Difference between revisions of "File:DoyaPlotT100.png"

From TORI
Jump to navigation Jump to search
(add more lines - as in the Book)
 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
  +
{{oq|DoyaPlotT100.png|}}
  +
 
[[Explicit plot]] of the [[Doya function]]
  
[[Explicit plot]] of the [[Doya function]]
   
−
$ \mathrm{Doya}_t(z)=\mathrm{Tania}(t+\mathrm{ArcTania}(z))$
 +
\( \mathrm{Doya}^n(z)=\mathrm{Tania}(n+\mathrm{ArcTania}(z))\)
   
 
where the [[Tania function]] is solution of equations
  
where the [[Tania function]] is solution of equations
   
−
$\displaystyle \mathrm{Tania}'(z)=
 +
\(\displaystyle \mathrm{Tania}'(z)=
−
\frac{ \mathrm{Tania}(z)}{1\!+\!\mathrm{Tania}(z)}~$, $~\mathrm{Tania}(0)\!=\!1$
+
\frac{ \mathrm{Tania}(z)}{1\!+\!\mathrm{Tania}(z)}~\), \(~\mathrm{Tania}(0)\!=\!1\)
   
 
At the picture,
 
At the picture,
−
$y=\mathrm{Doya}_t(x)$ is plotted versus $x$ for various values of $t$.
 +
\(y=\mathrm{Doya}^n(x)\) is plotted versus \(x\) for various values of \(n\).
  +
  +
The picture is used as Fig.5.6 at page 52 of book «[[Superfunctions]]»<ref>
  +
https://www.amazon.co.jp/Superfunctions-Non-integer-holomorphic-functions-superfunctions/dp/6202672862 Dmitrii Kouznetsov. [[Superfunctions]]: Non-integer iterates of holomorphic functions. [[Tetration]] and other [[superfunction]]s. Formulas,algorithms,tables,graphics ペーパーバック – 2020/7/28
  +
</ref><ref>https://mizugadro.mydns.jp/BOOK/468.pdf Dmitrii Kouznetsov (2020). [[Superfunctions]]: Non-integer iterates of holomorphic functions. [[Tetration]] and other [[superfunction]]s. Formulas, algorithms, tables, graphics. Publisher: [[Lambert Academic Publishing]].
  +
</ref><br>
  +
in order to show that the iterates are with the simple example
  +
related to the [[Laser science]].
   
 
==Generators==
  
==Generators==
 
The curves are generated with the [[C++]] code.
  
The curves are generated with the [[C++]] code.
−
The resulting file is imported into the [[Latex]] document for generation of labels.
+
The resulting file is imported into the [[Latex]] document for generation of labels.
  +
The resulting *.pdf is converted to *.png for the portability.
 
===[[C++]] generator of curves===
  
===[[C++]] generator of curves===
  +
<pre>
  +
#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.)
  +
z_type ArcTania(z_type z) {return z + log(z) - 1. ;}
  +
z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
  +
z_type TaniaTay(z_type z) { int n; z_type s;
  +
s=1.+z*(.5+z*(1./16.+z*(-1./192.+z*(-1./3072.+z*(1.3/6144.+z*(-4.7/147456.
  +
//+z*(7.3/4128768.) //some reserve term
  +
)))))); DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
  +
z_type TaniaNega(z_type z){int n;z_type s=exp(z-exp(z)+1.);
  +
DO(n,4) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
  +
z_type TaniaBig(z_type z){int n;z_type s=z; s=z-log(s)+1.;
  +
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
  +
z_type TaniaS(z_type z){int n; z_type s,t=z+z_type(2.,-M_PI);t*=2./9.; t=I*sqrt(t);
  +
s=-1.+t*(3.+t*(-3.+t*(.75+t*(.3+t*(.9/16.+t*(-.3/7.+t*(-12.51/224. //+t*(-.9/28.)
  +
)))))));
  +
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
  +
z_type Tania(z_type z){ z_type t;
  +
if( fabs(Im(z))< M_PI && Re(z)<-2.51) return TaniaNega(z);
  +
if( abs(z)>7. || Re(z)>3.8 ) return TaniaBig(z);
  +
if( Im(z) > .7 ) return TaniaS(z);
  +
if( Im(z) < -.7) return conj(TaniaS(conj(z)));
  +
return TaniaTay(z);
  +
}
  +
void ado(FILE *O, int X, int Y)
  +
{ fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
  +
fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
  +
fprintf(O,"/M {moveto} bind def\n");
  +
fprintf(O,"/L {lineto} bind def\n");
  +
fprintf(O,"/S {stroke} bind def\n");
  +
fprintf(O,"/s {show newpath} bind def\n");
  +
fprintf(O,"/C {closepath} bind def\n");
  +
fprintf(O,"/F {fill} bind def\n");
  +
fprintf(O,"/o {.1 0 360 arc C S} bind def\n");
  +
fprintf(O,"/times-Roman findfont 20 scalefont setfont\n");
  +
fprintf(O,"/W {setlinewidth} bind def\n");
  +
fprintf(O,"/RGB {setrgbcolor} bind def\n");}
  +
#define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
  +
#define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);
  +
int main(){ int j,k,m,n; DB x,y, a;
  +
FILE *o;o=fopen("doyaplo.eps","w");ado(o,408,408);
  +
fprintf(o,"4 4 translate\n 100 100 scale\n");
  +
for(m=0;m<5;m++){ M(m,0)L(m,4)}
  +
for(n=0;n<5;n++){ M(0,n)L(4,n)}
  +
M(0,0)L(4,4)
  +
fprintf(o,".01 W 0 0 0 RGB S\n");
   
  +
DO(n,181){x=.005+.01*n;y=Re(Tania(6.+ArcTania(x)));if(n==0)M(x,y)else L(x,y) if(y>4.) break;} fprintf(o,".02 W 0 .3 1 RGB S\n");
−
<!-- File [[ado.cin]] should be loaded to the working directory for the compilation of the code below: !-->
  
  +
DO(n,181){x=.005+.01*n;y=Re(Tania(5.+ArcTania(x)));if(n==0)M(x,y)else L(x,y) if(y>4.) break;} fprintf(o,".02 W 0 .3 1 RGB S\n");
  +
DO(n,181){x=.005+.01*n;y=Re(Tania(4.+ArcTania(x)));if(n==0)M(x,y)else L(x,y) if(y>4.) break;} fprintf(o,".02 W 0 .3 1 RGB S\n");
  +
DO(n,181){x=.005+.01*n;y=Re(Tania(3.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .3 1 RGB S\n");
  +
DO(n,249){x=.005+.01*n;y=Re(Tania(2.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .3 1 RGB S\n");
  +
DO(n,163){x=.005+.02*n;y=Re(Tania(1.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .3 1 RGB S\n");
  +
DO(n,101){x=.005+.04*n;y=Re(Tania(-1.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");
  +
DO(n,101){x=.005+.04*n;y=Re(Tania(-2.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");
  +
DO(n,101){x=.005+.04*n;y=Re(Tania(-3.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");
  +
DO(n,101){x=.005+.04*n;y=Re(Tania(-4.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");
  +
DO(n,101){x=.005+.04*n;y=Re(Tania(-5.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");
  +
DO(n,101){x=.005+.04*n;y=Re(Tania(-6.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");
   
  +
DO(m,61)
−
#include <math.h>
  
  +
{ a=-3.+.1*m; DO(n,400){x=.005+.01*n;y=Re(Tania(a+ArcTania(x)));if(n==0)M(x,y)else L(x,y) if(y>4.) break; }
−
#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 complex<double> z_type;
  
−
#define Re(x) x.real()
  
−
#define Im(x) x.imag()
  
−
#define I z_type(0.,1.)
  
−  
−
z_type ArcTania(z_type z) {return z + log(z) - 1. ;}
  
−  
−
z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
  
−  
−
z_type TaniaTay(z_type z) { int n; z_type s;
  
−
s=1.+z*(.5+z*(1./16.+z*(-1./192.+z*(-1./3072.+z*(1.3/6144.+z*(-4.7/147456.
  
−
//+z*(7.3/4128768.) //some reserve term
  
−
)))))); DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
  
−  
−
z_type TaniaNega(z_type z){int n;z_type s=exp(z-exp(z)+1.);
  
−
DO(n,4) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
  
−  
−
z_type TaniaBig(z_type z){int n;z_type s=z; s=z-log(s)+1.;
  
−
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
  
−
z_type TaniaS(z_type z){int n; z_type s,t=z+z_type(2.,-M_PI);t*=2./9.; t=I*sqrt(t);
  
−
s=-1.+t*(3.+t*(-3.+t*(.75+t*(.3+t*(.9/16.+t*(-.3/7.+t*(-12.51/224. //+t*(-.9/28.)
  
−
)))))));
 
−
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
  
−  
−
z_type Tania(z_type z){ z_type t;
  
−
if( fabs(Im(z))< M_PI && Re(z)<-2.51) return TaniaNega(z);
  
−
if( abs(z)>7. || Re(z)>3.8 ) return TaniaBig(z);
  
−
if( Im(z) > .7 ) return TaniaS(z);
  
−
if( Im(z) < -.7) return conj(TaniaS(conj(z)));
  
−
return TaniaTay(z);
  
 
}
  
}
  +
fprintf(o,".005 W 0 0 0 RGB S\n");
   
  +
fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
−
void ado(FILE *O, int X, int Y)
  
−
{ fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
 +
system("epstopdf doyaplo.eps");
  +
system( "open doyaplo.pdf"); //these 2 commands may be specific for macintosh
−
fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
  
  +
getchar(); system("killall Preview");// if run at another operational sysetm, may need to modify
−
fprintf(O,"/M {moveto} bind def\n");
  
  +
}
−
fprintf(O,"/L {lineto} bind def\n");
  
  +
</pre>
−
fprintf(O,"/S {stroke} bind def\n");
  
−
fprintf(O,"/s {show newpath} bind def\n");
  
−
fprintf(O,"/C {closepath} bind def\n");
  
−
fprintf(O,"/F {fill} bind def\n");
  
−
fprintf(O,"/o {.1 0 360 arc C S} bind def\n");
  
−
fprintf(O,"/times-Roman findfont 20 scalefont setfont\n");
  
−
fprintf(O,"/W {setlinewidth} bind def\n");
  
−
fprintf(O,"/RGB {setrgbcolor} bind def\n");}
  
−  
−
#define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
  
−
#define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);
  
−  
−
main(){ int j,k,m,n; DB x,y, a;
  
−
FILE *o;o=fopen("doyaplot.eps","w");ado(o,408,408);
  
−
fprintf(o,"4 4 translate\n 100 100 scale\n");
  
−
for(m=0;m<5;m++){ M(m,0)L(m,4)}
  
−
for(n=0;n<5;n++){ M(0,n)L(4,n)}
  
−
M(0,0)L(4,4)
  
−
fprintf(o,".01 W 0 0 0 RGB S\n");
  
−
DO(n,181){x=.005+.01*n;y=Re(Tania(3.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 .5 RGB S\n");
  
−
DO(n,249){x=.005+.01*n;y=Re(Tania(2.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 .5 RGB S\n");
  
−
DO(n,163){x=.005+.02*n;y=Re(Tania(1.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 .5 RGB S\n");
  
−
DO(n,101){x=.005+.04*n;y=Re(Tania(-1.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W .5 0 0 RGB S\n");
  
−
DO(n,101){x=.005+.04*n;y=Re(Tania(-2.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W .5 0 0 RGB S\n");
  
−
DO(n,101){x=.005+.04*n;y=Re(Tania(-3.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W .5 0 0 RGB S\n");
  
−
fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
  
−
system("epstopdf doyaplot.eps");
  
−
system( "open doyaplot.pdf"); //these 2 commands may be specific for macintosh
  
−
getchar(); system("killall Preview");// if run at another operational sysetm, may need to modify
  
−
}
  
   
 
===[[Latex]] generator of the picture===
  
===[[Latex]] generator of the picture===
  +
<pre>
−
<poem><nomathjax>
  
−
<nowiki>
  
 
\documentclass[12pt]{article}
  
\documentclass[12pt]{article}
 
\usepackage{geometry}
  
\usepackage{geometry}
Line 113: Line 125:
 
\begin{document} %<br>
  
\begin{document} %<br>
 
\sx{1}{ \begin{picture}(810,410) %<br>
  
\sx{1}{ \begin{picture}(810,410) %<br>
−
\put(1,9){\ing{doyaplot}} % <br>
 +
\put(1,9){\ing{doyaplo}} % <br>
−
\put(-12,394){\sx{2.8}{$y$}} % <br>
 +
\put(-12,394){\sx{2.8}{$y$}}
−
\put(-12,303){\sx{2.8}{$3$}} % <br>
 +
\put(-12,303){\sx{2.8}{$3$}}
−
\put(-12,203){\sx{2.8}{$2$}} % <br>
 +
\put(-12,203){\sx{2.8}{$2$}}
−
\put(-12,103){\sx{2.8}{$1$}} % <br>
 +
\put(-12,103){\sx{2.8}{$1$}}
−
\put(0,-9){\sx{2.5}{$0$}} % <br>
 +
\put(0,-9){\sx{2.5}{$0$}}
−
\put(100,-9){\sx{2.5}{$1$}} % <br>
 +
\put(100,-9){\sx{2.5}{$1$}}
−
\put(200,-9){\sx{2.5}{$2$}} % <br>
 +
\put(200,-9){\sx{2.5}{$2$}}
−
\put(300,-9){\sx{2.5}{$3$}} % <br>
 +
\put(300,-9){\sx{2.5}{$3$}}
−
\put(392,-7){\sx{2.6}{$x$}} % <br>
 +
\put(392,-7){\sx{2.6}{$x$}}
−
%\put(560,214){\rot{37}\sx{4}{$y=\mathrm{Tania}(x)$}\ero} % <br>
 +
%\put(560,214){\rot{37}\sx{4}{$y=\mathrm{Tania}(x)$}\ero}
−
\put(134,353){\rot{53}\sx{2.8}{$t\!=\!3$}\ero} %<br>
 +
\put(30,342){\rot{74}\sx{2.8}{$n\!=\!6$}\ero}
−
\put(194,354){\rot{50}\sx{2.8}{$t\!=\!2$}\ero} %<br>
 +
\put(54,342){\rot{68}\sx{2.8}{$n\!=\!5$}\ero}
−
\put(260,350){\rot{48}\sx{2.8}{$t\!=\!1$}\ero} %<br>
 +
\put(90,346){\rot{55}\sx{2.8}{$n\!=\!4$}\ero}
−
\put(336,350){\rot{45}\sx{2.8}{$t\!=\!0$}\ero} %<br>
 +
\put(146,348){\rot{53}\sx{2.8}{$n\!=\!3$}\ero}
−
\put(340,238){\rot{44}\sx{2.8}{$t\!=\!-1$}\ero} %<br>
 +
\put(210,350){\rot{50}\sx{2.8}{$n\!=\!2$}\ero}
−
\put(344,178){\rot{41}\sx{2.7}{$t\!=\!-2$}\ero} %<br>
 +
\put(270,340){\rot{48}\sx{2.8}{$n\!=\!1$}\ero}
−
\put(341,114){\rot{37}\sx{2.7}{$t\!=\!-3$}\ero} %<br>
 +
\put(324,318){\rot{45}\sx{3.0}{$n\!=\!0$}\ero}
  +
\put(332,252){\rot{43}\sx{2.8}{$n\!=\!-1$}\ero}
  +
\put(332,184){\rot{40}\sx{2.8}{$n\!=\!-2$}\ero}
  +
\put(332,125){\rot{36}\sx{2.8}{$n\!=\!-3$}\ero}
  +
\put(328,75){\rot{30}\sx{2.8}{$n\!=\!-4$}\ero}
  +
\put(320,36){\rot{22}\sx{2.8}{$n\!=\!-5$}\ero}
 
\end{picture} %<br>
  
\end{picture} %<br>
−
} %<br>
 +
} %<br>
 
\end{document}
  
\end{document}
−
</nowiki>
 +
</pre>
−
</nomathjax>
  
−
</poem>
  
   
 
==Copyleft status==
  
==Copyleft status==
 
This picture and its generators can be used for free; attribute the source.
  
This picture and its generators can be used for free; attribute the source.
  +
  +
==References==
  +
{{ref}}
  +
  +
{{fer}}
  +
==Keywords==
  +
«[[]]»,
  +
<b>«[[]]»</b>,
  +
<b>«[[Doya function]]»</b>,
  +
«[[Iterate]]»,
  +
«[[Superfunction]]»,
  +
«[[Superfunctions]]»,
  +
<b>«[[Tania function]]»</b>,
  +
«[[Transfer function]]»,
  +
  +
«[[Суперфункции]]»,
   
 
[[Category:Book]]
  
[[Category:Book]]
Line 147: Line 178:
 
[[Category:Doya function]]
  
[[Category:Doya function]]
 
[[Category:Laser science]]
  
[[Category:Laser science]]
  +
[[Category:Superfunctins]]
 
[[Category:Transfer function]]
  
[[Category:Transfer function]]

Latest revision as of 18:20, 18 August 2025


Explicit plot of the Doya function

\( \mathrm{Doya}^n(z)=\mathrm{Tania}(n+\mathrm{ArcTania}(z))\)

where the Tania function is solution of equations

\(\displaystyle \mathrm{Tania}'(z)= \frac{ \mathrm{Tania}(z)}{1\!+\!\mathrm{Tania}(z)}~\), \(~\mathrm{Tania}(0)\!=\!1\)

At the picture, \(y=\mathrm{Doya}^n(x)\) is plotted versus \(x\) for various values of \(n\).

The picture is used as Fig.5.6 at page 52 of book «Superfunctions»[1][2]
in order to show that the iterates are with the simple example related to the Laser science.

Generators

The curves are generated with the C++ code. The resulting file is imported into the Latex document for generation of labels. The resulting *.pdf is converted to *.png for the portability.

C++ generator of curves

#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.)
z_type ArcTania(z_type z) {return z + log(z) - 1. ;}
z_type ArcTaniap(z_type z) {return 1. + 1./z ;}
z_type TaniaTay(z_type z) { int n; z_type s;
s=1.+z*(.5+z*(1./16.+z*(-1./192.+z*(-1./3072.+z*(1.3/6144.+z*(-4.7/147456.
//+z*(7.3/4128768.) //some reserve term
)))))); DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
z_type TaniaNega(z_type z){int n;z_type s=exp(z-exp(z)+1.);
DO(n,4) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
z_type TaniaBig(z_type z){int n;z_type s=z; s=z-log(s)+1.;
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
z_type TaniaS(z_type z){int n; z_type s,t=z+z_type(2.,-M_PI);t*=2./9.; t=I*sqrt(t);
s=-1.+t*(3.+t*(-3.+t*(.75+t*(.3+t*(.9/16.+t*(-.3/7.+t*(-12.51/224. //+t*(-.9/28.)
))))))); 
DO(n,3) s+=(z-ArcTania(s))/ArcTaniap(s); return s ; }
z_type Tania(z_type z){ z_type t;
if( fabs(Im(z))< M_PI && Re(z)<-2.51) return TaniaNega(z);
if( abs(z)>7. || Re(z)>3.8 ) return TaniaBig(z);
if( Im(z) > .7 ) return TaniaS(z);
if( Im(z) < -.7) return conj(TaniaS(conj(z)));
return TaniaTay(z);
}
void ado(FILE *O, int X, int Y)
{      fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
      fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
      fprintf(O,"/M {moveto} bind def\n");
      fprintf(O,"/L {lineto} bind def\n");
      fprintf(O,"/S {stroke} bind def\n");
      fprintf(O,"/s {show newpath} bind def\n");
      fprintf(O,"/C {closepath} bind def\n");
      fprintf(O,"/F {fill} bind def\n");
      fprintf(O,"/o {.1 0 360 arc C S} bind def\n");
      fprintf(O,"/times-Roman findfont 20 scalefont setfont\n");
      fprintf(O,"/W {setlinewidth} bind def\n");
      fprintf(O,"/RGB {setrgbcolor} bind def\n");}
#define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);
int main(){ int j,k,m,n; DB x,y, a;
FILE *o;o=fopen("doyaplo.eps","w");ado(o,408,408);
fprintf(o,"4 4 translate\n 100 100 scale\n");
for(m=0;m<5;m++){ M(m,0)L(m,4)}
for(n=0;n<5;n++){ M(0,n)L(4,n)}
M(0,0)L(4,4)
fprintf(o,".01 W 0 0 0 RGB S\n");

DO(n,181){x=.005+.01*n;y=Re(Tania(6.+ArcTania(x)));if(n==0)M(x,y)else L(x,y) if(y>4.) break;} fprintf(o,".02 W 0 .3 1 RGB S\n");
DO(n,181){x=.005+.01*n;y=Re(Tania(5.+ArcTania(x)));if(n==0)M(x,y)else L(x,y) if(y>4.) break;} fprintf(o,".02 W 0 .3 1 RGB S\n");
DO(n,181){x=.005+.01*n;y=Re(Tania(4.+ArcTania(x)));if(n==0)M(x,y)else L(x,y) if(y>4.) break;} fprintf(o,".02 W 0 .3 1 RGB S\n");
DO(n,181){x=.005+.01*n;y=Re(Tania(3.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .3 1 RGB S\n");
DO(n,249){x=.005+.01*n;y=Re(Tania(2.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .3 1 RGB S\n");
DO(n,163){x=.005+.02*n;y=Re(Tania(1.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .3 1 RGB S\n");
DO(n,101){x=.005+.04*n;y=Re(Tania(-1.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");
DO(n,101){x=.005+.04*n;y=Re(Tania(-2.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");
DO(n,101){x=.005+.04*n;y=Re(Tania(-3.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");
DO(n,101){x=.005+.04*n;y=Re(Tania(-4.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");
DO(n,101){x=.005+.04*n;y=Re(Tania(-5.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");
DO(n,101){x=.005+.04*n;y=Re(Tania(-6.+ArcTania(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 1 .3 0 RGB S\n");

DO(m,61)
 {  a=-3.+.1*m;  DO(n,400){x=.005+.01*n;y=Re(Tania(a+ArcTania(x)));if(n==0)M(x,y)else L(x,y) if(y>4.) break; } 
 }
fprintf(o,".005 W 0 0 0 RGB S\n");

fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
     system("epstopdf doyaplo.eps");
     system(    "open doyaplo.pdf"); //these 2 commands may be specific for macintosh
getchar(); system("killall Preview");// if run at another operational sysetm, may need to modify
}

Latex generator of the picture

\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{graphicx}
\usepackage{rotating} %<br>
\paperwidth 419pt %<br>
\paperheight 426pt %<br>
\topmargin -103pt %<br>
\oddsidemargin -83pt %<br>
\textwidth 1200pt %<br>
\textheight 600pt %<br>
\pagestyle {empty} %<br>
\newcommand \sx {\scalebox} %<br>
\newcommand \rot {\begin{rotate}} %<br>
\newcommand \ero {\end{rotate}} %<br>
\newcommand \ing {\includegraphics} %<br>
\begin{document} %<br>
\sx{1}{ \begin{picture}(810,410) %<br>
\put(1,9){\ing{doyaplo}} % <br>
\put(-12,394){\sx{2.8}{$y$}}
\put(-12,303){\sx{2.8}{$3$}}
\put(-12,203){\sx{2.8}{$2$}}
\put(-12,103){\sx{2.8}{$1$}}
\put(0,-9){\sx{2.5}{$0$}}
\put(100,-9){\sx{2.5}{$1$}}
\put(200,-9){\sx{2.5}{$2$}}
\put(300,-9){\sx{2.5}{$3$}}
\put(392,-7){\sx{2.6}{$x$}}
 %\put(560,214){\rot{37}\sx{4}{$y=\mathrm{Tania}(x)$}\ero}
\put(30,342){\rot{74}\sx{2.8}{$n\!=\!6$}\ero}
\put(54,342){\rot{68}\sx{2.8}{$n\!=\!5$}\ero}
\put(90,346){\rot{55}\sx{2.8}{$n\!=\!4$}\ero}
\put(146,348){\rot{53}\sx{2.8}{$n\!=\!3$}\ero}
\put(210,350){\rot{50}\sx{2.8}{$n\!=\!2$}\ero}
\put(270,340){\rot{48}\sx{2.8}{$n\!=\!1$}\ero}
\put(324,318){\rot{45}\sx{3.0}{$n\!=\!0$}\ero}
\put(332,252){\rot{43}\sx{2.8}{$n\!=\!-1$}\ero}
\put(332,184){\rot{40}\sx{2.8}{$n\!=\!-2$}\ero}
\put(332,125){\rot{36}\sx{2.8}{$n\!=\!-3$}\ero}
\put(328,75){\rot{30}\sx{2.8}{$n\!=\!-4$}\ero}
\put(320,36){\rot{22}\sx{2.8}{$n\!=\!-5$}\ero}
\end{picture} %<br>
} %<br>
\end{document}

Copyleft status

This picture and its generators can be used for free; attribute the source.

References

  1. ↑ https://www.amazon.co.jp/Superfunctions-Non-integer-holomorphic-functions-superfunctions/dp/6202672862 Dmitrii Kouznetsov. Superfunctions: Non-integer iterates of holomorphic functions. Tetration and other superfunctions. Formulas,algorithms,tables,graphics ペーパーバック – 2020/7/28
  2. ↑ https://mizugadro.mydns.jp/BOOK/468.pdf Dmitrii Kouznetsov (2020). Superfunctions: Non-integer iterates of holomorphic functions. Tetration and other superfunctions. Formulas, algorithms, tables, graphics. Publisher: Lambert Academic Publishing.

Keywords

«[[]]», «[[]]», «Doya function», «Iterate», «Superfunction», «Superfunctions», «Tania function», «Transfer function»,

«Суперфункции»,

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current18:18, 18 August 2025Thumbnail for version as of 18:18, 18 August 2025834 × 848 (338 KB)T (talk | contribs)add more lines - as in the Book
17:50, 20 June 2013Thumbnail for version as of 17:50, 20 June 2013580 × 590 (77 KB)Maintenance script (talk | contribs)Importing image file

You cannot overwrite this file.

The following 2 pages use this file:

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Retrieved from "https://mizugadro.mydns.jp/t/index.php?title=File:DoyaPlotT100.png&oldid=45247"