File:Moriamap1.jpg

Complex map of function mori, prepared for comparison with the imilar map of its asymptotic approximation morias.

C++ generator of map
// FIles ado.cin, conto.cin, besselj0.cin should be loaded in order to compile the code below. // typedef std::complex z_type; //#include "korias.cin" //#include "korifit76.cin" //#include "morias.cin"
 * 1) include 
 * 2) include 
 * 3) define DB double
 * 4) define DO(x,y) for(x=0;x<y;x++)
 * 5) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)
 * 4) include "conto.cin"
 * 1) include "besselj0.cin"

DB L1=2.404825557695772768621631879326454643124; int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; int M=301,M1=M+1; int N=176,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("moriama.eps","w");ado(o,1220,720); fprintf(o,"210 210 translate\n 100 100 scale\n"); DO(m,M1)X[m]=-2.+.04*(m-.5); DO(n,N1)Y[n]=-2.+.04*(n-.5);;

for(m=-2;m<11;m+=1){M(m,-2)L(m,5)} for(n=-2;n<6;n+=1){ M(-2,n)L(10,n)} fprintf(o,".01 W 0 0 0 RGB S\n");

//DB po=.05; DB po=.1; //DB xo=4*L1/po; //M(xo,po); DO(m,100){ x=xo+1.+m; y=x/xo-1.; L(x,y); if(y>100) break;} //fprintf(o,".1 W 1 0 0 RGB S\n");

// DB x0=L1/po; M(0,0)L(x0,0)L(40.,40.-x0); fprintf(o,".2 W 0 1 0 RGB S\n");

DO(m,M1)DO(n,N1){g[m*N1+n]=99999999; f[m*N1+n]=999999999;} DO(m,M1){x=X[m]; //printf("%5.2f\n",x); DO(n,N1){y=Y[n]; z=z_type(x,y); //     c=BesselJ0(L1*sqrt(z))/(1.-z); c=BesselJ0(L1*z)/(1.-z*z); //     c=korifit76(z); //     c=korias(z); //     c*=c*exp(po*I*z); //    c=log(c); //c=exp(I*(-2.*L1+po*z)*z)/z ; //c=(I*(-2.*L1+po*z)*z) ; //c=(-2.*L1+po*z)*z ; //c=morias(z); // c*=c*exp(I*po*z*z)*z; p=Re(c);   q=Im(c); if(p>-999999. && p<999999. && q>-999999. && q<999999 ){g[m*N1+n]=p; f[m*N1+n]=q; }                    }} //#include "plodi.cin" /* fprintf(o,"1 setlinejoin 1 setlinecap\n"); q=.05; for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,( .01*n),-q, q); fprintf(o,".002 W 0 .7 0 RGB S\n"); for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,(-.01*n),-q, q); fprintf(o,".002 W 0 .7 0 RGB S\n"); for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,( .01*n),-q, q); fprintf(o,".002 W 0 0 .8 RGB S\n"); for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,(-.01*n),-q, q); fprintf(o,".002 W .8 0 0 RGB S\n");

p=16;q=1; for(m=-4;m<4;m++)for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".004 W 0 .8 0 RGB S\n"); for(m=0;m<4;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".004 W 1 0 0 RGB S\n"); for(m=0;m<4;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".004 W 0 0 1 RGB S\n"); for(m=1;m<9;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".03 W 1 0 0 RGB S\n"); for(m=1;m<9;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".03 W 0 0 1 RGB S\n"); conto(o,f,w,v,X,Y,M,N, (0. ),-4*p,4*p); fprintf(o,".03 W .9 0 .9 RGB S\n"); for(m=-8;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n"); m=0;         conto(o,g,w,v,X,Y,M,N, (0.+m),-4*p,4*p); fprintf(o,".02 W 0 0 0 RGB S\n"); for(m=1;m<9;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".02 W 0 0 0 RGB S\n"); //#include "plofu.cin" fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); system("epstopdf moriama.eps"); system(   "open moriama.pdf"); getchar; system("killall Preview");//for mac } //

Latex generator labels
% \documentclass[12pt]{article} \usepackage{graphicx} \usepackage{geometry} \usepackage{rotating} \paperwidth 1034px \paperheight 630px \textwidth 2000pt \textheight 900pt \newcommand \sx \scalebox \newcommand \ing \includegraphics \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \oddsidemargin -70pt \topmargin -100pt \parindent 0pt \begin{document} \begin{picture}(1020,616) \put(20,10){\ing{moriama1}} %\put(20,10){\ing{moriasma}} \put( 8,610){\sx{2.8}{$y$}} %\put( 8,610){\sx{2.8}{$4$}} \put( 8,510){\sx{2.8}{$3$}} \put( 8,410){\sx{2.6}{$2$}} \put( 8,310){\sx{2.8}{$1$}} \put( 8,210){\sx{2.8}{$0$}} \put(-11,110){\sx{2.8}{$-1$}} \put(0,-6){\sx{2.8}{$-2$}} \put(100,-6){\sx{2.8}{$-1$}} \put(223,-6){\sx{2.8}{$0$}} \put(323,-6){\sx{2.8}{$1$}} \put(424,-6){\sx{2.8}{$2$}} \put(524,-6){\sx{2.8}{$3$}} \put(625,-6){\sx{2.8}{$4$}} \put(725,-6){\sx{2.8}{$5$}} \put(825,-6){\sx{2.8}{$6$}} \put(926,-6){\sx{2.8}{$7$}} %\put(1027,-6){\sx{2.8}{$8$}} %\put(1127,-6){\sx{2.8}{$9$}} \put(1020,-6){\sx{2.8}{$x$}} % \put(116,534){\rot{76}\sx{2.5}{$u\!=\!-8$}\ero} \put(170,544){\rot{90}\sx{2.5}{$u\!=\!8$}\ero} % \put(212,542){\rot{80}\sx{2.5}{$v\!=\!8$}\ero} \put(262,538){\rot{92}\sx{2.5}{$v\!=\!-8$}\ero} % \put(250,230){\rot{47}\sx{2.5}{$u\!=\!1$}\ero} % \put(400,134){\rot{62}\sx{2.5}{$u\!=\!0.1$}\ero} \put(402,114){\rot{27}\sx{2.5}{$u\!=\!-0.1$}\ero} % \put(480,431){\rot{0}\sx{2.6}{$v\!=\!2$}\ero} \put(490,400){\rot{0}\sx{2.6}{$v\!=\!1$}\ero} \put(498,329){\rot{0}\sx{2.6}{$v\!=\!0.2$}\ero} \put(514,296){\rot{0}\sx{2.6}{$v\!=\!0.1$}\ero} % \put(564,419){\rot{0}\sx{2.6}{$u\!=\!1$}\ero} % \put(468,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero} \put(518,213){\rot{0}\sx{2.6}{$v\!=\!0$}\ero} \put(518,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero} \put(600,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero} \put(656,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero} \put(730,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero} \put(790,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero} \put(862,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero} \put(922,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero} \put(992,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero} %\put(1054,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero} %\put(1124,186){\rot{90}\sx{2.7}{$u\!=\!0$}\ero} %\put(1186,186){\rot{90}\sx{2.7}{$v\!=\!0$}\ero} \end{picture} \end{document} %