File:Hades500.png

Complex map of the Doya function, rotated counter-clock vice for 90^o.

$f=\mathrm{Doya}_1(y\!+\! \mathrm i x)$ is shown in the $x,y$ plane with lines $u\!=\!\Re(f)\!=\!\mathrm{const}$ and lines $v\!=\!\Im(f)\!=\!\mathrm{const}$.

Levels $v\!=\!\pm 1.2$, $v\!=\!\pm 1.4$, $u\!=\!-0.4$ are shown with thick lines.

C++ generator of the image

The files ado.cin, conto.cin and doya.cin should be loaded to the working directory for the compillation of 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 "doya.cin"

main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
 int M=230,M1=M+1;
 int N=330,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("hades2.eps","w");ado(o,22,34);
fprintf(o,"11 30.5 translate\n 10 10 scale\n");
DO(m,M1) X[m]=-1.1+.01*(m-.5);
DO(n,N1) Y[n]=-3.+.01*(n-.5);
// for(m=-4;m<5;m++){if(m==0){M(m,-4.2)L(m,4.2)} else{M(m,-4)L(m,4)}}
// for(n=-4;n<5;n++){  M(  -4,n)L(4,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(y,x);        
 c=Doya(1.,z); 
 p=Re(c);q=Im(c);      
 if(p>-99. && p<99. &&  q>-99. && q<99. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
        }}
fprintf(o,"1 setlinejoin 1 setlinecap\n");  p=1.;q=.9;
conto(o,f,w,v,X,Y,M,N,1.2,-q, q); fprintf(o,".1 W 0 .3 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N,-1.2,-q, q); fprintf(o,".1 W 0 .3 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N,1.4,-q, q); fprintf(o,".1 W 0 .3 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N,-1.4,-q, q); fprintf(o,".1 W 0 .3 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N,-.4,-q, q); fprintf(o,".1 W .3 0 0 RGB S\n");
for(m=-6;m<5;m++)for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".003 W 0 .9 0 RGB S\n");
for(m=0;m<6;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".003 W 1 0 0 RGB S\n");
for(m=0;m<6;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".003 W 0 0 1 RGB S\n");
for(m=1;m<5;m++)  conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".006 W .9 0 0 RGB S\n");
for(m=1;m<5;m++)  conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".006 W 0 0 .9 RGB S\n");
                   conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".006 W .6 0 .6 RGB S\n");
for(m=-1;m<2;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 hades2.eps");  
       system(    "open hades2.pdf");
       getchar(); system("killall Preview");
}

Copyleft status

Copyleft 2011 by Dmitrii Kouznetsov. The image and the generator may be used for free, but the source should be attributed. (The attribution helps to trace errors if any.)