Difference between revisions of "File:Figlogzo2t.jpg"

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[[File:Filogbigmap100.png|300px|thumb| large version of this map]]
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Importing image file
  
  +
[[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
  +
  +
$u\!+\!\mathrm i v= \mathrm{Filog} (x\!+\!\mathrm i y)$
  +
  +
==Meaning==
  +
  +
$z=\mathrm{Filog}(a)~$ expresses solution $z$ of equation $\ln(z)/a=z$.
  +
  +
==[[C++]] generator of curves==
  +
// Files [[ado.cin]], [[conto.cin]], [[filog.cin]], [[tania.cin]] should be loaded to the working directory in order to compile the [[C++]] 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 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
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of labels==
  +
<poem><nomathjax><nowiki>
  +
\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}
  +
</nowiki></nomathjax></poem>
  +
  +
[[Category:Filog]]
  +
[[Category:Complex map]]
  +
[[Category:Fixed point]]
  +
[[Category:Logarithm]]
  +
[[Category:C++]]
  +
[[Category:Latex]]
  +
[[Category:Zoom]]
  +
[[Category:Book]]

Latest revision as of 08:36, 1 December 2018

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

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

Meaning

$z=\mathrm{Filog}(a)~$ expresses solution $z$ of equation $\ln(z)/a=z$.

C++ generator of curves

// Files ado.cin, conto.cin, filog.cin, tania.cin should be loaded to the working directory 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}

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