Difference between revisions of "File:Tetsheldonzoo.jpg"

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  +
[[Complex map]] of [[tetration to Sheldon base]], zoom-in from the central part of figure
−
Importing image file
  
  +
http://mizugadro.mydns.jp/t/index.php/File:Tetsheldonmap03.png
  +
  +
$b=s=1.52598338517+0.0178411853321 i$.
  +
  +
$f=tet_s(x+\mathrm i y)$ is shown in ths $x,y$ plane with levels $u=\Re(f)=\mathrm{const}$
  +
and levels $v=\Im(f)=\mathrm{const}$;
  +
thick lines correspond ot the integer values.
  +
  +
==Usage==
  +
This image should be second picture of figure 18.3 of English version of book [[Superfunctions]]
  +
<ref>
  +
http://www.ils.uec.ac.jp/~dima/BOOK/437.pdf <br>
  +
http://mizugadro.mydns.jp/BOOK/437.pdf
  +
D.Kouznetov. Superfunctions. 2015.
  +
</ref>
  +
  +
==References==
  +
<references/>
  +
==[[C++]] generator of map==
  +
Files
  +
[[ado.cin]],
  +
[[conto.cin]],
  +
[[filog.cin]],
  +
[[GLxw2048.inc]],
  +
[[TetSheldonIma.inc]]
  +
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++)
  +
// 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 "conto.cin"
  +
#include "filog.cin"
  +
z_type b=z_type( 1.5259833851700000, 0.0178411853321000);
  +
z_type a=log(b);
  +
z_type Zo=Filog(a);
  +
z_type Zc=conj(Filog(conj(a)));
  +
DB A=32.;
  +
z_type tetb(z_type z){ int k; DB t; z_type c, cu,cd;
  +
#include "GLxw2048.inc"
  +
int K=2048;
  +
//#include "ima6.inc"
  +
#include "TetSheldonIma.inc"
  +
z_type E[2048],G[2048];
  +
DO(k,K){c=F[k]; E[k]=log(c)/a; G[k]=exp(a*c);}
  +
c=0.;
  +
//z+=z_type(0.1196573712872846, 0.1299776198056910);
  +
z+=z_type( 0.1196591376539 , 0.1299777213955 );
  +
DO(k,K){t=A*GLx[k];c+=GLw[k]*(G[k]/(z_type( 1.,t)-z)-E[k]/(z_type(-1.,t)-z));}
  +
cu=.5-I/(2.*M_PI)*log( (z_type(1.,-A)+z)/(z_type(1., A)-z) );
  +
cd=.5-I/(2.*M_PI)*log( (z_type(1.,-A)-z)/(z_type(1., A)+z) );
  +
c=c*(A/(2.*M_PI)) +Zo*cu+Zc*cd;
  +
return c;}
  +
  +
int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d;
  +
//int M=161,M1=M+1;
  +
int M=201,M1=M+1;
  +
int N=701,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
  +
// FILE *o;o=fopen("09.eps","w");ado(o,2030,2020);
  +
FILE *o;o=fopen("tetsheldonzo.eps","w");ado(o,2030,2020);
  +
fprintf(o,"1010 1010 translate\n 100 100 scale\n");
  +
DO(m,M1)X[m]=-10.+.1*(m-.5);
  +
DO(n,400)Y[n]=-10.+.025*n;
  +
Y[400]=-.001;
  +
Y[401]= .001;
  +
for(n=202;n<N1;n++) Y[n]=-10.+.025*(n-1.);
  +
for(m=-10;m<11;m++){if(m==0){M(m,-10.2)L(m,10.2)} else{M(m,-10)L(m,10)}}
  +
for(n=-10;n<11;n++){ M( -10,n)L(10,n)}
  +
fprintf(o,".008 W 0 0 0 RGB S\n");
  +
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
  +
DO(n,N1){y=Y[n];
  +
for(m=95;m<105;m++)
  +
{x=X[m]; //printf("%5.2f\n",x);
  +
z=z_type(x,y);
  +
c=tetb(z);
  +
p=Re(c);q=Im(c);
  +
if(p>-99. && p<99. && q>-99. && q<99. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
  +
d=c;
  +
for(k=1;k<11;k++)
  +
{ m1=m+k*10; if(m1>M) break;
  +
d=exp(a*d);
  +
p=Re(d);q=Im(d);
  +
if(p>-99. && p<99. && q>-99. && q<99. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;}
  +
}
  +
d=c;
  +
for(k=1;k<11;k++)
  +
{ m1=m-k*10; if(m1<0) break;
  +
d=log(d)/a;
  +
p=Re(d);q=Im(d);
  +
if(p>-99. && p<99. && q>-99. && q<99. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;}
  +
}
  +
}}
  +
fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=1.6;q=.7;
  +
for(m=-10;m<10;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<10;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<10;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<10;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".08 W .9 0 0 RGB S\n");
  +
for(m=1;m<10;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".08 W 0 0 .9 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".08 W .6 0 .6 RGB S\n");
  +
for(m=-9;m<10;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".08 W 0 0 0 RGB S\n");
  +
// y= 0; for(m=0;m<260;m+=6) {x=-2.-.1*m; M(x,y) L(x-.1,y)}
  +
// fprintf(o,".07 W 1 .5 0 RGB S\n");
  +
// y= 0; for(m=3;m<260;m+=6) {x=-2-.1*m; M(x,y) L(x-.1,y)}
  +
// fprintf(o,".07 W 0 .5 1 RGB S\n");
  +
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
  +
system("epstopdf tetsheldonzo.eps");
  +
system( "open tetsheldonzo.pdf");
  +
getchar(); system("killall Preview");
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of labels==
  +
<poem><nomathjax><nowiki>
  +
\documentclass[12pt]{article}
  +
\usepackage{geometry}
  +
\paperwidth 2090pt
  +
\paperheight 2080pt
  +
\textwidth 2090pt
  +
\textheight 2090pt
  +
%\textwidth 700pt
  +
\usepackage{graphics}
  +
\newcommand \sx \scalebox
  +
\newcommand \ing \includegraphics
  +
\parindent 0pt
  +
\topmargin -104pt
  +
\oddsidemargin -54pt
  +
%\usepackage{rotate}
  +
\usepackage{rotating}
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
\begin{document}
  +
\begin{picture}(2064,2056)
  +
%\put(0,0){\ing{04}}
  +
%\put(0,0){\ing{tetshelim}}
  +
\put(50,40){\ing{tetsheldonzo}}
  +
\put(10,2024){\sx{6.2}{$y$}}
  +
\put(10,1832){\sx{6}{$8$}}
  +
\put(10,1632){\sx{6}{$6$}}
  +
\put(10,1432){\sx{6}{$4$}}
  +
\put(10,1232){\sx{6}{$2$}}
  +
\put(10,1032){\sx{6}{$0$}}
  +
\put(-36, 832){\sx{6}{$-2$}}
  +
\put(-36, 632){\sx{6}{$-4$}}
  +
\put(-36, 432){\sx{6}{$-6$}}
  +
\put(-36, 232){\sx{6}{$-8$}}
  +
\put(-16, -8){\sx{6}{$-10$}}
  +
\put(200, -8){\sx{6}{$-8$}}
  +
\put(400, -8){\sx{6}{$-6$}}
  +
\put(600, -8){\sx{6}{$-4$}}
  +
\put(800, -8){\sx{6}{$-2$}}
  +
\put(1049, -8){\sx{6}{$0$}}
  +
\put(1249, -8){\sx{6}{$2$}}
  +
\put(1449, -8){\sx{6}{$4$}}
  +
\put(1649, -8){\sx{6}{$6$}}
  +
\put(1849, -8){\sx{6}{$8$}}
  +
\put(2020, -8){\sx{6.2}{$x$}}
  +
%\put(1000,1000}{\sx{6}{\rot{-8} $u\!=\!0$ \ero}}
  +
\put(1070,940){\sx{8}{\rot{82}$u\!=\!1$\ero}}
  +
\put(1300,930){\sx{8}{\rot{82}$u\!=\!2$\ero}}
  +
\put(1566,900){\sx{8}{\rot{76}$u\!=\!3$\ero}}
  +
\put(1300,1516){\sx{8}{\rot{-19}$v\!=\!1$\ero}}%
  +
\put(1330,1008){\sx{8}{\rot{-11}$v\!=\!0$\ero}}
  +
\put(1330, 618){\sx{8}{\rot{19}$v\!=\!-1$\ero}}%
  +
\end{picture}
  +
\end{document}
  +
</nowiki></nomathjax></poem>
  +
  +
==References==
  +
  +
Дмитрий Кузнецов. Суперфункции. Lambert Academic Press, 2014.
  +
  +
[[Category:Complex map]]
  +
[[Category:Tetration]]
  +
[[Category:Tetration to Sheldon base]]
  +
[[Category:Superfunction]]
  +
[[Category:Sheldon Levenstein]]
  +
[[Category:Problem with fig]]
  +
[[Category:Book]]
  +
[[Category:BookMap]]
  +
[[Category:C++]]
  +
[[Category:Latex]]
  +
[[Category:Fragment]]
  +
[[Category:Zoomin]]

Latest revision as of 08:54, 1 December 2018

Complex map of tetration to Sheldon base, zoom-in from the central part of figure http://mizugadro.mydns.jp/t/index.php/File:Tetsheldonmap03.png

$b=s=1.52598338517+0.0178411853321 i$.

$f=tet_s(x+\mathrm i y)$ is shown in ths $x,y$ plane with levels $u=\Re(f)=\mathrm{const}$ and levels $v=\Im(f)=\mathrm{const}$; thick lines correspond ot the integer values.

Usage

This image should be second picture of figure 18.3 of English version of book Superfunctions [1]

References

  1. ↑ http://www.ils.uec.ac.jp/~dima/BOOK/437.pdf
    http://mizugadro.mydns.jp/BOOK/437.pdf D.Kouznetov. Superfunctions. 2015.

C++ generator of map

Files ado.cin, conto.cin, filog.cin, GLxw2048.inc, TetSheldonIma.inc 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++)
// 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 "conto.cin"
 #include "filog.cin"
z_type b=z_type( 1.5259833851700000, 0.0178411853321000);
z_type a=log(b);
z_type Zo=Filog(a);
z_type Zc=conj(Filog(conj(a)));
DB A=32.;
z_type tetb(z_type z){ int k; DB t; z_type c, cu,cd;
#include "GLxw2048.inc"
int K=2048;
//#include "ima6.inc"
#include "TetSheldonIma.inc"
z_type E[2048],G[2048];
DO(k,K){c=F[k]; E[k]=log(c)/a; G[k]=exp(a*c);}
c=0.;
//z+=z_type(0.1196573712872846, 0.1299776198056910);
z+=z_type( 0.1196591376539 , 0.1299777213955 );
DO(k,K){t=A*GLx[k];c+=GLw[k]*(G[k]/(z_type( 1.,t)-z)-E[k]/(z_type(-1.,t)-z));}
 cu=.5-I/(2.*M_PI)*log( (z_type(1.,-A)+z)/(z_type(1., A)-z) );
 cd=.5-I/(2.*M_PI)*log( (z_type(1.,-A)-z)/(z_type(1., A)+z) );
 c=c*(A/(2.*M_PI)) +Zo*cu+Zc*cd;
 return c;}

int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d;
 //int M=161,M1=M+1;
 int M=201,M1=M+1;
 int N=701,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
// FILE *o;o=fopen("09.eps","w");ado(o,2030,2020);
 FILE *o;o=fopen("tetsheldonzo.eps","w");ado(o,2030,2020);
 fprintf(o,"1010 1010 translate\n 100 100 scale\n");
 DO(m,M1)X[m]=-10.+.1*(m-.5);
 DO(n,400)Y[n]=-10.+.025*n;
         Y[400]=-.001;
         Y[401]= .001;
 for(n=202;n<N1;n++) Y[n]=-10.+.025*(n-1.);
 for(m=-10;m<11;m++){if(m==0){M(m,-10.2)L(m,10.2)} else{M(m,-10)L(m,10)}}
 for(n=-10;n<11;n++){ M( -10,n)L(10,n)}
 fprintf(o,".008 W 0 0 0 RGB S\n");
 DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
 DO(n,N1){y=Y[n];
          for(m=95;m<105;m++)
          {x=X[m]; //printf("%5.2f\n",x);
           z=z_type(x,y);
           c=tetb(z);
           p=Re(c);q=Im(c);
           if(p>-99. && p<99. && q>-99. && q<99. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
           d=c;
           for(k=1;k<11;k++)
                { m1=m+k*10; if(m1>M) break;
                d=exp(a*d);
                p=Re(d);q=Im(d);
                if(p>-99. && p<99. && q>-99. && q<99. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;}
                }
           d=c;
           for(k=1;k<11;k++)
                { m1=m-k*10; if(m1<0) break;
                d=log(d)/a;
                p=Re(d);q=Im(d);
                if(p>-99. && p<99. && q>-99. && q<99. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;}
                }
        }}
 fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=1.6;q=.7;
 for(m=-10;m<10;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<10;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<10;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<10;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".08 W .9 0 0 RGB S\n");
 for(m=1;m<10;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".08 W 0 0 .9 RGB S\n");
                    conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".08 W .6 0 .6 RGB S\n");
 for(m=-9;m<10;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".08 W 0 0 0 RGB S\n");
// y= 0; for(m=0;m<260;m+=6) {x=-2.-.1*m; M(x,y) L(x-.1,y)}
// fprintf(o,".07 W 1 .5 0 RGB S\n");
// y= 0; for(m=3;m<260;m+=6) {x=-2-.1*m; M(x,y) L(x-.1,y)}
// fprintf(o,".07 W 0 .5 1 RGB S\n");
 fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf tetsheldonzo.eps");
        system( "open tetsheldonzo.pdf");
        getchar(); system("killall Preview");
 }

Latex generator of labels


 \documentclass[12pt]{article}
 \usepackage{geometry}
 \paperwidth 2090pt
 \paperheight 2080pt
 \textwidth 2090pt
 \textheight 2090pt
 %\textwidth 700pt
 \usepackage{graphics}
 \newcommand \sx \scalebox
 \newcommand \ing \includegraphics
\parindent 0pt
\topmargin -104pt
\oddsidemargin -54pt
%\usepackage{rotate}
\usepackage{rotating}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\begin{document}
\begin{picture}(2064,2056)
%\put(0,0){\ing{04}}
%\put(0,0){\ing{tetshelim}}
\put(50,40){\ing{tetsheldonzo}}
\put(10,2024){\sx{6.2}{$y$}}
\put(10,1832){\sx{6}{$8$}}
\put(10,1632){\sx{6}{$6$}}
\put(10,1432){\sx{6}{$4$}}
\put(10,1232){\sx{6}{$2$}}
\put(10,1032){\sx{6}{$0$}}
\put(-36, 832){\sx{6}{$-2$}}
\put(-36, 632){\sx{6}{$-4$}}
\put(-36, 432){\sx{6}{$-6$}}
\put(-36, 232){\sx{6}{$-8$}}
\put(-16, -8){\sx{6}{$-10$}}
\put(200, -8){\sx{6}{$-8$}}
\put(400, -8){\sx{6}{$-6$}}
\put(600, -8){\sx{6}{$-4$}}
\put(800, -8){\sx{6}{$-2$}}
\put(1049, -8){\sx{6}{$0$}}
\put(1249, -8){\sx{6}{$2$}}
\put(1449, -8){\sx{6}{$4$}}
\put(1649, -8){\sx{6}{$6$}}
\put(1849, -8){\sx{6}{$8$}}
\put(2020, -8){\sx{6.2}{$x$}}
%\put(1000,1000}{\sx{6}{\rot{-8} $u\!=\!0$ \ero}}
\put(1070,940){\sx{8}{\rot{82}$u\!=\!1$\ero}}
\put(1300,930){\sx{8}{\rot{82}$u\!=\!2$\ero}}
\put(1566,900){\sx{8}{\rot{76}$u\!=\!3$\ero}}
\put(1300,1516){\sx{8}{\rot{-19}$v\!=\!1$\ero}}%
\put(1330,1008){\sx{8}{\rot{-11}$v\!=\!0$\ero}}
\put(1330, 618){\sx{8}{\rot{19}$v\!=\!-1$\ero}}%
\end{picture}
\end{document}

References

Дмитрий Кузнецов. Суперфункции. Lambert Academic Press, 2014.

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