Difference between revisions of "File:Figlogzo2t.jpg"

From TORI
Jump to navigation Jump to search
(Importing image file)
 
 
(2 intermediate revisions by 2 users not shown)
Line 1: Line 1:
  +
{{oq|Figlogzo2t.jpg|Original file ‎(2,137 × 2,137 pixels, file size: 1.84 MB, MIME type: image/jpeg)}}
−
Importing image file
  
  +
  +
{{fig|Filogbigmap100.png|300|-8|0|8|Large version of this map}}
  +
  +
[[Complex map]] of function [[Filog]], zoomin of the square of size unity from the central part of figure http://mizugadro.mydns.jp/t/index.php/File:Filogbigmap100.png
  +
\[
  +
u\!+\!\mathrm i v= \mathrm{Filog} (x\!+\!\mathrm i y)
  +
\]
  +
Lines of constant \(u\) and <br>
  +
lines of constant \(v\) are drawn in the \(x\),\(y\) plane.
  +
==Meaning==
  +
  +
\[
  +
z=\mathrm{Filog}(a)
  +
\]
  +
  +
expresses solution \(z\) of equation
  +
\[
  +
\ln(z)/a=z
  +
\]
  +
This solution is described in article «[[Filog]]» and in book «[[Superfunctions]]»
  +
<ref>
  +
https://mizugadro.mydns.jp/BOOK/468.pdf
  +
Dmitrii Kouznetsov. [[Superfunctions]]. [[Lambert Academic Publishing]], 2020.
  +
</ref><ref>
  +
https://www.morebooks.de/shop-ui/shop/product/978-620-2-67286-3
  +
[[Superfunctions]]
  +
Non-integer iterates of holomorphic functions. Tetration and other superfunctions. Formulas,algorithms,tables,graphics 978-620-2-67286-3
  +
Tools for evaluation of superfunctions, abelfunctions and non-integer iterates of holomorphic functions are collected. ..
  +
Authors Dmitrii Kouznetsov
  +
Book language English
  +
Published on 2020-07-28
  +
Publishing house LAP LAMBERT Academic Publishing
  +
Number of pages 328
  +
Price (EUR ) €52.90</ref>;
  +
the picture is used as the bottom part of Fig.18.2 at page 248 of that book.
  +
  +
Function [[Filog]] allows to evaluate two fixed points \(L\) of logarithm
  +
to base \(b\) as follows:
  +
\[
  +
L=\mathrm{Filog}\big( \ln(b)\big)
  +
\]
  +
and
  +
\[
  +
L=\mathrm{Filog}\big( \ln(b^*)\big)^*
  +
\]
  +
  +
==[[C++]] generator of curves==
  +
// Files [[ado.cin]], [[conto.cin]], [[filog.cin]], [[tania.cin]] should be loaded in order to compile the [[C++]] code below
  +
<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 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"
  +
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
  +
int M=500,M1=M+1;
  +
int N=501,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("filogzo2.eps","w");ado(o,1020,1020);
  +
fprintf(o,"510 510 translate\n 1000 1000 scale\n");
  +
DO(m,M1) X[m]=-.5+.002*(m-.2);
  +
DO(n,250)Y[n]=-.5+.002*n;
  +
Y[250]=-.00001;
  +
Y[251]= .00001;
  +
for(n=252;n<N1;n++) Y[n]=-.5+.002*(n-1.);
  +
  +
for(m=-5;m<6;m++){M(.1*m,-.5)L(.1*m,.5)}
  +
for(n=-5;n<6;n++){M( -.5,.1*n)L(.5,.1*n)}
  +
fprintf(o,"2 setlinecap .001 W 0 0 0 RGB S\n");
  +
M(exp(-1.),-.5)
  +
L(exp(-1.), .5)
  +
//M(M_PI/2.,-.5)
  +
//L(M_PI/2., .5)
  +
fprintf(o,".0007 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("%5.2f\n",x);
  +
DO(n,N1){y=Y[n]; z=z_type(x,y);
  +
// c=Tania(z_type(-1.,-M_PI)+log(z))/(-z);
  +
c=Filog(z);
  +
p=Re(c);q=Im(c);
  +
if(p>-201. && p<201. && q>-201. && q<201. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
  +
}}
  +
fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=5.;q=1;
  +
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,".0008 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,".0008 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,".0008 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,".002 W .9 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,".002 W 0 0 .9 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".002 W .6 0 .6 RGB S\n");
  +
for(m=-20;m<21;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
  +
p=10.;
  +
conto(o,g,w,v,X,Y,M,N, 30 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N, 40 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N, 50 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N,-30 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N,-40 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
  +
conto(o,g,w,v,X,Y,M,N,-50 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, -30,-p,p); fprintf(o,".002 W .9 0 0 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, -40,-p,p); fprintf(o,".002 W .9 0 0 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, -50,-p,p); fprintf(o,".002 W .9 0 0 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, 30,-p,p); fprintf(o,".002 W 0 0 .9 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, 40,-p,p); fprintf(o,".002 W 0 0 .9 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, 50,-p,p); fprintf(o,".002 W 0 0 .9 RGB S\n");
  +
  +
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
  +
system("epstopdf filogzo2.eps");
  +
system( "open filogzo2.pdf"); //for mac
  +
// getchar(); system("killall Preview"); // for mac
  +
// Copyleft 2012 by Dmitrii Kouznetsov
  +
}
  +
</pre>
  +
  +
==[[Latex]] generator of labels==
  +
<pre>
  +
\documentclass[12pt]{article}
  +
\usepackage{geometry}
  +
\paperwidth 1030pt
  +
\paperheight 1030pt
  +
\textwidth 1140pt
  +
\textheight 1140pt
  +
\topmargin -103pt
  +
\oddsidemargin -86pt
  +
\usepackage{graphicx}
  +
\usepackage{rotating}
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
\newcommand \rme {\mathrm{e}}
  +
\newcommand \sx {\scalebox}
  +
\begin{document}
  +
\begin{picture}(1020,1020)
  +
\put(10,10){\includegraphics{filogzo2}}
  +
  +
\put(0,1012){\sx{2.3}{$y$}}
  +
\put(-7,914){\sx{2.3}{$\frac{4}{10}$}}
  +
\put(-7,814){\sx{2.3}{$\frac{3}{10}$}}
  +
\put(-7,714){\sx{2.3}{$\frac{2}{10}$}}
  +
\put(-7,614){\sx{2.3}{$\frac{1}{10}$}}
  +
\put( 2,514){\sx{2.3}{$0$}}
  +
\put(-7,414){\sx{2.3}{$\frac{-\!1}{10}$}}
  +
\put(-7,314){\sx{2.3}{$\frac{-\!1}{5}$}}
  +
\put(-7,214){\sx{2.3}{$\frac{-\!3}{10}$}}
  +
\put(-7,114){\sx{2.3}{$\frac{-\!2}{5}$}}
  +
\put(-7, 14){\sx{2.3}{$\frac{-\!1}{2}$}}
  +
\put(90, -1){\sx{2.3}{$-0.4$}}
  +
\put(190, -1){\sx{2.3}{$-0.3$}}
  +
\put(290, -1){\sx{2.3}{$-0.2$}}
  +
\put(390, -1){\sx{2.3}{$-0.1$}}
  +
\put(516, -1){\sx{2.3}{$0$}}
  +
\put(609, -1){\sx{2.3}{$0.1$}}
  +
\put(709, -1){\sx{2.3}{$0.2$}}
  +
\put(809, -1){\sx{2.3}{$0.3$}}
  +
\put(866, -1){\sx{2.2}{$1/\mathrm e$}}
  +
\put(910, -1){\sx{2.3}{$0.4$}}
  +
\put(1010, 0){\sx{2.4}{$x$}}
  +
\put(250,540){\sx{3}{\rot{82}$u\!=\!0.8$ \ero} }
  +
\put(530,540){\sx{3}{\rot{81}$u\!=\!1$ \ero} }
  +
\put(680,524){\sx{2.8}{\rot{77}$u\!=\!1.2$ \ero} }
  +
\put(768,524){\sx{2.8}{\rot{72}$u\!=\!1.4$ \ero} }
  +
\put(816,524){\sx{2.8}{\rot{56}$u\!=\!1.6$ \ero} }
  +
\put(600,684){\sx{2.8}{\rot{-33}$v\!=\!0.2$ \ero} }
  +
\put(720,798){\sx{2.8}{\rot{-62}$v\!=\!0.4$ \ero} }
  +
\put(820,490){\sx{3}{\rot{-4}$v\!=\!1$ \ero} }
  +
\put(820,466){\sx{3}{\rot{-12}$v\!=\!2$ \ero} }
  +
\put(808,446){\sx{3}{\rot{-26}$v\!=\!3$ \ero} }
  +
\put(768,372){\sx{3}{\rot{36}$u\!=\!5$ \ero} }
  +
\put(770,350){\sx{3}{\rot{26}$u\!=\!4$ \ero} }
  +
\put(770,324){\sx{3}{\rot{16}$u\!=\!3$ \ero} }
  +
\put(768,297){\sx{3}{\rot{2}$u\!=\!2$ \ero} }
  +
\put(766,262){\sx{3}{\rot{-8}$u\!=\!1$ \ero} }
  +
\put(752,230){\sx{3}{\rot{-28}$u\!=\!0$ \ero} }
  +
  +
\put(94,99){\sx{3}{\rot{41}$v\!=\!-2$ \ero} }
  +
\put(162,50){\sx{3}{\rot{57}$v\!=\!-1$ \ero} }
  +
\put(242,30){\sx{3}{\rot{75}$v\!=\!0$ \ero} }
  +
\put(315,30){\sx{3}{\rot{87}$v\!=\!1$ \ero} }
  +
  +
\end{picture}
  +
\end{document}
  +
</pre>
  +
  +
==Similar picture==
  +
{{fig|Fig1802.jpg|300|-80|2|8|Fig.18.2 generated with «[[Conrec6.cin]]»}}
  +
Similar [[complex map]] is generated as test of routine «[[Conrec6.cin]]».
  +
  +
It is shown in figure at right.
  +
  +
The same set of labels is used in both
  +
pictures.
  +
  +
These pictures are compared in articles
  +
«[[Conrec6 demo‎]]»,
  +
«[[MapConrec6demo‎‎]]»;
  +
no visual difference is seen,
  +
the pictures look the same.
  +
  +
In this sense, routines
  +
«[[Conrec6.cin]]» and
  +
«[[Conto.cin]]» are equivalent.
  +
  +
==References==
  +
{{ref}}
  +
  +
{{fer}}
  +
==Keywords==
  +
«[[Book]]»,
  +
«[[C++]]»,
  +
«[[Complex map]]»,
  +
«[[Filog]]»,
  +
«[[Fixed point]]»,
  +
«[[Latex]]»,
  +
«[[Logarithm]]»,
  +
«[[Superfunctions]»,
  +
«[[Tetration]]»,
  +
«[[Zoom]]»,
  +
  +
[[Category:Book]]
  +
[[Category:C++]]
  +
[[Category:Complex map]]
  +
[[Category:Filog]]
  +
[[Category:Fixed point]]
  +
[[Category:Latex]]
  +
[[Category:Logarithm]]
  +
[[Category:Tetration]]
  +
[[Category:Zoom]]

Latest revision as of 21:18, 7 September 2025


Filogbigmap100.png
Large version of this map

Complex map of function Filog, zoomin of the square of size unity from the central part of figure http://mizugadro.mydns.jp/t/index.php/File:Filogbigmap100.png \[ u\!+\!\mathrm i v= \mathrm{Filog} (x\!+\!\mathrm i y) \] Lines of constant \(u\) and
lines of constant \(v\) are drawn in the \(x\),\(y\) plane.

Meaning

\[ z=\mathrm{Filog}(a) \]

expresses solution \(z\) of equation \[ \ln(z)/a=z \] This solution is described in article «Filog» and in book «Superfunctions» [1][2]; the picture is used as the bottom part of Fig.18.2 at page 248 of that book.

Function Filog allows to evaluate two fixed points \(L\) of logarithm to base \(b\) as follows: \[ L=\mathrm{Filog}\big( \ln(b)\big) \] and \[ L=\mathrm{Filog}\big( \ln(b^*)\big)^* \]

C++ generator of curves

// Files ado.cin, conto.cin, filog.cin, tania.cin should be loaded in order to compile the C++ 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 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"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=500,M1=M+1;
int N=501,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("filogzo2.eps","w");ado(o,1020,1020);
fprintf(o,"510 510 translate\n 1000 1000 scale\n");
DO(m,M1) X[m]=-.5+.002*(m-.2);
DO(n,250)Y[n]=-.5+.002*n;
        Y[250]=-.00001;
        Y[251]= .00001;
for(n=252;n<N1;n++) Y[n]=-.5+.002*(n-1.);

for(m=-5;m<6;m++){M(.1*m,-.5)L(.1*m,.5)}
for(n=-5;n<6;n++){M( -.5,.1*n)L(.5,.1*n)}
fprintf(o,"2 setlinecap .001 W 0 0 0 RGB S\n");
M(exp(-1.),-.5)
L(exp(-1.), .5)
//M(M_PI/2.,-.5)
//L(M_PI/2., .5)
fprintf(o,".0007 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("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);        
// c=Tania(z_type(-1.,-M_PI)+log(z))/(-z); 
c=Filog(z);
p=Re(c);q=Im(c);  
if(p>-201. && p<201. &&  q>-201. && q<201. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
       }}
fprintf(o,"1 setlinejoin 1 setlinecap\n");  p=5.;q=1;
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,".0008 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,".0008 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,".0008 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,".002 W .9 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,".002 W 0 0 .9 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (0.  ),-p,p); fprintf(o,".002 W .6 0 .6 RGB S\n");
for(m=-20;m<21;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
p=10.;
conto(o,g,w,v,X,Y,M,N, 30 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, 40 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, 50 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,-30 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,-40 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,-50 ,-p,p); fprintf(o,".002 W 0 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, -30,-p,p); fprintf(o,".002 W .9 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, -40,-p,p); fprintf(o,".002 W .9 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, -50,-p,p); fprintf(o,".002 W .9 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, 30,-p,p); fprintf(o,".002 W 0 0 .9 RGB S\n");
conto(o,f,w,v,X,Y,M,N, 40,-p,p); fprintf(o,".002 W 0 0 .9 RGB S\n");
conto(o,f,w,v,X,Y,M,N, 50,-p,p); fprintf(o,".002 W 0 0 .9 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
      system("epstopdf filogzo2.eps");    
     system(    "open filogzo2.pdf"); //for mac
//    getchar(); system("killall Preview"); // for mac
// Copyleft 2012 by Dmitrii Kouznetsov
}

Latex generator of labels

\documentclass[12pt]{article}
\usepackage{geometry}
\paperwidth 1030pt
\paperheight 1030pt
\textwidth 1140pt
\textheight 1140pt
\topmargin -103pt
\oddsidemargin -86pt
\usepackage{graphicx}
\usepackage{rotating}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \rme {\mathrm{e}}
\newcommand \sx {\scalebox}
\begin{document}
\begin{picture}(1020,1020)
\put(10,10){\includegraphics{filogzo2}}

\put(0,1012){\sx{2.3}{$y$}}
\put(-7,914){\sx{2.3}{$\frac{4}{10}$}}
\put(-7,814){\sx{2.3}{$\frac{3}{10}$}}
\put(-7,714){\sx{2.3}{$\frac{2}{10}$}}
\put(-7,614){\sx{2.3}{$\frac{1}{10}$}}
\put( 2,514){\sx{2.3}{$0$}}
\put(-7,414){\sx{2.3}{$\frac{-\!1}{10}$}}
\put(-7,314){\sx{2.3}{$\frac{-\!1}{5}$}}
\put(-7,214){\sx{2.3}{$\frac{-\!3}{10}$}}
\put(-7,114){\sx{2.3}{$\frac{-\!2}{5}$}}
\put(-7, 14){\sx{2.3}{$\frac{-\!1}{2}$}}
\put(90, -1){\sx{2.3}{$-0.4$}}
\put(190, -1){\sx{2.3}{$-0.3$}}
\put(290, -1){\sx{2.3}{$-0.2$}}
\put(390, -1){\sx{2.3}{$-0.1$}}
\put(516, -1){\sx{2.3}{$0$}}
\put(609, -1){\sx{2.3}{$0.1$}}
\put(709, -1){\sx{2.3}{$0.2$}}
\put(809, -1){\sx{2.3}{$0.3$}}
\put(866, -1){\sx{2.2}{$1/\mathrm e$}}
\put(910, -1){\sx{2.3}{$0.4$}}
\put(1010, 0){\sx{2.4}{$x$}}
\put(250,540){\sx{3}{\rot{82}$u\!=\!0.8$ \ero} }
\put(530,540){\sx{3}{\rot{81}$u\!=\!1$ \ero} }
\put(680,524){\sx{2.8}{\rot{77}$u\!=\!1.2$ \ero} }
\put(768,524){\sx{2.8}{\rot{72}$u\!=\!1.4$ \ero} }
\put(816,524){\sx{2.8}{\rot{56}$u\!=\!1.6$ \ero} }
\put(600,684){\sx{2.8}{\rot{-33}$v\!=\!0.2$ \ero} }
\put(720,798){\sx{2.8}{\rot{-62}$v\!=\!0.4$ \ero} }
\put(820,490){\sx{3}{\rot{-4}$v\!=\!1$ \ero} }
\put(820,466){\sx{3}{\rot{-12}$v\!=\!2$ \ero} }
\put(808,446){\sx{3}{\rot{-26}$v\!=\!3$ \ero} }
\put(768,372){\sx{3}{\rot{36}$u\!=\!5$ \ero} }
\put(770,350){\sx{3}{\rot{26}$u\!=\!4$ \ero} }
\put(770,324){\sx{3}{\rot{16}$u\!=\!3$ \ero} }
\put(768,297){\sx{3}{\rot{2}$u\!=\!2$ \ero} }
\put(766,262){\sx{3}{\rot{-8}$u\!=\!1$ \ero} }
\put(752,230){\sx{3}{\rot{-28}$u\!=\!0$ \ero} }

\put(94,99){\sx{3}{\rot{41}$v\!=\!-2$ \ero} }
\put(162,50){\sx{3}{\rot{57}$v\!=\!-1$ \ero} }
\put(242,30){\sx{3}{\rot{75}$v\!=\!0$ \ero} }
\put(315,30){\sx{3}{\rot{87}$v\!=\!1$ \ero} }

\end{picture}
\end{document}

Similar picture

Fig1802.jpg
Fig.18.2 generated with «Conrec6.cin»

Similar complex map is generated as test of routine «Conrec6.cin».

It is shown in figure at right.

The same set of labels is used in both pictures.

These pictures are compared in articles «Conrec6 demo‎», «MapConrec6demo‎‎»; no visual difference is seen, the pictures look the same.

In this sense, routines «Conrec6.cin» and «Conto.cin» are equivalent.

References

  1. ↑ https://mizugadro.mydns.jp/BOOK/468.pdf Dmitrii Kouznetsov. Superfunctions. Lambert Academic Publishing, 2020.
  2. ↑ https://www.morebooks.de/shop-ui/shop/product/978-620-2-67286-3 Superfunctions Non-integer iterates of holomorphic functions. Tetration and other superfunctions. Formulas,algorithms,tables,graphics 978-620-2-67286-3 Tools for evaluation of superfunctions, abelfunctions and non-integer iterates of holomorphic functions are collected. .. Authors Dmitrii Kouznetsov Book language English Published on 2020-07-28 Publishing house LAP LAMBERT Academic Publishing Number of pages 328 Price (EUR ) €52.90

Keywords

«Book», «C++», «Complex map», «Filog», «Fixed point», «Latex», «Logarithm», «[[Superfunctions]», «Tetration», «Zoom»,

File history

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

Date/TimeThumbnailDimensionsUserComment
current06:12, 1 December 2018Thumbnail for version as of 06:12, 1 December 20182,137 × 2,137 (1.84 MB)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:Figlogzo2t.jpg&oldid=45467"