Difference between revisions of "File:Vladi02.jpg"

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[[Complex map]] of [[arctetration]] ate;
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Importing image file
  
  +
  +
$u\!+\!\mathrm i v=\mathrm{ate}(x\!+\!\mathrm i y)$
  +
  +
  +
Usage: this is figure 15.1 of the book [[Суперфункции]] (2014, In Russian) <ref>
  +
https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0 <br>
  +
http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf <br>
  +
http://mizugadro.mydns.jp/BOOK/202.pdf
  +
Д.Кузнецов. Суперфункции. [[Lambert Academic Publishing]], 2014.
  +
</ref>; the English version is in preparation in 2015.
  +
  +
First time published in the [[Vladikavkaz Matehmatical Journal]]
  +
<ref>
  +
http://mizugadro.mydns.jp/PAPERS/2010vladie.pdf
  +
D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
  +
Figure 2.
  +
</ref>.
  +
  +
==Refereces==
  +
<references/>
  +
  +
  +
==[[C++]] generator of map==
  +
  +
[[ado.cin]],
  +
[[conto.cin]],
  +
[[fslog.cin]]
  +
should be loaded in order to compile the code below.
  +
  +
<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++)
  +
#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 "superlo.cin"
  +
#include "fslog.cin"
  +
#include "conto.cin"
  +
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
  +
//z_type Zo=z_type(.31813150520476413, 1.3372357014306895);
  +
//z_type Zc=z_type(.31813150520476413,-1.3372357014306895);
  +
  +
int M=400,M1=M+1;
  +
int N=364,N1=N+1;
  +
//DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
  +
DB X[401],Y[365], g[146365],f[146365], w[146365]; // w is working array.
  +
//DB X[401],Y[365], g[160000],f[16000], w[16000]; // w is working array.
  +
//char v[M1*N1]; // v is working array
  +
char v[146365]; // v is working array
  +
FILE *o;o=fopen("vladi02c.eps","w");ado(o,202,122);
  +
fprintf(o,"101 61 translate\n 10 10 scale\n");
  +
  +
z_type L=z_type(.31813150520476413, 1.3372357014306895);
  +
p=Re(L); q=Im(L); DB R=abs(L); DB A=arg(L);
  +
fprintf(o,"0 0 %9.6f %9.6f %9.6f arc C .6 1 .5 RGB F\n",R,-180/M_PI*A,180/M_PI*A);
  +
  +
DB sx=8./sinh(.01*M);
  +
DO(m,M1) X[m]=sx*sinh(.02*(m-M/2));
  +
for(n=0;n<N1;n++){y =-5. +.03*(n-.5); if(y>-Im(L)) break; Y[n]=y;}
  +
m=n; y=-Im(L)-.001; Y[m]=y;
  +
m++; y=-Im(L)+.001; Y[m]=y;
  +
for(n=m+1;n<N1;n++){y =-5. +.03*(n-2-.5); if(y>Im(L)) break; Y[n]=y;}
  +
m=n; y=Im(L)-.001; Y[m]=y;
  +
m++; y=Im(L)+.001; Y[m]=y;
  +
for(n=m+1;n<N1;n++){y =-5. +.03*(n-4-.5); Y[n]=y;}
  +
  +
for(m=-8;m<9;m++) { if(m==0){M(m,-5.2)L(m,5.2)}
  +
else {M(m,-5)L(m,5)} }
  +
for(n=-5;n<6;n++) {M( -8,n)L(8,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; }
  +
// z_type F[M1*N1];
  +
DO(m,M1){x=X[m]; printf("50 run at x=%6.3f\n",x);
  +
DO(n,N1){y=Y[n]; z=z_type(x,y);
  +
c=FSLOG(z); p=Re(c); q=Im(c);
  +
if(p>-999 && p<999 && fabs(p)> 1.e-8 && fabs(p-1.)>1.e-8) g[m*N1+n]=p;
  +
if(q>-999 && q<999 && fabs(q)> 1.e-8) f[m*N1+n]=q;
  +
}}
  +
  +
p=.4;q=.4;
  +
//#include"plofu.cin"
  +
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,".01 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,".01 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,".01 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,".03 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,".03 W 0 0 .8 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".03 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,".03 W 0 0 0 RGB S\n");
  +
  +
  +
M(Re(L), Im(L)) L(-10, Im(L))
  +
M(Re(L),-Im(L)) L(-10,-Im(L)) fprintf(o,".02 W 1 1 1 RGB S\n");
  +
  +
DO(m,17){ M(Re(L)-.5*m, Im(L)) L(Re(L)-.5*(m+.5), Im(L))}
  +
DO(m,17){ M(Re(L)-.5*m,-Im(L)) L(Re(L)-.5*(m+.5),-Im(L))}
  +
fprintf(o,".08 W 0 0 0 RGB S\n");
  +
  +
// fprintf(o,".1 W 0 0 0 RGB [.12 .14] 1 setdash S\n");
  +
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
  +
system("epstopdf vladi02c.eps");
  +
system( "open vladi02c.pdf");
  +
//getchar(); system("killall Preview");//macintosh
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of labels==
  +
<poem><nomathjax><nowiki>
  +
\documentclass[12pt]{article}
  +
\usepackage{graphicx}
  +
\usepackage{rotating}
  +
\usepackage{geometry}
  +
\paperwidth 418px
  +
%\paperheight 134px
  +
\paperheight 292px
  +
\topmargin -104pt
  +
\oddsidemargin -94pt
  +
\pagestyle{empty}
  +
\begin{document}
  +
\newcommand \ing {\includegraphics}
  +
\newcommand \sx {\scalebox}
  +
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
\parindent 0pt
  +
\hskip -14pt
  +
\sx{2.5}{\begin{picture}(220,120)
  +
%\put(0,0){\includegraphics{figslogG}}
  +
\put(0,0){\includegraphics{vladi02c}}
  +
\put(17,114){\sx{.6}{$y$}}
  +
\put(17, 99){\sx{.58}{$4$}}
  +
\put(17, 89){\sx{.58}{$3$}}
  +
\put(17, 79){\sx{.58}{$2$}}
  +
\put(17, 69){\sx{.58}{$1$}}
  +
\put(17, 59){\sx{.58}{$0$}}
  +
\put(12, 49){\sx{.58}{$-1$}}
  +
\put(12, 39){\sx{.58}{$-2$}}
  +
\put(12, 29){\sx{.58}{$-3$}}
  +
\put(12, 19){\sx{.58}{$-4$}}
  +
\put(12, 9){\sx{.58}{$-5$}}
  +
\put(178,5){\sx{.6}{$x$}}
  +
%\put(180,4){\sx{.6}{$8$}}
  +
\put(160,5.2){\sx{.6}{$6$}}
  +
\put(140,5.2){\sx{.6}{$4$}}
  +
\put(120,5.2){\sx{.6}{$2$}}
  +
\put( 99.8,5.2){\sx{.6}{$0$}}
  +
\put( 76,5.2){\sx{.6}{$-2$}}
  +
\put( 56,5.2){\sx{.6}{$-4$}}
  +
\put( 36,5.2){\sx{.6}{$-6$}}
  +
%\put(105,57){\sx{1}{$G$}}
  +
  +
\put( 64,118){\sx{.5}{$u\!=\!2.2$}}
  +
\put( 94,118){\sx{.5}{$u\!=\!2$}}
  +
\put(118,118){\sx{.5}{$v\!=\!0.6$}}
  +
\put(148,118){\sx{.5}{$v\!=\!0.4$}}
  +
%\put(182,100){\sx{.5}{$v\!=\!0.2$}}
  +
%\put(182, 92){\sx{.5}{$u\!=\!1.8$}}
  +
\put(166, 59.8){\sx{.5}{$v\!=\!0$}}
  +
\end{picture}}
  +
\end{document}
  +
</nowiki></nomathjax></poem>
  +
  +
[[Category:Abel function]]
  +
[[Category:Abelfunction]]
  +
[[Category:Arctetration]]
  +
[[Category:Book]]
  +
[[Category:BookMap]]
  +
[[Category:C++]]
  +
[[Category:Complex map]]
  +
[[Category:Exp]]
  +
[[Category:Latex]]
  +
[[Category:Natural tetration]]
  +
[[Category:Tetration]]
  +
[[Category:Generator]]

Latest revision as of 08:56, 1 December 2018

Complex map of arctetration ate;

$u\!+\!\mathrm i v=\mathrm{ate}(x\!+\!\mathrm i y)$


Usage: this is figure 15.1 of the book Суперфункции (2014, In Russian) [1]; the English version is in preparation in 2015.

First time published in the Vladikavkaz Matehmatical Journal [2].

Refereces

  1. ↑ https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0
    http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf
    http://mizugadro.mydns.jp/BOOK/202.pdf Д.Кузнецов. Суперфункции. Lambert Academic Publishing, 2014.
  2. ↑ http://mizugadro.mydns.jp/PAPERS/2010vladie.pdf D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45. Figure 2.


C++ generator of map

ado.cin, conto.cin, fslog.cin should be loaded in order to compile the code below.



#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#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 "superlo.cin"
#include "fslog.cin"
#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
//z_type Zo=z_type(.31813150520476413, 1.3372357014306895);
//z_type Zc=z_type(.31813150520476413,-1.3372357014306895);

  int M=400,M1=M+1;
  int N=364,N1=N+1;
//DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
DB X[401],Y[365], g[146365],f[146365], w[146365]; // w is working array.
//DB X[401],Y[365], g[160000],f[16000], w[16000]; // w is working array.
//char v[M1*N1]; // v is working array
char v[146365]; // v is working array
FILE *o;o=fopen("vladi02c.eps","w");ado(o,202,122);
fprintf(o,"101 61 translate\n 10 10 scale\n");

z_type L=z_type(.31813150520476413, 1.3372357014306895);
p=Re(L); q=Im(L); DB R=abs(L); DB A=arg(L);
fprintf(o,"0 0 %9.6f %9.6f %9.6f arc C .6 1 .5 RGB F\n",R,-180/M_PI*A,180/M_PI*A);

  DB sx=8./sinh(.01*M);
  DO(m,M1) X[m]=sx*sinh(.02*(m-M/2));
 for(n=0;n<N1;n++){y =-5. +.03*(n-.5); if(y>-Im(L)) break; Y[n]=y;}
  m=n; y=-Im(L)-.001; Y[m]=y;
  m++; y=-Im(L)+.001; Y[m]=y;
for(n=m+1;n<N1;n++){y =-5. +.03*(n-2-.5); if(y>Im(L)) break; Y[n]=y;}
  m=n; y=Im(L)-.001; Y[m]=y;
  m++; y=Im(L)+.001; Y[m]=y;
for(n=m+1;n<N1;n++){y =-5. +.03*(n-4-.5); Y[n]=y;}

for(m=-8;m<9;m++) { if(m==0){M(m,-5.2)L(m,5.2)}
                        else {M(m,-5)L(m,5)} }
for(n=-5;n<6;n++) {M( -8,n)L(8,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; }
// z_type F[M1*N1];
DO(m,M1){x=X[m]; printf("50 run at x=%6.3f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
         c=FSLOG(z); p=Re(c); q=Im(c);
        if(p>-999 && p<999 && fabs(p)> 1.e-8 && fabs(p-1.)>1.e-8) g[m*N1+n]=p;
        if(q>-999 && q<999 && fabs(q)> 1.e-8) f[m*N1+n]=q;
        }}

p=.4;q=.4;
//#include"plofu.cin"
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,".01 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,".01 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,".01 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,".03 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,".03 W 0 0 .8 RGB S\n");
                conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".03 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,".03 W 0 0 0 RGB S\n");


M(Re(L), Im(L)) L(-10, Im(L))
M(Re(L),-Im(L)) L(-10,-Im(L)) fprintf(o,".02 W 1 1 1 RGB S\n");

DO(m,17){ M(Re(L)-.5*m, Im(L)) L(Re(L)-.5*(m+.5), Im(L))}
DO(m,17){ M(Re(L)-.5*m,-Im(L)) L(Re(L)-.5*(m+.5),-Im(L))}
fprintf(o,".08 W 0 0 0 RGB S\n");

// fprintf(o,".1 W 0 0 0 RGB [.12 .14] 1 setdash S\n");
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf vladi02c.eps");
        system( "open vladi02c.pdf");
//getchar(); system("killall Preview");//macintosh
}

Latex generator of labels


\documentclass[12pt]{article}
\usepackage{graphicx}
\usepackage{rotating}
\usepackage{geometry}
\paperwidth 418px
%\paperheight 134px
\paperheight 292px
\topmargin -104pt
\oddsidemargin -94pt
\pagestyle{empty}
\begin{document}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}

\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\parindent 0pt
\hskip -14pt
\sx{2.5}{\begin{picture}(220,120)
%\put(0,0){\includegraphics{figslogG}}
\put(0,0){\includegraphics{vladi02c}}
\put(17,114){\sx{.6}{$y$}}
\put(17, 99){\sx{.58}{$4$}}
\put(17, 89){\sx{.58}{$3$}}
\put(17, 79){\sx{.58}{$2$}}
\put(17, 69){\sx{.58}{$1$}}
\put(17, 59){\sx{.58}{$0$}}
\put(12, 49){\sx{.58}{$-1$}}
\put(12, 39){\sx{.58}{$-2$}}
\put(12, 29){\sx{.58}{$-3$}}
\put(12, 19){\sx{.58}{$-4$}}
\put(12, 9){\sx{.58}{$-5$}}
\put(178,5){\sx{.6}{$x$}}
%\put(180,4){\sx{.6}{$8$}}
\put(160,5.2){\sx{.6}{$6$}}
\put(140,5.2){\sx{.6}{$4$}}
\put(120,5.2){\sx{.6}{$2$}}
\put( 99.8,5.2){\sx{.6}{$0$}}
\put( 76,5.2){\sx{.6}{$-2$}}
\put( 56,5.2){\sx{.6}{$-4$}}
\put( 36,5.2){\sx{.6}{$-6$}}
%\put(105,57){\sx{1}{$G$}}

\put( 64,118){\sx{.5}{$u\!=\!2.2$}}
\put( 94,118){\sx{.5}{$u\!=\!2$}}
\put(118,118){\sx{.5}{$v\!=\!0.6$}}
\put(148,118){\sx{.5}{$v\!=\!0.4$}}
%\put(182,100){\sx{.5}{$v\!=\!0.2$}}
%\put(182, 92){\sx{.5}{$u\!=\!1.8$}}
\put(166, 59.8){\sx{.5}{$v\!=\!0$}}
\end{picture}}
\end{document}

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