File:E1eAuMap600.jpg

Complex maps of the abel function of the exponent to the Henryk base $\eta\!=\!\exp(1/\mathrm e)\!\approx\! 1.444667861$

$u\!+\!\mathrm i v\!=\!G(x\!+\!\mathrm i y)$

for arctetration $G\!=\! \mathrm{ate}_\eta$

and for inverse of the growing superexponent, id est, $G\!=\! \mathrm{AuExp}_{\eta,3}$

C++ generator of upper map
Fiels ado.cin, conto.cin, e1eti.cin should be loaded

//using namespace std; typedef std::complex z_type; //#include "e1egf.cin" int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; int M=501,M1=M+1; int N=601,N1=N+1; DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array. char v[M1*N1]; // v is working array //E1E Growung Funciton //FILE *o;o=fopen("e1eti.eps","w");ado(o,402,302); FILE *o;o=fopen("e1eatemap.eps","w");ado(o,402,302); fprintf(o,"101 151 translate\n 10 10 scale\n"); //DO(m,M1) X[m]=-10.+.08*(m-.5); DO(m,M1) X[m]=-10.+.055*(m-.5); DO(n,N1) Y[n]=-15.+.05*(n-.5); for(m=-10;m<31;m++){ //if(m==0){       M(m,-10.2)L(m,10.2)} else {      M(m,-15)L(m,15)         }} for(n=-15;n<16;n++){ M(-10,n)L(30,n)} fprintf(o,".006 W 0 0 0 RGB S\n"); DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;} DO(m,M1){x=X[m]; printf("run at x=%6.3f\n",x); DO(n,N1){y=Y[n]; z=z_type(x,y); c=E1ETI(z); //     c=E1EGF(z); //     d=z; //     p=abs(c-d)/abs(c+d); p=-log(p)/log(10.); p=Re(c); q=Im(c); //     if(p>-85 && p<85)  g[m*N1+n]=p; if(p>-33 && p<33 && fabs(p)> 1.e-6 && //             fabs(p-1.)>1.e-8 &&                fabs(p+3.)>1.e-8 &&          q >-33 && q<33 && fabs(q)> 1.e-8) { g[m*N1+n]=p; f[m*N1+n]=q; } }}
 * 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.)
 * 1) include "e1eti.cin"
 * 2) include "conto.cin"

fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=.6;q=.3; //#include"plofu.cin" //p=2;q=1; for(m=-19;m<19;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".02 W 0 .6 0 RGB S\n"); for(m=0;m<29;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q); fprintf(o,".02 W .9 0 0 RGB S\n"); for(m=0;m<29;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".02 W 0 0 .9 RGB S\n");

for(m= 1;m<20;m++) conto(o,f,w,v,X,Y,M,N,(0.-m),-p,p);fprintf(o,".07 W .8 0 0 RGB S\n"); for(m= 1;m<20;m++) conto(o,f,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".07 W 0 0 .8 RGB S\n"); conto(o,f,w,v,X,Y,M,N,(0. ),-p,p);fprintf(o,".07 W .5 0 .5 RGB S\n"); for(m=-31;m<32;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".07 W 0 0 0 RGB S\n");

/* fprintf(o,"0 setlinecap\n"); M(-2,0)L(-8,0) fprintf(o,".08 W 1 1 1 RGB S\n"); DO(m,16){M(-2-.4*(m),0)L(-2-.4*(m+.5),0)} fprintf(o,".09 W 0 0 0 RGB S\n"); fprintf(o,"showpage\n%cTrailer",'%'); fclose(o); system("epstopdf e1eatemap.eps"); system(   "open e1eatemap.pdf"); //mac //     system(    "xpdf e1eti.pdf"); // linux getchar; system("killall Preview");// mac }

C++ generator of lower map
Fiels ado.cin, conto.cin, e1eti.cin should be loaded

//using namespace std; typedef std::complex z_type; //#include "e1egf.cin" int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; int M=501,M1=M+1; int N=601,N1=N+1; DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array. char v[M1*N1]; // v is working array //E1E Growing Funciton //FILE *o;o=fopen("e1egi.eps","w");ado(o,402,302); FILE *o;o=fopen("e1eauexpmap.eps","w");ado(o,402,302); fprintf(o,"101 151 translate\n 10 10 scale\n"); DO(m,M1) X[m]=-10.+.08*(m-.5); DO(n,N1) Y[n]=-15.+.05*(n-.5); for(m=-10;m<31;m++){ //if(m==0){       M(m,-10.2)L(m,10.2)} else {      M(m,-15)L(m,15)         }} for(n=-15;n<16;n++){ M(-10,n)L(30,n)} fprintf(o,".006 W 0 0 0 RGB S\n"); DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;} DO(m,M1){x=X[m]; printf("run at x=%6.3f\n",x); DO(n,N1){y=Y[n]; z=z_type(x,y); c=E1EGI(z); //     c=E1EGF(z); //     d=z; //     p=abs(c-d)/abs(c+d); p=-log(p)/log(10.); p=Re(c); q=Im(c); //     if(p>-85 && p<85)  g[m*N1+n]=p; if(p>-33 && p<33 && fabs(p)> 1.e-9 && fabs(p-1.)>1.e-9 &&         q >-33 && q<33 && fabs(q)> 1.e-9) { g[m*N1+n]=p; f[m*N1+n]=q; } }}
 * 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.)
 * 1) include "e1egi.cin"
 * 2) include "conto.cin"

fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.4;q=.6; //#include"plofu.cin" //p=2;q=1; for(m=-19;m<19;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".02 W 0 .6 0 RGB S\n"); for(m=0;m<29;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q); fprintf(o,".02 W .9 0 0 RGB S\n"); for(m=0;m<29;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".02 W 0 0 .9 RGB S\n");

for(m= 1;m<20;m++) conto(o,f,w,v,X,Y,M,N,(0.-m),-p,p);fprintf(o,".07 W .8 0 0 RGB S\n"); for(m= 1;m<20;m++) conto(o,f,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".07 W 0 0 .8 RGB S\n"); conto(o,f,w,v,X,Y,M,N,(0. ),-p,p);fprintf(o,".07 W .5 0 .5 RGB S\n"); for(m=-31;m<32;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".07 W 0 0 0 RGB S\n");

fprintf(o,"0 setlinecap\n"); M(M_E,0)L(-10,0) fprintf(o,".08 W 1 1 1 RGB S\n"); DO(m,36){M(M_E-.4*(m),0)L(M_E-.4*(m+.5),0)} fprintf(o,".09 W 1 0 1 RGB S\n");

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o); system("epstopdf e1eauexpmap.eps"); system(   "open e1eauexpmap.pdf"); //mac //     system(    "xpdf e1egi.pdf"); // linux getchar; system("killall Preview");// mac }

Latex generator labels
\documentclass[12pt,a4paper,oneside]{book} %\newcommand \EN[1]   	% make the English version \newcommand \EN[1] –     	% suppress the English version \newcommand \RU[1]   	% make the Russian version (in this document not supported) %\newcommand \RU[1] –       	% suppress the Russian version %The Japanese version is not yet supported. While \JP is used to suppress several lines at once. \newcommand \JP[1] –    	 % ореsuppress some text %\usepackage[space]{cite }% If exist. \usepackage[utf8]{inputenc} \usepackage[T2A]{fontenc} \usepackage[russian]{babel} \usepackage{latexsym,amsmath,amssymb,amsbsy,graphicx}

\usepackage{rotating} \usepackage{hyperref} \usepackage{wrapfig} \usepackage{geometry} %\renewcommand\baselinestretch{.94} %\renewcommand\baselinestretch{.94} %\renewcommand\baselinestretch{1.15} %\renewcommand\baselinestretch{1.2} %\renewcommand\baselinestretch{1.2}

%\paperwidth150mm \paperwidth150mm %\paperheight 257mm %\paperheight 216mm %\paperheight 106mm \paperheight 226mm %\textwidth 175mm \textwidth 150mm %\oddsidemargin 5mm %\oddsidemargin -72pt \oddsidemargin -54pt %\topmargin -17mm %\topmargin -100pt \topmargin -110pt \textheight 267mm \pagestyle{empty} \large \usepackage{color} \definecolor{rose}{rgb}{1,.9,1} \renewcommand\thesection{\arabic{section}} \renewcommand\figurename{Рис.} %\renewcommand\refname{References} %\renewcommand\figurename{Fig.} \newcommand \be {\begin{eqnarray}} \newcommand \ee {\end{eqnarray} } \newcommand \sx {\scalebox} \newcommand \rme 	 %%makes the base of natural logarithms Roman font %\newcommand \rme 	%%makes the base of natural logarithms Italics font; choose one of these \newcommand \rmi 	 %%imaginary unity is always roman font \newcommand \ds {\displaystyle} \newcommand \bN {\mathbb{N}} \newcommand \bC {\mathbb{C}} \newcommand \bR {\mathbb{R}} \newcommand \cO {\mathcal{O}} \newcommand \cF {\mathcal{F}} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \nS {\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!} \newcommand \pS {{~}~{~}} \newcommand \fac {\mathrm{Factorial}} \newcommand {\rf}[1] {(\ref{#1})} \newcommand{\iL}[1] {~\label{#1}\pS \rm[#1]\nS}	%make the labels visible %\newcommand{\iL}[1] {\label{#1}}			%make the labels invisible; choose one of these options \newcommand \eL[1] {\iL{#1}\ee} \newcommand \ing \includegraphics \newcommand \tet {\mathrm{tet}} \parindent 0pt \begin{document} \parindent 0pt \newcommand \figaxe { \put( -6,298){\sx{1}{$y$}} %\put( -11,289){\sx{1}{$14$}} \put( -11,269){\sx{1}{$12$}} \put( -11,249){\sx{1}{$10$}} \put( -7,229){\sx{1}{$8$}} \put( -7,209){\sx{1}{$6$}} \put( -7,189){\sx{1}{$4$}} \put( -7,169){\sx{1}{$2$}} \put( -7, 149){\sx{1}{$0$}} \put(-17,129){\sx{1}{$-2$}} \put(-17,109){\sx{1}{$-4$}} \put(-17, 89){\sx{1}{$-6$}} \put(-17, 69){\sx{1}{$-8$}} \put(-21, 49){\sx{1}{$-10$}} \put(-21, 29){\sx{1}{$-12$}} \put(-21,  9){\sx{1}{$-14$}} %\put(-13, 79){\sx{1}{$-6$}} \put(398,-7.5){\sx{1}{$x$}} \put(377,-8){\sx{.9}{$28$}} \put(357,-8){\sx{.9}{$26$}} \put(337,-8){\sx{.9}{$24$}} \put(317,-8){\sx{.9}{$22$}} \put(297,-8){\sx{.9}{$20$}} \put(277,-8){\sx{.9}{$18$}} \put(257,-8){\sx{.9}{$16$}} \put(237,-8){\sx{.9}{$14$}} \put(217,-8){\sx{.9}{$12$}} \put(197,-8){\sx{.9}{$10$}} \put(179,-8){\sx{.9}{$8$}} \put(159,-8){\sx{.9}{$6$}} \put(139,-8){\sx{.9}{$4$}} \put(119,-8){\sx{.9}{$2$}} \put( 99,-8){\sx{.9}{$0$}} \put( 73,-8){\sx{.9}{$-2$}} \put( 53,-8){\sx{.9}{$-4$}} \put( 33,-8){\sx{.9}{$-6$}} \put( 13,-8){\sx{.9}{$-8$}} } %\hskip -28pt %\vskip 18pt \sx{1.}{\begin{picture}(415,310) % \put(0,0){\ing{e1eti} } % suppress to boost \put(0,0){\ing{e1eatemap} } % suppress to boost \figaxe \put(10,233){\sx{1.4}{$v\!=\!0$}} \put(142,245){\sx{1.}{$u\!=\!-3$}} \put(142,225){\sx{1.}{$u\!=\!-3$}} \put(10,192){\sx{1.6}{$u\!=\!-2$}} \put(10,147){\sx{1.6}{$v\!=\!0$}} \put(10,108){\sx{1.6}{$u\!=\!-2$}} \put(10, 61){\sx{1.6}{$v\!=\!0$}} \put(142, 72){\sx{1.}{$u\!=\!-3$}} \put(142, 52){\sx{1.}{$u\!=\!-3$}} \put(229,290){\sx{1.4}{\bf complicated structure}} \put(250,230){\sx{1.5}{$G_1(x\!+\!\rmi y) \approx -3$}} \put(229,148){\sx{1.4}{\bf complicated structure}} \put(250,60){\sx{1.6}{$G_1(x\!+\!\rmi y) \approx -3$}} \put(229,5){\sx{1.4}{\bf complicated structure}} \end{picture}} \vskip 8pt \sx{1.}{\begin{picture}(415,320) \put(0,0){\ing{e1egi} } % suppress below to boost \figaxe \put( 4,220){\sx{1.2}{$u\!=\!19$}} %\put(166,216){\sx{1.4}{$p\!=\!18$}} \put(352,276){\sx{1.2}{$v\!=\!0.2$}} \put(350, 26){\sx{1.2}{$v\!=\!-0.2$}} \put(350,186){\sx{1.2}{$u\!=\!18.4$}} \put(270,176){\sx{1.2}{$u\!=\!18.2$}} \put(233,158){\sx{1.2}{$u\!=\!18$}} \put( 4, 74){\sx{1.2}{$u\!=\!19$}} % \put(166, 80){\sx{1.4}{$p\!=\!18$}} \put(20,186){\sx{1.2}{$v\!=\!1$}} \put(20,110){\sx{1.2}{$v\!=\!-1$}} \put(20,148.4){\sx{1.2}{\bf cut }} \put(377,148.4){\sx{1.1}{$v\!=\!0$}} \end{picture}} %\end{center} \end{document}