics} \newcommand \rmi {\mathrm{i}} \parindent 0pt \pagestyle{empty} \begin{document} \parindent 0pt \sx{1}{\begin{picture}(1004,1004) \put(40,20){\ing{z2itmap}} \put(15,1008){\sx{3.3}{$y$}} \put(15,910){\sx{3.3}{$4$}} \put(15,810){\sx{3.3}{$3$}} \put(15,710){\sx{3.3}{$2$}} \put(15,610){\sx{3.3}{$1$}} \put(15,510){\sx{3.3}{$0$}} \put(-8,410){\sx{3.3}{$-1$}} \put(-8,310){\sx{3.3}{$-2$}} \put(-8,210){\sx{3.3}{$-3$}} \put(-8,110){\sx{3.3}{$-4$}} \put(-8,10){\sx{3.3}{$-5$}} \put(8,-9){\sx{3.3}{$-5$}} \put(108,-9){\sx{3.3}{$-4$}} \put(208,-9){\sx{3.3}{$-3$}} \put(308,-9){\sx{3.3}{$-2$}} \put(408,-9){\sx{3.3}{$-1$}} \put(534,-9){\sx{3.3}{$0$}} \put(634,-9){\sx{3.3}{$1$}} \put(734,-9){\sx{3.3}{$2$}} \put(834,-9){\sx{3.3}{$3$}} \put(934,-9){\sx{3.3}{$4$}} \put(1026,-9){\sx{3.3}{$x$}} \put(889,649){\sx{5}{\rot{-15}$\nu\!=\!10$\ero}} \put(884,579){\sx{5}{\rot{-7}$\nu\!=\!5$\ero}} \put(884,510){\sx{5}{$\nu\!=\!0$}} \put(884,438){\sx{5}{\rot{6}$\nu\!=\!-5$\ero}} \put(890,338){\sx{5}{\rot{-58}$\mu\!=\!10$\ero}} \put(838,308){\sx{5}{\rot{-55}$\mu\!=\!5$\ero}} \put(784,264){\sx{5}{\rot{-45}$\mu\!=\!0$\ero}} \put(726,214){\sx{5}{\rot{-37}$\mu\!=\!-5$\ero}} \put(706,154){\sx{5}{\rot{-33}$\mu\!=\!-10$\ero}} \end{picture}} \end{document} %