Difference between revisions of "File:E1eAuMap600.jpg"

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(Importing image file)
 
 
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  +
[[Complex map]]s of the [[abel function]] of the [[exponent]] to the [[Henryk base]]
−
Importing image file
  
  +
$\eta\!=\!\exp(1/\mathrm e)\!\approx\! 1.444667861$
  +
  +
$u\!+\!\mathrm i v\!=\!G(x\!+\!\mathrm i y)$
  +
  +
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
  +
  +
<poem><nomathjax><nowiki>
  +
#include <math.h>
  +
#include <stdio.h>
  +
#include <stdlib.h>
  +
#define DB double
  +
#define DO(x,y) for(x=0;x<y;x++)
  +
//using namespace std;
  +
#include <complex>
  +
typedef std::complex<double> z_type;
  +
#define Re(x) x.real()
  +
#define Im(x) x.imag()
  +
#define I z_type(0.,1.)
  +
//#include "e1egf.cin"
  +
#include "e1eti.cin"
  +
#include "conto.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; }
  +
}}
  +
  +
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
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[C++]] generator of lower map==
  +
  +
Fiels
  +
[[ado.cin]],
  +
[[conto.cin]],
  +
[[e1eti.cin]]
  +
should be loaded
  +
  +
<poem><nomathjax><nowiki>
  +
#include <math.h>
  +
#include <stdio.h>
  +
#include <stdlib.h>
  +
#define DB double
  +
#define DO(x,y) for(x=0;x<y;x++)
  +
//using namespace std;
  +
#include <complex>
  +
typedef std::complex<double> z_type;
  +
#define Re(x) x.real()
  +
#define Im(x) x.imag()
  +
#define I z_type(0.,1.)
  +
//#include "e1egf.cin"
  +
#include "e1egi.cin"
  +
#include "conto.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; }
  +
}}
  +
  +
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
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator labels==
  +
  +
<poem><nomathjax><nowiki>
  +
\documentclass[12pt,a4paper,oneside]{book}
  +
%\newcommand \EN[1] {{#1}} % make the English version
  +
\newcommand \EN[1] {{}} % suppress the English version
  +
\newcommand \RU[1] {{#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 {{\rm e}} %%makes the base of natural logarithms Roman font
  +
%\newcommand \rme {{e}} %%makes the base of natural logarithms Italics font; choose one of these
  +
\newcommand \rmi {{\rm i}} %%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}
  +
</nowiki></nomathjax></poem>
  +
  +
==References==
  +
<references/>
  +
  +
http://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2012-02590-7/S0025-5718-2012-02590-7.pdf
  +
http://www.ils.uec.ac.jp/~dima/PAPERS/2011e1e.pdf H.Trappmann, D.Kouznetsov. Computation of the Two Regular Super-Exponentials to base exp(1/e). Mathematics of computation, 2012 February 8. ISSN 1088-6842(e) ISSN 0025-5718(p)
  +
  +
[[Category:Abel function]]
  +
[[Category:Arctetration]]
  +
[[Category:Book]]
  +
[[Category:BookMap]]
  +
[[Category:C++]]
  +
[[Category:e1e]]
  +
[[Category:Latex]]
  +
[[Category:Superfunction]]
  +
[[Category:Tetration]]

Latest revision as of 08:34, 1 December 2018

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


#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
//using namespace std;
#include <complex>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
//#include "e1egf.cin"
#include "e1eti.cin"
#include "conto.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; }
        }}

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


#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
//using namespace std;
#include <complex>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
//#include "e1egf.cin"
#include "e1egi.cin"
#include "conto.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; }
        }}

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] {{#1}} % make the English version
\newcommand \EN[1] {{}} % suppress the English version
\newcommand \RU[1] {{#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 {{\rm e}} %%makes the base of natural logarithms Roman font
%\newcommand \rme {{e}} %%makes the base of natural logarithms Italics font; choose one of these
\newcommand \rmi {{\rm i}} %%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}

References


http://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2012-02590-7/S0025-5718-2012-02590-7.pdf http://www.ils.uec.ac.jp/~dima/PAPERS/2011e1e.pdf H.Trappmann, D.Kouznetsov. Computation of the Two Regular Super-Exponentials to base exp(1/e). Mathematics of computation, 2012 February 8. ISSN 1088-6842(e) ISSN 0025-5718(p)

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