File:FilogmT1000a.jpg: Difference between revisions

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 it. 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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For any reuse or distribution, you must make clear to others the licence terms of this work (the best way to do this is with a link to this licence's web page). Any of the above conditions can be waived if you get permission from the copyright holder. Nothing in this licence impairs or restricts the author's moral rights.
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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