Difference between pages "File:Vladi06.jpg" and "File:Vladi07.jpg"

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Line 1: Line 1:
−
[[Complex map]] of the approximation "tai" of natural [[tetration]], left, and the map of the corresponding agreement function $D$.
 +
Maps of agreement of approximations of natural [[tetration]] with elementary functions [[fima]] and [[maclo]], used in the implementation [[fsexp.cin]].
   
  +
Left: $D=D_6(x\!+\!\mathrm i y)$;
−
<b>Left:</b>
  
   
  +
$\displaystyle
−
$u\!+\!\mathrm i v = \mathrm{tai}(x+\mathrm i y)$
  
  +
D_6(z)= - \ln \left( \frac
  +
{|\mathrm{tai}(z) - \mathrm{fima}(z)|}
  +
{|\mathrm{tai}(z)|+|\mathrm{fima}(z)|}
  +
\right)$
   
  +
right: $D=D_7(x\!+\!\mathrm i y)$;
−
<b>Right:</b>
  
   
−
$\displaystyle
+
$\displaystyle
−
D_6=D_6(z)=-\lg\left( \frac
 +
D_7(z)= - \ln \left( \frac
−
{|\exp(\mathrm{tai}(z\!-\!1)-\mathrm{tai}(z)|}
 +
{|\mathrm{tai}(z) - \mathrm{maclo}(z)|}
−
{|\exp(\mathrm{tai}(z\!-\!1)|+|\mathrm{tai}(z)|} \right)
 +
{|\mathrm{tai}(z)|+|\mathrm{maclo}(z)|}
  +
\right)$
−
$
  
   
−
levels $D=1,2,4,6,8,10,12,14 ~ ~ $ are drawn. Level $D=1$ is drawn with thick line.
+
Levels $D=\mathrm{const}$ are drawn with step 2, but the exception is dome for level $D=1$, this level is drawn with thick lines.
   
−
Usage: this is figure 14.8 of the book [[Суперфункции]] (2014, In Russian)
 +
Usage: this is figure 14.10 of the book [[Суперфункции]] (2014, In Russian) <ref>
−
<ref>
  
 
https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0 <br>
  
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://www.ils.uec.ac.jp/~dima/BOOK/202.pdf <br>
 
http://mizugadro.mydns.jp/BOOK/202.pdf
 
http://mizugadro.mydns.jp/BOOK/202.pdf
 
Д.Кузнецов. Суперфункции. [[Lambert Academic Publishing]], 2014.
  
Д.Кузнецов. Суперфункции. [[Lambert Academic Publishing]], 2014.
  +
</ref>; the English version is in preparation in 2015.
−
</ref>
  
−
; the English version is in preparation in 2015.
  
   
 
First time published in the [[Vladikavkaz Matehmatical Journal]]
  
First time published in the [[Vladikavkaz Matehmatical Journal]]
Line 28: Line 30:
 
http://mizugadro.mydns.jp/PAPERS/2010vladie.pdf
  
http://mizugadro.mydns.jp/PAPERS/2010vladie.pdf
 
D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
 
D.Kouznetsov. Superexponential as special function. Vladikavkaz Mathematical Journal, 2010, v.12, issue 2, p.31-45.
−
Figure 6.
 +
Figure 7.
 
</ref>.
  
</ref>.
  +
  +
==Refereces==
  +
<references/>
   
 
==[[C++]] generator of the first picture==
  
==[[C++]] generator of the first picture==
−
[[fsexp.cin]],
 +
[[Fsexp.cin]],
 
[[ado.cin]],
  
[[ado.cin]],
−
[[conto.cin]]
 +
[[conto.cin]],
  +
[[plodi.cin]]
 
should be loaded in order to compile the code below
  
should be loaded in order to compile the code below
  +
 
<poem><nomathjax><nowiki>
  
<poem><nomathjax><nowiki>
  +
#include <math.h>
 
#include <stdio.h>
  
#include <stdio.h>
 
#include <stdlib.h>
  
#include <stdlib.h>
 
#define DB double
  
#define DB double
 
#define DO(x,y) for(x=0;x<y;x++)
  
#define DO(x,y) for(x=0;x<y;x++)
−
//using namespace std;
  
 
#include <complex>
  
#include <complex>
 
typedef std::complex<double> z_type;
  
typedef std::complex<double> z_type;
  +
//#include <complex.h>
  +
//#define z_type complex<double>
 
#define Re(x) x.real()
  
#define Re(x) x.real()
 
#define Im(x) x.imag()
  
#define Im(x) x.imag()
Line 49: Line 58:
   
 
#include "fsexp.cin"
  
#include "fsexp.cin"
  +
−
//#include "superex.cin"
  
−
//#include "superlo.cin"
  
 
#include "conto.cin"
  
#include "conto.cin"
 
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
  
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=201,M1=M+1;
 +
int M=100,M1=M+1;
−
int N=201,N1=N+1;
 +
int N=101,N1=N+1;
 
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
  
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
  
char v[M1*N1]; // v is working array
−
//FILE *o;o=fopen("figtai3.eps","w");ado(o,0,0,82,82);
 +
FILE *o;o=fopen("vladi07a.eps","w");ado(o,82,82);
−
FILE *o;o=fopen("vladi06a.eps","w");ado(o,82,82);
  
 
fprintf(o,"41 11 translate\n 10 10 scale\n");
  
fprintf(o,"41 11 translate\n 10 10 scale\n");
   
−
DO(m,M1) X[m]=-4.+.04*(m-.5);
 +
DO(m,M1) X[m]=-4.+.08*(m-.5);
−
//DO(n,N1) Y[n]=-1.2 +.02*n*(1.+.000008*(n-8.)*(n-8));
 +
DO(n,N1)Y[n]= -1 +.08*(n-.5);
−
DO(n,N1) Y[n]=-1. +.04*(n-.5);
  
   
  +
for(m=-3;m<4;m++) { if(m==0){M(m,-0.1)L(m,6.1)} else {M(m,0)L(m,6)} }
−
//DB sy=6./sinh(.005*N);
  
  +
for(n=0;n<7;n++) { M( -3,n)L(3,n)}
−
//DO(n,N1) Y[n]=sy*sinh(.01*(n-N/2-.5+10));
  
  +
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;}
−
for(m=-4;m<5;m++) { if(m==0){M(m,-1.1)L(m,6.1)}
  
  +
DO(m,M1){x=X[m]; printf("run at x=%6.3f\n",x);
−
else {M(m,-1)L(m,6)} }
  
−
for(n=-1;n<7;n++) {M( -4,n)L(4,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("50 run at x=%6.3f\n",x);
  
 
DO(n,N1){y=Y[n]; z=z_type(x,y);
  
DO(n,N1){y=Y[n]; z=z_type(x,y);
−
c=tai3(z);
 +
c=tai3(z);
−
p=Re(c); q=Im(c);
 +
// d=fima1(z);
−
if(p>-9 && p<9) g[m*N1+n]=p;
 +
d=fima(z);
−
if(q>-9 && q<9) f[m*N1+n]=q;
 +
p=abs(c-d)/(abs(c)+abs(d));
  +
p=-log(p)/log(10.);
  +
// 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=1;q=.5;
  
−
conto(o,g,w,v,X,Y,M,N, ( Re(Zo) ),-q,q); fprintf(o,".1 W 1 .5 1 RGB S\n");
  
−
conto(o,f,w,v,X,Y,M,N, ( Im(Zo) ),-q,q); fprintf(o,".1 W .2 1 .5 RGB S\n");
  
−
conto(o,f,w,v,X,Y,M,N, (-Im(Zo) ),-q,q); fprintf(o,".1 W .5 1 .2 RGB S\n");
  
   
−
#include"plofu.cin"
 +
#include"plodi.cin"
   
 
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
  
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
−
system("epstopdf vladi06a.eps");
 +
system("epstopdf vladi07a.eps");
−
system( "open vladi06a.pdf");//for macintosh
 +
system( "open vladi07a.pdf");//macintosh
−
// system( "xpdf fig06a.pdf");//for linux
 +
// getchar(); system("killall Preview"); //macintosh
−
//getchar(); system("killall Preview");//for macintosh
  
 
}
  
}
 
</nowiki></nomathjax></poem>
  
</nowiki></nomathjax></poem>
  +
 
==[[C++]] generator of the second picture==
  
==[[C++]] generator of the second picture==
−
[[fsexp.cin]],
  
−
[[ado.cin]],
  
−
[[conto.cin]]
  
−
should be loaded in order to compile the code below
  
 
<poem><nomathjax><nowiki>
  
<poem><nomathjax><nowiki>
  +
  +
#include <math.h>
 
#include <stdio.h>
  
#include <stdio.h>
 
#include <stdlib.h>
  
#include <stdlib.h>
Line 110: Line 108:
 
#include <complex>
  
#include <complex>
 
typedef std::complex<double> z_type;
  
typedef std::complex<double> z_type;
  +
//#include <complex.h>
  +
//#define z_type complex<double>
 
#define Re(x) x.real()
  
#define Re(x) x.real()
 
#define Im(x) x.imag()
  
#define Im(x) x.imag()
Line 115: Line 115:
   
 
#include "fsexp.cin"
  
#include "fsexp.cin"
  +
 
#include "conto.cin"
  
#include "conto.cin"
 
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
  
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=200,M1=M+1;
 +
int M=100,M1=M+1;
−
int N=201,N1=N+1;
 +
int N=101,N1=N+1;
 
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
  
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
  
char v[M1*N1]; // v is working array
−
//FILE *o;o=fopen("figtai3L.eps","w");ado(o,0,0,82,82);
 +
FILE *o;o=fopen("vladi07b.eps","w");ado(o,82,82);
−
FILE *o;o=fopen("vladi06b.eps","w");ado(o,82,82);
  
 
fprintf(o,"41 11 translate\n 10 10 scale\n");
  
fprintf(o,"41 11 translate\n 10 10 scale\n");
   
−
DO(m,M1) X[m]=-4.+.04*m;
 +
DO(m,M1) X[m]=-4.+.08*(m-.5);
−
DO(n,N1) Y[n]=-1.+.04*n;
 +
DO(n,N1)Y[n]= -1 +.08*(n-.5);
   
  +
for(m=-3;m<4;m++) { if(m==0){M(m,-0.1)L(m,6.1)} else {M(m,0)L(m,6)} }
−
//DB sy=6./sinh(.005*N);
  
  +
for(n=0;n<7;n++) { M( -3,n)L(3,n)}
−
//DO(n,N1) Y[n]=sy*sinh(.01*(n-N/2-.5+10));
  
  +
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;}
−
for(m=-4;m<5;m++) { if(m==0){M(m,-1.1)L(m,6.1)}
  
−
else {M(m,-1)L(m,6)} }
  
−
for(n=-1;n<7;n++) {M( -4,n)L(4,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(m,M1){x=X[m]; printf("run at x=%6.3f\n",x);
 
DO(n,N1){y=Y[n]; z=z_type(x,y);
  
DO(n,N1){y=Y[n]; z=z_type(x,y);
−
c=log(tai3(z+1.));
 +
c=tai3(z);
−
d=tai3(z);
 +
d=maclo(z);
−
p=abs(c-d);
 +
// d=fima1(z);
  +
p=abs(c-d)/(abs(c)+abs(d));
 
p=-log(p)/log(10.);
  
p=-log(p)/log(10.);
−
if(p>-999 && p<999) g[m*N1+n]=p;
 +
// 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;
 
}}
  
}}
−
fprintf(o,"1 setlinecap 1 setlinejoin\n");
  
   
 
#include"plodi.cin"
  
#include"plodi.cin"
   
 
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
  
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
−
system("epstopdf vladi06b.eps");
+
system("epstopdf vladi07b.eps");
−
system( "open vladi06b.pdf"); //for macintosh
 +
system( "open vladi07b.pdf");//macintosh
−
// system( "xpdf vladi06b.pdf"); //for linux
+
// getchar(); system("killall Preview");//macintosh
−
//getchar(); system("killall Preview");//for macintosh
  
 
}
  
}
  +
 
</nowiki></nomathjax></poem>
  
</nowiki></nomathjax></poem>
  +
 
==[[Latex]] combiner==
  
==[[Latex]] combiner==
 
<poem><nomathjax><nowiki>
  
<poem><nomathjax><nowiki>
Line 165: Line 162:
 
\usepackage{rotating}
  
\usepackage{rotating}
 
\usepackage{geometry}
  
\usepackage{geometry}
−
\paperwidth 418px
 +
\paperwidth 356px
 
%\paperheight 134px
 
%\paperheight 134px
−
\paperheight 190px
+
\paperheight 184px
−
\topmargin -108pt
 +
\topmargin -98pt
−
\oddsidemargin -80pt
 +
\oddsidemargin -94pt
 
\pagestyle{empty}
  
\pagestyle{empty}
 
\begin{document}
  
\begin{document}
Line 178: Line 175:
 
\newcommand \ero {\end{rotate}}
  
\newcommand \ero {\end{rotate}}
   
−
\newcommand \taiax {
 +
\newcommand \tafiax {
−
\put(-3,77){\sx{.5}{$y$}}
 +
\put(7,68){\sx{.5}{$y$}}
−
\put(-3,69){\sx{.5}{$6$}}
 +
%\put(5,74){\sx{.5}{$\Im(z)$}}
−
\put(-3,59){\sx{.5}{$5$}}
 +
%\put(7,69){\sx{.5}{$6$}}
−
\put(-3,49){\sx{.5}{$4$}}
 +
\put(7,59){\sx{.5}{$5$}}
−
\put(-3,39){\sx{.5}{$3$}}
 +
\put(7,49){\sx{.5}{$4$}}
−
\put(-3,29){\sx{.5}{$2$}}
 +
\put(7,39){\sx{.5}{$3$}}
−
\put(-3,19){\sx{.5}{$1$}}
 +
\put(7,29){\sx{.5}{$2$}}
−
\put(-3, 9){\sx{.5}{$0$}}
 +
\put(7,19){\sx{.5}{$1$}}
−
\put(-5,-1){\sx{.5}{$-\!1$}}
 +
\put(7, 9){\sx{.5}{$0$}}
−
\put( 7 ,-4){\sx{.5}{$-\!3$}}
 +
\put( 7 ,6){\sx{.5}{$-\!3$}}
−
\put(17 ,-4){\sx{.5}{$-\!2$}}
 +
\put(17 ,6){\sx{.5}{$-\!2$}}
−
\put(27 ,-4){\sx{.5}{$-\!1$}}
 +
\put(27 ,6){\sx{.5}{$-\!1$}}
−
\put(40 , -4){\sx{.5}{$0$}}
 +
\put(40 , 6){\sx{.5}{$0$}}
−
\put(50 , -4){\sx{.5}{$1$}}
 +
\put(50 , 6){\sx{.5}{$1$}}
−
\put(60 , -4){\sx{.5}{$2$}}
 +
\put(60 , 6){\sx{.5}{$2$}}
−
\put(70 , -4){\sx{.5}{$3$}}
 +
%\put(70 , 6){\sx{.5}{$3$}}
−
\put(78.8 , -4){\sx{.5}{$x$}}
 +
%\put(78 , 6){\sx{.5}{$\Re(z)$}}
  +
\put(70 , 6){\sx{.5}{$x$}}
 
}
  
}
−
\sx{2.23}{\begin{picture}(100,80)
 +
%\sx{2.33}{\begin{picture}(96,75)
  +
\sx{2.33}{\begin{picture}(80,75)
−
%\put(0,0){\includegraphics{figtai3}}
  
−
\put(0,0){\includegraphics{vladi06a}}
 +
%\put(0,0){\includegraphics{figtaifima}}
  +
\put(0,0){\includegraphics{vladi07a}}
−
\put(13,55){\sx{.44}{\rot{-77} $ v\!=\!\Im(L)$ \ero }}
  
  +
\tafiax
−
\put(23,62.4){\sx{.44}{\rot{-77} $ u\!=\!\Re(L)$ \ero }}
  
−
\put(34,65){\sx{.44}{\rot{-76} $ v\!=\!\Im(L)$ \ero }}
 +
\put(31,54){\sx{.45}{$D\!>\!14$}}
−
\put(45.6,66){\sx{.44}{\rot{-76} $ u\!=\!\Re(L)$ \ero }}
  
−
\put(57.6,65){\sx{.44}{\rot{-77} $ v\!=\!\Im(L)$ \ero }}
  
−
%\put(33,5){\sx{.4}{\rot{67} $ v\!=\!\Im(L^*)$ \ero }}
  
−
\put(42,7){\sx{.4}{\rot{86} $ u\!=\!1$ \ero }}
  
−
\put(35,24.6){\sx{.4}{\rot{-31} $ v\!=\!1$ \ero }}
  
−
%\put(28,16){\sx{.4}{\rot{37} $ v\!=\!-1$ \ero }}
  
−
\taiax
  
 
\end{picture}}
  
\end{picture}}
−
\sx{2.23}{\begin{picture}(80,80)
 +
\sx{2.33}{\begin{picture}(84,70)
−
%\put(0,0){\includegraphics{figtai3L}}
 +
%\put(0,0){\includegraphics{figtaimaclo}}
−
\put(0,0){\includegraphics{vladi06b}}
 +
\put(0,0){\includegraphics{vladi07b}}
  +
\tafiax
−
\taiax
  
−
\put(26,40){\sx{.58}{$D_{5}\!>\!14$}}
 +
\put(33,55){\sx{.52}{$D\!<\!1$}}
−
\put(62,15){\sx{.58}{$D_{5}\!<\!1$}}
 +
\put(33,24){\sx{.45}{$D\!>\!14$}}
 
\end{picture}}
  
\end{picture}}
  +
 
\end{document}
  
\end{document}
 
</nowiki></nomathjax></poem>
  
</nowiki></nomathjax></poem>
−
==References==
  
−
<references/>
  
   
−
[[Category:Tetration]]
 +
[[Category:Agreement]]
 
[[Category:Book]]
  
[[Category:Book]]
−
[[Category:Complex map]]
  
 
[[Category:Agreement]]
  
[[Category:Agreement]]
  +
[[Category:Complex map]]
  +
[[Category:BookMap]]
  +
[[Category:Tetration]]
  +
[[Category:C++]]
  +
[[Category:Latex]]

Latest revision as of 08:56, 1 December 2018

Maps of agreement of approximations of natural tetration with elementary functions fima and maclo, used in the implementation fsexp.cin.

Left: $D=D_6(x\!+\!\mathrm i y)$;

$\displaystyle D_6(z)= - \ln \left( \frac

\right)$ right: $D=D_7(x\!+\!\mathrm i y)$; $\displaystyle D_7(z)= - \ln \left( \frac
\right)$ Levels $D=\mathrm{const}$ are drawn with step 2, but the exception is dome for level $D=1$, this level is drawn with thick lines. Usage: this is figure 14.10 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 7.

C++ generator of the first picture

Fsexp.cin, ado.cin, conto.cin, plodi.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;
//#include <complex.h>
//#define z_type complex<double>
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)

#include "fsexp.cin"

#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;

  int M=100,M1=M+1;
  int N=101,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("vladi07a.eps","w");ado(o,82,82);
fprintf(o,"41 11 translate\n 10 10 scale\n");

DO(m,M1) X[m]=-4.+.08*(m-.5);
DO(n,N1)Y[n]= -1 +.08*(n-.5);

for(m=-3;m<4;m++) { if(m==0){M(m,-0.1)L(m,6.1)} else {M(m,0)L(m,6)} }
for(n=0;n<7;n++) { M( -3,n)L(3,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=tai3(z);
// d=fima1(z);
        d=fima(z);
        p=abs(c-d)/(abs(c)+abs(d));
        p=-log(p)/log(10.);
        // 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;
        }}

#include"plodi.cin"

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf vladi07a.eps");
        system( "open vladi07a.pdf");//macintosh
// getchar(); system("killall Preview"); //macintosh
}

C++ generator of the second picture



#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;
//#include <complex.h>
//#define z_type complex<double>
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)

#include "fsexp.cin"

#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;

  int M=100,M1=M+1;
  int N=101,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("vladi07b.eps","w");ado(o,82,82);
fprintf(o,"41 11 translate\n 10 10 scale\n");

DO(m,M1) X[m]=-4.+.08*(m-.5);
DO(n,N1)Y[n]= -1 +.08*(n-.5);

for(m=-3;m<4;m++) { if(m==0){M(m,-0.1)L(m,6.1)} else {M(m,0)L(m,6)} }
for(n=0;n<7;n++) { M( -3,n)L(3,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=tai3(z);
        d=maclo(z);
// d=fima1(z);
        p=abs(c-d)/(abs(c)+abs(d));
        p=-log(p)/log(10.);
        // 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;
        }}

#include"plodi.cin"

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf vladi07b.eps");
        system( "open vladi07b.pdf");//macintosh
// getchar(); system("killall Preview");//macintosh
}

Latex combiner


\documentclass[12pt]{article}
\usepackage{graphicx}
\usepackage{rotating}
\usepackage{geometry}
\paperwidth 356px
%\paperheight 134px
\paperheight 184px
\topmargin -98pt
\oddsidemargin -94pt
\pagestyle{empty}
\begin{document}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}

\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}

\newcommand \tafiax {
\put(7,68){\sx{.5}{$y$}}
%\put(5,74){\sx{.5}{$\Im(z)$}}
%\put(7,69){\sx{.5}{$6$}}
\put(7,59){\sx{.5}{$5$}}
\put(7,49){\sx{.5}{$4$}}
\put(7,39){\sx{.5}{$3$}}
\put(7,29){\sx{.5}{$2$}}
\put(7,19){\sx{.5}{$1$}}
\put(7, 9){\sx{.5}{$0$}}
\put( 7 ,6){\sx{.5}{$-\!3$}}
\put(17 ,6){\sx{.5}{$-\!2$}}
\put(27 ,6){\sx{.5}{$-\!1$}}
\put(40 , 6){\sx{.5}{$0$}}
\put(50 , 6){\sx{.5}{$1$}}
\put(60 , 6){\sx{.5}{$2$}}
%\put(70 , 6){\sx{.5}{$3$}}
%\put(78 , 6){\sx{.5}{$\Re(z)$}}
\put(70 , 6){\sx{.5}{$x$}}
}
%\sx{2.33}{\begin{picture}(96,75)
\sx{2.33}{\begin{picture}(80,75)
%\put(0,0){\includegraphics{figtaifima}}
\put(0,0){\includegraphics{vladi07a}}
\tafiax
\put(31,54){\sx{.45}{$D\!>\!14$}}
\end{picture}}
\sx{2.33}{\begin{picture}(84,70)
%\put(0,0){\includegraphics{figtaimaclo}}
\put(0,0){\includegraphics{vladi07b}}
\tafiax
\put(33,55){\sx{.52}{$D\!<\!1$}}
\put(33,24){\sx{.45}{$D\!>\!14$}}
\end{picture}}

\end{document}

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