File:FilogmT1000a.jpg

Summary

Title / Description	Complex map of function Filog, zoom-in from the central part. ${\displaystyle u\!+\!\mathrm {i} v=\mathrm {Filog} (x\!+\!\mathrm {i} y)}$
Citizendium author & Copyright holder	Copyright © Dmitrii Kouznetsov. See below for licence/re-use information.
Date created	2013.03.05
Country of first publication	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. Dmitrii Kouznetsov 02:40, 8 March 2013 (UTC)
Other versions	http://en.citizendium.org/wiki/File:FilogbigT.jpg
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Licensing

   

This media, FilogmT1000a.jpg, is licenced under the Creative Commons Attribution 3.0 Unported License

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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