View source for File:FilogmT1000a.jpg

== Summary ==
{{Image_Details|user
|description  = [[Complex map]] of function [[Filog]], zoom-in from the central part. <math>u\!+\!\mathrm i v=\mathrm{Filog}(x\!+\!\mathrm i y)</math>
|author       = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
|date-created = 2013.03.05
|pub-country  = Japan
|notes        = 2013.02.27, 17:30, Server http://tori.ils.uec.ac.jp/TORI is cracked by [[Nishio Shigeaki]] from computer identified as gigabyte.ils.uec.ac.jp and, perhaps, we'll never be able to recover TORI. From the vandalized copy, I try to save the most important pictures, formulas and algorithms. [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]] 02:40, 8 March 2013 (UTC)
|versions     = http://en.citizendium.org/wiki/File:FilogbigT.jpg
}}
== Licensing ==
{{CC|by|3.0}}

==[[C++]] generator of curves==

// FIles [[filog.cin]], [[ado.cin]] and [[conto.cin]] should be loaded to the working directory 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 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"
 main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
 int M=600,M1=M+1;
 int N=401,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("filogm.eps","w");ado(o,302,202);
 fprintf(o,"101 101 translate\n 100 100 scale\n");
 DO(m,M1) X[m]=-1.+.005*(m-.2);
 DO(n,200)Y[n]=-1.+.005*n;
         Y[200]=-.0001;
         Y[201]= .0001;
 for(n=202;n<N1;n++) Y[n]=-1.+.005*(n-1.);
 for(m=-1;m<3;m++){M(m,-1)L(m,1)}
 for(n=-1;n<2;n++){M( -1,n)L(2,n)}
 fprintf(o,"2 setlinecap .004 W 0 0 0 RGB S\n");
 M(exp(-1.),-1)
 L(exp(-1.), 1)
 M(M_PI/2.,-1)
 L(M_PI/2., 1)
 fprintf(o,".002 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>-41. && p<41. &&  q>-41. && q<41. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
        }}
 fprintf(o,"1 setlinejoin 2 setlinecap\n");  p=5.;q=.8;
 for(m=-10;m<11;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".001 W 0 .6 0 RGB S\n");
 for(m=0;m<11;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".001 W .9 0 0 RGB S\n");
 for(m=0;m<11;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".001 W 0 0 .9 RGB S\n");
 for(m=1;m<21;m++)  conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".003 W .9 0 0 RGB S\n");
 for(m=1;m<121;m++)  conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".003 W 0 0 .9 RGB S\n");
                   conto(o,f,w,v,X,Y,M,N, (0.  ),-p,p); fprintf(o,".003 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,".003 W 0 0 0 RGB S\n");
 fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
      system("epstopdf filogm.eps");    
      system(    "open filogm.pdf"); //for mac
 //    getchar(); system("killall Preview"); // for mac
 }
 // Copyleft 2013 by Dmitrii Kouznetsov

==[[Latex]] generator of labels==

\documentclass[12pt]{article} %<br>
\usepackage{geometry} %<br>
\paperwidth 315pt %<br>
\paperheight 216pt %<br>
\topmargin -102pt %<br>
\oddsidemargin -88pt %<br>
\usepackage{graphicx} %<br>
\usepackage{rotating} %<br>
\newcommand \rot {\begin{rotate}} %<br>
\newcommand \ero {\end{rotate}} %<br>
\newcommand \rme {\mathrm{e}} %<br>
\newcommand \sx {\scalebox} %<br>
\begin{document} %<br>
\begin{picture}(208,208) %<br>
\put(10,10){\includegraphics{filogm}} %<br>
\put(4,207){$1$} %<br>
\put(0,147){$y$} %<br>
\put(4,107){$0$} %<br>
\put(-3, 8){$-\!1$} %<br>
\put(2, 0){$-\!1$} %<br>
\put(108, 0){$0$} %<br>
\put(140, 2){\sx{.8}{$1/\rme$}} %<br>
\put(209, 0){\sx{1}{$1$}} %<br>
\put(264, 2){\sx{.8}{$\pi/2$}} %<br>
\put(307, 2){\sx{.9}{$x$}} %<br>
\put(185,43){\sx{.8}{\rot{64}$v\!=\!2$ \ero} } %<br>
\put(250,49){\sx{.6}{\rot{84}$v\!=\!1.2$ \ero} } %<br>
\put(281.5,43){\sx{.8}{\rot{80}$v\!=\!1$ \ero} } %<br>
\put(283,161){\sx{.6}{\rot{-40}$v\!=\!0.8$ \ero} } %<br>
\put(250,143){\sx{.6}{\rot{60}$u\!=\!0.2$ \ero} } %<br>
\put(283,118){\sx{.8}{\rot{35}$u\!=\!0$ \ero} } %<br>
\put(284,74){\sx{.6}{\rot{5}$u\!=\!-0.2$ \ero} } %<br>
\put(28.4,120){\sx{.7}{\rot{79}$u\!=\!0.6$\ero}} %<br>
\put(84.4,113){\sx{.7}{\rot{74}$u\!=\!0.8$\ero}} %<br>
\end{picture} %<br>
\end{document}   %<br>