File:B271t3T.png

Complex map of tetration to base $\mathrm e\approx 2.71$

$f=\mathrm {tet}(x\!+\!\mathrm i y)$;

$u\!=\!\Re(f)~$; $~v\!=\!\Im(f)$

C++ generator of curves
// Files fsexp.cin, ado.cin and conto.cin should be loaded to the working directory in order to compile the C++ code below

using namespace std; typedef complex z_type; //#include "fslog.cin" main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd; int M=801,M1=M+1; int N=401,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("b271tMap3.eps","w"); ado(o,802,802); fprintf(o,"401 401 translate\n 100 100 scale\n"); fprintf(o,"1 setlinejoin 2 setlinecap\n"); DO(m,M1) X[m]=-4.+.01*(m-.5); for(n=0;n.019) { //     c=log(z+2.); c=FSEXP(z); //    c=FSLOG(z); p=Re(c); q=Im(c); if(p>-12 && p<12 && fabs(q)>1.e-12) g[m*N1+n]=p; if(q>-12 && q<12 && fabs(q)>1.e-12) f[m*N1+n]=q; }       }} fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.;q=.3; 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<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. ),-p,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"); M(-2,0)L(-4,0)fprintf(o,"0 setlinecap .03 W 1 1 1 RGB S\n"); for(n=0;n<11;n++){ M(-2-.2*(n+.2),0) L(-2-.2*(n+.45),0) } fprintf(o,".04 W 1 .5 0 RGB S\n"); for(n=0;n<21;n++){ M(-2-.2*(n+.7),0) L(-2-.2*(n+.95),0) } fprintf(o,".04 W 0 .5 1 RGB S\n"); //#include "plofu.cin" fprintf(o,"0 setlinejoin 0 setlinecap\n"); fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o); free(f); free(g); free(w); system("epstopdf b271tMap3.eps"); system(   "open b271tMap3.pdf"); //for macintosh getchar; system("killall Preview"); // For macintosh }
 * 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"
 * 5) include "fsexp.cin"

Latex generator of labels
% \documentclass[12pt]{article} % \paperheight 828px % \paperwidth 836px % \textwidth 1294px % \textheight 1100px % \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, 806){\sx{3.3}{$y$}} % \put(18, 713){\sx{3}{$3$}} % \put(18, 613){\sx{3}{$2$}} % \put(18, 513){\sx{3}{$1$}} % \put(18, 413){\sx{3}{$0$}} % \put(-6, 313){\sx{3}{$-1$}} % \put(-6, 213){\sx{3}{$-2$}} % \put(-6, 113){\sx{3}{$-3$}} % \put(014, -5){\sx{3}{$-4$}} % \put(114, -5){\sx{3}{$-3$}} % \put(214, -5){\sx{3}{$-2$}} % \put(314, -5){\sx{3}{$-1$}} % \put(435, -5){\sx{3}{$0$}} % \put(535, -5){\sx{3}{$1$}} % \put(635, -5){\sx{3}{$2$}} % \put(735, -5){\sx{3}{$3$}} % \put(827,-4){\sx{3}{$x$}} % } % \parindent 0pt % \sx{1}{\begin{picture}(852,820) \put(40,20){\ing{b271tMap3}} % \zoomax % \put(60,415){\sx{2.8}{\bf cut}} % \put(340,548){\sx{3}{$v\!=\!1$}} % \put(360,414){\sx{3}{$v\!=\!0$}} % \put(760,414){\sx{3}{$v\!=\!0$}} % \put(340,280){\sx{3}{$v\!=\!-1$}} % \put(70,800){\sx{2.5}{$f\approx L\approx0.318+1.337i$}} % \put(60,60){\sx{2.5}{$f\approx L^*\approx0.318-1.337i$}} % \put(100,638){\sx{2.5}{$v\!=\!1.4$}} % \put(552,745){\sx{2.5}{$v\!=\!1.4$}} % \put(100,198){\sx{2.5}{$v\!=\!-\!1.4$}}% \put(540,90){\sx{2.5}{$v\!=\!-\!1.4$}} % \put(666,726){\sx{2.5}{$u\!=\!0.2$}} % \put(216,616){\sx{2.5}{$u\!=\!0.2$}} % \put(660,642){\sx{3}{$u\!=\!0$}} % \put(210,536){\sx{3}{$u\!=\!0$}} % \put(410,700){\sx{2.5}{$u\!=\!0.4$}} % \put(217,213){\sx{2.5}{$u\!=\!0.2$}} % \put(410,130){\sx{2.5}{$u\!=\!0.4$}} % \end{picture}} % \end{document} %