File:Doya20map4bT100.png

complex map of the Doya function at with parameter equal to 2.

$f=\mathrm{Doya}_2(x+\mathrm i y)$ in the $x,y$ plane with lines $u\!=\!\Re(f)\!=\!\mathrm{const}$ and lines $v\!=\!\Im(f)\!=\!\mathrm{const}$.

C++ generator of curves

// The conto.cin, the ado.cin and the doya.cin should be loaded in the working directory for the compilation 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=160,M1=M+1;
 int N=161,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("doya20map4b.eps","w");ado(o,82,82);
fprintf(o,"41 41 translate\n 10 10 scale\n");
DO(m,M1) X[m]=-4.01+.05*(m);
DO(n,N1) Y[n]=-4.+.05*(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(x,y);        
 c=Doya(2.,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 2 setlinecap\n");  p=1.;q=.9;
for(m=-6;m<5;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".016 W 0 .6 0 RGB S\n");
for(m=0;m<6;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".016 W .9 0 0 RGB S\n");
for(m=0;m<6;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".016 W 0 0 .9 RGB S\n");
for(m=1;m<5;m++)  conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".05 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,".05 W 0 0 .9 RGB S\n");
                   conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".05 W .6 0 .6 RGB S\n");
for(m=-5;m<6;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".05 W 0 0 0 RGB S\n");
DO(m,13) {x=-4.1+.29*(m+1); M(x,0) L(x+.04,0) }
fprintf(o,".07 W 0 .5 1 RGB S\n");
DO(m,14) {x=-3.96+.29*m; M(x,0) L(x+.04,0) }
fprintf(o,".07 W 1 .5 0 RGB S\n");
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
       system("epstopdf doya20map4b.eps");     
       system(    "open doya20map4b.pdf");
       getchar(); system("killall Preview");
}

Latex generator of labels

Copyleft

The image and its generators may be used for free, attribute the source.