File:Doya500.png

Автор открывает суперфункции.

Author opens/discovers the Superfunctions.

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.

This map is used as Fig.5.14 at page 58 of book «Superfunctions» ^[1][2].

C++ generator of the image

//Files ado.cin, conto.cin and doya.cin should be loaded 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("doya2.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 doya2.eps");  
        system(    "open doya2.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.)

References

Keywords

«Doya function», «Transferfunction», «Superfunctions»,