Difference between revisions of "File:KellerMapT.png"

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[[Complex map]] of the [[Keller function]],
Importing image file
 
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$\mathrm{Keller}(z)=z+\ln\!\Big(\mathrm e-(\mathrm e\!-\!1) \mathrm e^{-z}\Big)$.
  +
  +
: $ u\!+\!\mathrm i v = \mathrm{Keller}(x\!+\! \mathrm i y)$
  +
  +
==C++ generator of curves==
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// Files [[ado.cin]] and [[conto.cin]] should be loaded in the working directory in order to compile the [[C++]] code below.
  +
  +
#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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#define DB double
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#define DO(x,y) for(x=0;x<y;x++)
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using namespace std;
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#include <complex>
  +
typedef complex<double> z_type;
  +
#define Re(x) x.real()
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#define Im(x) x.imag()
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#define I z_type(0.,1.)
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#include "conto.cin"
  +
  +
z_type Shoka(z_type z) { return z + log(exp(-z)+(M_E-1.)); }
  +
z_type Keller(z_type z) { return z + log(M_E- exp(-z)*(M_E-1.) );}
  +
  +
main(){ int j,k,m,n; DB x,y, p,q, t,r; z_type z,c,d;
  +
r=log(1-1./M_E); printf("r=%16.14f\n",r);
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int M=400,M1=M+1;
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int N=801,N1=N+1;
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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
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FILE *o;o=fopen("KellerMap.eps","w");ado(o,162,162);
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fprintf(o,"81 81 translate\n 10 10 scale 2 setlinecap\n ");
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DO(m,M1){ t=(m-200)/200.; X[m]=4.005*t*(.5+1.5*t*t);}
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DO(n,N1)Y[n]=-8.+.02*(n-.5);
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for(m=-8;m<9;m++){if(m==0){M(m,-8.5)L(m,8.5)} else{M(m,-8)L(m,8)}}
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for(n=-8;n<9;n++){ M( -8,n)L(8,n)}
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fprintf(o,".008 W 0 0 0 RGB S\n");
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DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
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DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
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DO(n,N1){y=Y[n]; z=z_type(x,y);
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// c=Tania(z); p=Re(c);q=Im(c);
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c=Keller(z); p=Re(c);q=Im(c);
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if(p>-19. && p<19. && q>-19. && q<19. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
  +
}}
  +
fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.4;q=.5;
  +
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,".01 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,".01 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,".01 W 0 0 .9 RGB S\n");
  +
for(m=1;m<10;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".04 W .9 0 0 RGB S\n");
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for(m=1;m<10;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 .9 RGB S\n");
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conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".04 W .6 0 .6 RGB S\n");
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for(m=-9;m<10;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 0 RGB S\n");
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for(y=-2*M_PI; y<7; y+=2*M_PI)
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{M(r,y)L(-8.1,y) fprintf(o,"0 setlinecap .04 W 1 1 1 RGB S\n");
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for(m=0;m<75;m+=4) {x=r-.04-.1*m; M(x,y) L(x-.12,y)} fprintf(o,".06 W 1 .5 0 RGB S\n");
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for(m=2;m<75;m+=4) {x=r-.04-.1*m; M(x,y) L(x-.12,y)} fprintf(o,".06 W 0 .5 1 RGB S\n");
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}
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fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
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system("epstopdf KellerMap.eps");
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system( "open KellerMap.pdf");
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printf("r=%16.14f\n",r);
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getchar(); system("killall Preview");
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}
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==Latex source of labels==
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% File [[KellerMap.pdf]] should be generated with the code above in order to compile the [[Latex]] document below.
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  +
%<poem><nomathjax><nowiki>
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% Copyleft 2011 by Dmitrii Kouznetsov %<br>
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\documentclass[12pt]{article} %<br>
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\usepackage{geometry} %<br>
  +
\usepackage{graphicx} %<br>
  +
\usepackage{rotating} %<br>
  +
\paperwidth 854pt %<br>
  +
\paperheight 844pt %<br>
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\topmargin -96pt %<br>
  +
\oddsidemargin -98pt %<br>
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\textwidth 1100pt %<br>
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\textheight 1100pt %<br>
  +
\pagestyle {empty} %<br>
  +
\newcommand \sx {\scalebox} %<br>
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\newcommand \rot {\begin{rotate}} %<br>
  +
\newcommand \ero {\end{rotate}} %<br>
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\newcommand \ing {\includegraphics} %<br>
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\begin{document} %<br>
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\sx{5}{ \begin{picture}(164,165) %<br>
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\put(6,5){\ing{KellerMap}} %<br>
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\put(2,163){\sx{.7}{$y$}} %<br>
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\put(2,144){\sx{.6}{$6$}} %<br>
  +
\put(2,124){\sx{.6}{$4$}} %<br>
  +
\put(2,104){\sx{.6}{$2$}} %<br>
  +
% \put(3,116){\sx{.6}{$\pi$}} %<br>
  +
\put(18,147){\sx{.8}{\bf cut}} %<br>
  +
\put(2, 84){\sx{.6}{$0$}} %<br>
  +
\put(18,84){\sx{.8}{\bf cut}} %<br>
  +
\put(-2,64){\sx{.6}{$-2$}} %<br>
  +
\put(18,20.8){\sx{.8}{\bf cut}} %<br>
  +
\put(-2,44){\sx{.6}{$-4$}} %<br>
  +
\put(-2,24){\sx{.6}{$-6$}} %<br>
  +
\put( 22,0){\sx{.6}{$-6$}} %<br>
  +
\put( 42,0){\sx{.6}{$-4$}} %<br>
  +
\put( 62,0){\sx{.6}{$-2$}} %<br>
  +
\put( 86,0){\sx{.6}{$0$}} %<br>
  +
\put(106,0){\sx{.6}{$2$}} %<br>
  +
\put(126,0){\sx{.6}{$4$}} %<br>
  +
\put(146,0){\sx{.6}{$6$}} %<br>
  +
\put(164,0){\sx{.7}{$x$}} %<br>
  +
\put( 79.5, 109){\rot{90}\sx{.7}{$u\!=\!1$}\ero}%<br>
  +
\put( 97.0, 108){\rot{90}\sx{.7}{$u\!=\!2$}\ero}%<br>
  +
\put(108.8, 108){\rot{90}\sx{.7}{$u\!=\!3$}\ero}%<br>
  +
\put(119.4, 108){\rot{90}\sx{.7}{$u\!=\!4$}\ero}%<br>
  +
\put(129.6, 108){\rot{90}\sx{.7}{$u\!=\!5$}\ero}%<br>
  +
\put(132,154.4){\sx{.8}{$v\!=\!7$}}%<br>
  +
\put(132,144.3){\sx{.8}{$v\!=\!6$}}%<br>
  +
\put(132,134.3){\sx{.8}{$v\!=\!5$}}%<br>
  +
\put(132,124.2){\sx{.8}{$v\!=\!4$}}%<br>
  +
\put(132,114.2){\sx{.8}{$v\!=\!3$}}%<br>
  +
\put(132,104.2){\sx{.8}{$v\!=\!2$}}%<br>
  +
\put(132, 94.2){\sx{.8}{$v\!=\!1$}}%<br>
  +
\put(132, 84){\sx{.8}{$v\!=\!0$}}%<br>
  +
\put(132, 73.9){\sx{.8}{$v\!=\!-\!1$}}%<br>
  +
\put(132, 63.4){\sx{.8}{$v\!=\!-\!2$}}%<br>
  +
\put(132, 53.4){\sx{.8}{$v\!=\!-\!3$}}%<br>
  +
\put(132, 43.4){\sx{.8}{$v\!=\!-\!4$}}%<br>
  +
\put(132, 33.4){\sx{.8}{$v\!=\!-\!5$}}%<br>
  +
\put(132, 23.4){\sx{.8}{$v\!=\!-\!6$}}%<br>
  +
\put(132, 13.4){\sx{.8}{$v\!=\!-\!7$}}%<br>
  +
\end{picture} %<br>
  +
} %<br>
  +
\end{document} %<br>
  +
%</nowiki></nomathjax></poem>
  +
  +
==Copyleft==
  +
  +
Copyleft 2012 by Dmitrii Kouznetsov. The image above and its generators can be used for free; attribute the the source.
  +
  +
==References==
  +
<references/>
  +
  +
[[Category:Book]]
  +
[[Category:BookMap]]
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[[Category:Keller function]]
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[[Category:Transfer function]]
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[[Category:Shoka function]]
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[[Category:ArcShoka]]
  +
[[Category:Laser science]]
  +
[[Category:Complex map]]
  +
[[Category:C++]]
  +
[[Category:Latex]]

Latest revision as of 08:39, 1 December 2018

Complex map of the Keller function, $\mathrm{Keller}(z)=z+\ln\!\Big(\mathrm e-(\mathrm e\!-\!1) \mathrm e^{-z}\Big)$.

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

C++ generator of curves

// Files ado.cin and conto.cin should be loaded in 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"
z_type Shoka(z_type  z) { return z + log(exp(-z)+(M_E-1.)); }
z_type Keller(z_type z) { return z + log(M_E- exp(-z)*(M_E-1.) );}
main(){ int j,k,m,n; DB x,y, p,q, t,r; z_type z,c,d;
r=log(1-1./M_E); printf("r=%16.14f\n",r); 
int M=400,M1=M+1;
int N=801,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("KellerMap.eps","w");ado(o,162,162);
fprintf(o,"81 81 translate\n 10 10 scale 2 setlinecap\n ");
DO(m,M1){ t=(m-200)/200.; X[m]=4.005*t*(.5+1.5*t*t);}
DO(n,N1)Y[n]=-8.+.02*(n-.5);
for(m=-8;m<9;m++){if(m==0){M(m,-8.5)L(m,8.5)} else{M(m,-8)L(m,8)}}
for(n=-8;n<9;n++){     M(  -8,n)L(8,n)}
fprintf(o,".008 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); p=Re(c);q=Im(c);  
c=Keller(z); p=Re(c);q=Im(c);  
if(p>-19. && p<19. &&  q>-19. && q<19. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
       }}
fprintf(o,"1 setlinejoin 1 setlinecap\n");  p=1.4;q=.5;
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,".01 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,".01 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,".01 W 0 0 .9 RGB S\n");
for(m=1;m<10;m++)  conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".04 W .9 0 0 RGB S\n");
for(m=1;m<10;m++)  conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 .9 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (0.  ),-p,p); fprintf(o,".04 W .6 0 .6 RGB S\n");
for(m=-9;m<10;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 0 RGB S\n");
for(y=-2*M_PI; y<7; y+=2*M_PI) 
 {M(r,y)L(-8.1,y) fprintf(o,"0 setlinecap .04 W 1 1 1 RGB S\n");
  for(m=0;m<75;m+=4) {x=r-.04-.1*m; M(x,y) L(x-.12,y)}  fprintf(o,".06 W 1 .5 0 RGB S\n");
  for(m=2;m<75;m+=4) {x=r-.04-.1*m; M(x,y) L(x-.12,y)}  fprintf(o,".06 W 0 .5 1 RGB S\n");
 }
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
      system("epstopdf KellerMap.eps");    
      system(    "open KellerMap.pdf");
printf("r=%16.14f\n",r); 
      getchar(); system("killall Preview");
}

Latex source of labels

% File KellerMap.pdf should be generated with the code above in order to compile the Latex document below.

%


 % Copyleft 2011 by Dmitrii Kouznetsov %<br>
 \documentclass[12pt]{article} %<br>
 \usepackage{geometry} %<br>
 \usepackage{graphicx} %<br>
 \usepackage{rotating} %<br>
 \paperwidth 854pt %<br>
 \paperheight 844pt %<br>
 \topmargin -96pt %<br>
 \oddsidemargin -98pt %<br>
 \textwidth 1100pt %<br>
 \textheight 1100pt %<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{5}{ \begin{picture}(164,165) %<br>
 \put(6,5){\ing{KellerMap}} %<br>
 \put(2,163){\sx{.7}{$y$}} %<br>
 \put(2,144){\sx{.6}{$6$}} %<br>
 \put(2,124){\sx{.6}{$4$}} %<br>
 \put(2,104){\sx{.6}{$2$}} %<br>
 % \put(3,116){\sx{.6}{$\pi$}} %<br>
 \put(18,147){\sx{.8}{\bf cut}} %<br>
 \put(2, 84){\sx{.6}{$0$}} %<br>
 \put(18,84){\sx{.8}{\bf cut}} %<br>
 \put(-2,64){\sx{.6}{$-2$}} %<br>
 \put(18,20.8){\sx{.8}{\bf cut}} %<br>
 \put(-2,44){\sx{.6}{$-4$}} %<br>
 \put(-2,24){\sx{.6}{$-6$}} %<br>
 \put( 22,0){\sx{.6}{$-6$}} %<br>
 \put( 42,0){\sx{.6}{$-4$}} %<br>
 \put( 62,0){\sx{.6}{$-2$}} %<br>
 \put( 86,0){\sx{.6}{$0$}} %<br>
 \put(106,0){\sx{.6}{$2$}} %<br>
 \put(126,0){\sx{.6}{$4$}} %<br>
 \put(146,0){\sx{.6}{$6$}} %<br>
 \put(164,0){\sx{.7}{$x$}} %<br>
 \put( 79.5, 109){\rot{90}\sx{.7}{$u\!=\!1$}\ero}%<br>
 \put( 97.0, 108){\rot{90}\sx{.7}{$u\!=\!2$}\ero}%<br>
 \put(108.8, 108){\rot{90}\sx{.7}{$u\!=\!3$}\ero}%<br>
 \put(119.4, 108){\rot{90}\sx{.7}{$u\!=\!4$}\ero}%<br>
 \put(129.6, 108){\rot{90}\sx{.7}{$u\!=\!5$}\ero}%<br>
 \put(132,154.4){\sx{.8}{$v\!=\!7$}}%<br>
 \put(132,144.3){\sx{.8}{$v\!=\!6$}}%<br>
 \put(132,134.3){\sx{.8}{$v\!=\!5$}}%<br>
 \put(132,124.2){\sx{.8}{$v\!=\!4$}}%<br>
 \put(132,114.2){\sx{.8}{$v\!=\!3$}}%<br>
 \put(132,104.2){\sx{.8}{$v\!=\!2$}}%<br>
 \put(132, 94.2){\sx{.8}{$v\!=\!1$}}%<br>
 \put(132, 84){\sx{.8}{$v\!=\!0$}}%<br>
 \put(132, 73.9){\sx{.8}{$v\!=\!-\!1$}}%<br>
 \put(132, 63.4){\sx{.8}{$v\!=\!-\!2$}}%<br>
 \put(132, 53.4){\sx{.8}{$v\!=\!-\!3$}}%<br>
 \put(132, 43.4){\sx{.8}{$v\!=\!-\!4$}}%<br>
 \put(132, 33.4){\sx{.8}{$v\!=\!-\!5$}}%<br>
 \put(132, 23.4){\sx{.8}{$v\!=\!-\!6$}}%<br>
 \put(132, 13.4){\sx{.8}{$v\!=\!-\!7$}}%<br>
 \end{picture} %<br>
 } %<br>
 \end{document} %<br>
%

Copyleft

Copyleft 2012 by Dmitrii Kouznetsov. The image above and its generators can be used for free; attribute the the source.

References

File history

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

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