File:E1eSuMap600.jpg
Complex maps of two superexponentials to the Henryk base $\eta\!=\!\exp(1/\mathrm e)\!\approx\! 1.444667861$
$u\!+\!\mathrm i v\!=\!F(x\!+\!\mathrm i y)$
for tetration $F\!=\! \mathrm{tet}_\eta$
and for growing superexponent $F\!=\! \mathrm{SuExp}_{\eta,3}$
Contents
C++ generator of upper map
Fiels ado.cin, conto.cin, e1etf.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 "e1etf.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 Function
//FILE *o;o=fopen("e1etf.eps","w");ado(o,402,302);
FILE *o;o=fopen("e1etetmap.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,"2 setlinecap .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=E1ETF(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-8 && fabs(p-1.)>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=1.8;q=1.;
//#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(-10.1,0) fprintf(o,"0 setlinecap .08 W 1 0 1 RGB S\n");
// M(-1.,0)L(-10.1,0) fprintf(o,"0 setlinecap .08 W 1 0 1 RGB S\n");
// M(-1.6,0)L(-10.1,0) fprintf(o,"0 setlinecap .08 W 1 0 1 RGB S\n");
M(-2.,0)L(-10.1,0) fprintf(o,"0 setlinecap .08 W 1 1 1 RGB S\n");
DO(m,15){M(-2.-.6*(m+.5),0)L(-2-.6*(m+1.),0)} fprintf(o,".09 W 1 0 1 RGB S\n");
fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
system("epstopdf e1etetmap.eps");
system( "open e1etetmap.pdf"); //mac
getchar(); system("killall Preview");// mac
}
C++ generator of lower map
#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 Function
//FILE *o;o=fopen("e1egf.eps","w");ado(o,402,302);
FILE *o;o=fopen("e1esuexpmap.eps","w");ado(o,402,302);
fprintf(o,"101 151 translate\n 10 10 scale\n");
// DO(m,M1) X[m]=-10.+.05*(m-.5);
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,"2 setlinecap .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=E1ETF(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.;q=.5;
//#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 e1esuexpmap.eps");
system( "open e1esuexpmap.pdf"); //mac
// system( "xpdf e1egf.pdf"); // linux
getchar(); system("killall Preview");// mac
}
Latex generator of 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
\paperwidth143mm
%\paperheight 257mm
%\paperheight 216mm
%\paperheight 106mm
\paperheight 214mm
%\textwidth 175mm
\textwidth 150mm
%\oddsidemargin 5mm
%\oddsidemargin -72pt
\oddsidemargin -54pt
%\topmargin -17mm
%\topmargin -100pt
\topmargin -110pt
\textheight 257mm
\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{.96}{\begin{picture}(410,310)
%\put(0,0){\ing{e1etf}}
\put(0,0){\ing{e1etetmap}}
\figaxe
\put( 4,225){\sx{1.3}{$u\!=\!3$}}
\put( 22,288){\sx{1.1}{$u\!=\!2.8$}} \put(108,288){\sx{1.1}{$u\!=\!2.6$}}
\put( 22, 8){\sx{1.1}{$u\!=\!2.8$}} \put(108, 8){\sx{1.1}{$u\!=\!2.6$}}
\put(112,250){\sx{1.1}{$v\!=\!0.4$}}
\put(120, 40){\sx{1.1}{$v\!=\!-0.4$}}
%\put(140,230){\sx{1.1}{$p\!=\!2.4$}}
\put(214,110){\sx{1.1}{$u\!=\!2.4$}}
%\put(140, 64){\sx{1.1}{$p\!=\!2.4$}}
%\put(160,198){\sx{1.1}{$q\!=\!0.2$}}
\put(190,260){\sx{1.1}{$v\!=\!0.2$}}
\put(130,156){\sx{1.3}{$u\!=\!2$}}
\put(277, 148.4){\sx{1.3}{$v\!=\!0$}}
\put(158,132){\sx{1.1}{$u\!=\!2.2$}}
\put(190, 17){\sx{1.1}{$v\!=\!-0.2$}}
\end{picture}}
\sx{.96}{\begin{picture}(410,320)
%\put(0,0){\ing{e1egf} } % suppress this string to boost
\put(0,0){\ing{e1esuexpmap} } % suppress this string to boost
\figaxe
\put(100,194){\sx{1.4}{$u\!=\!3$}}
\put(150,280){\sx{1.2}{$v\!=\!0.2$}}
\put(150, 30){\sx{1.2}{$v\!=\!-0.2$}}
\put(218,224){\sx{1.2}{$v\!=\!0.4$}}
\put(259,266){\sx{1.2}{$u\!=\!2.8$}}%
\put(258, 38){\sx{1.2}{$u\!=\!2.8$}}
\put(306,260){\sx{1.2}{$u\!=\!2.6$}}
\put(308, 39){\sx{1.2}{$u\!=\!2.6$}}
\put(350,252){\sx{1.2}{$v\!=\!0.4$}}
% \put(390,239){\sx{1.2}{$u\!=\!2.4$}}
\put(365,240){\sx{1.2}{$u\!=\!2.4$}}
% \put(370, 59){\sx{1.2}{$u\!=\!2.4$}}
% \put(390,205){\sx{1.2}{$v\!=\!0.2$}}
% \put(380, 88){\sx{1.2}{$v\!=\!-0.2$}}
\put(352, 73){\sx{1.2}{$v\!=\!-0.4$}}
% \put(390,172){\sx{1.2}{$u\!=\!2.2$}}
% \put(390,122){\sx{1.2}{$u\!=\!2.2$}}
\put(403,158){\sx{1.1}{$v\!=\!0$}}
\put(403,143){\sx{1.1}{$v\!=\!0$}}
\put(362,130){\sx{1.4}{$u\!=\!2$}}
\put(174,165){\sx{1.2}{$u\!=\!3.2$}}
\put( 60,148){\sx{1.4}{$v\!=\!0$}}
\put(334,149){\sx{.9}{\bf huge values}}
\end{picture}}
\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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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 06:11, 1 December 2018 | | 3,377 × 5,055 (1.37 MB) | Maintenance script (talk | contribs) | Importing image file |
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