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:

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=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 2011 by Dmitrii Kouznetsov \documentclass[12pt]{article} % \usepackage{geometry} % \usepackage{graphicx} % \usepackage{rotating} % \paperwidth 860pt % \paperheight 843pt % \topmargin -94pt % \oddsidemargin -96pt % \textwidth 1200pt % \textheight 1800pt % \pagestyle {empty} % \newcommand \sx {\scalebox} % \newcommand \rot {\begin{rotate}} % \newcommand \ero {\end{rotate}} % \newcommand \ing {\includegraphics} % \begin{document} % \sx{10}{ \begin{picture}(41,81) % \put(1,1){\ing{doya20map4b}} % \put(-.5,79.6){\sx{.4}{$t$}} % \put(-1,71){\sx{.4}{$3$}} % \put(-1,61){\sx{.4}{$2$}} % \put(-1,51){\sx{.4}{$1$}} % \put(-1,41){\sx{.4}{$0$}} % \put(-4,31){\sx{.4}{$-1$}} % \put(-4,21){\sx{.4}{$-2$}} % \put(-4,11){\sx{.4}{$-3$}} % \put(9,-1.5){\sx{.4}{$-3$}} % \put(18,-1.5){\sx{.4}{$-2$}} % \put(28,-1.5){\sx{.4}{$-1$}} % \put(41,-1.5){\sx{.4}{0}} % \put(51,-1.5){\sx{.4}{1}} % \put(61,-1.5){\sx{.4}{2}} % \put(71,-1.5){\sx{.4}{3}} % \put(79.8,-1.2){\sx{.42}{$x$}} % \put(10.7,60){\rot{85}\sx{.62}{$u\!=\!-1$}\ero} % \put(23.4,61){\rot{88}\sx{.6}{$u\!=\!0$}\ero} % \put(36,63){\rot{94}\sx{.6}{$u\!=\!1$}\ero} % \put(47.3,63){\rot{94}\sx{.6}{$u\!=\!2$}\ero} % \put(57.5,63){\rot{93}\sx{.6}{$u\!=\!3$}\ero} % \put(67.5,63){\rot{93}\sx{.6}{$u\!=\!4$}\ero} % \put(68,68.6){\rot{1}\sx{.6}{$v\!=\!3$}\ero} % \put(68,59){\rot{1}\sx{.6}{$v\!=\!2$}\ero} % \put(68,50){\rot{1}\sx{.6}{$v\!=\!1$}\ero} % \put(68,40.6){\rot{0}\sx{.6}{$v\!=\!0$}\ero} % \put(63,31){\rot{-1}\sx{.6}{$v\!=\!-1$}\ero} % \put(63,22){\rot{-2}\sx{.6}{$v\!=\!-2$}\ero} % \put(63,13){\rot{-2}\sx{.6}{$v\!=\!-3$}\ero} % \end{picture} % } % \end{document}

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