File:Doya500.png

Автор открывает суперфункции.

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

\(f=\mathrm{Doya}_1(y\!+\! \mathrm i x)\) 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.

using namespace std; typedef complex z_type;
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 1) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)
 * 4) include "conto.cin"
 * 5) 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.)