File:SuperFacZoomT.png

Zoom-in of the central part of the complex map of the SuperFactorial function.

$u\!+\!\mathrm i = \mathrm{SuperFactorial}(x\!+\!\mathrm i y))$

C++ generator of curves
// Files fac.cin, facp.cin, afacc.cin, suerfactorial.cin, ado.cin and conto.cin shoulr be loaded to the working directory in order to compile the C++ code below.

using namespace std; typedef complex z_type; //#include "sinc.cin"
 * 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 "fac.cin"
 * 1) include "facp.cin"
 * 2) include "afacc.cin"
 * 3) include "superfactorial.cin"
 * 4) include "conto.cin"

main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; int M=551,M1=M+1; int N=221,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("SuperFacZoom.eps","w");ado(o,552,222); fprintf(o,"1 1 translate\n 100 100 scale\n"); DO(m,M1)X[m]=.01*(m-.5); DO(n,N1)Y[n]=.01*(n-.5); for(m=0;m<6;m++){M(m,0)L(m,2)} for(n=0;n<3;n++){M( 0,n)L(5,n)} fprintf(o,".004 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=afacc(z); //    c=fac(z); c=superfac(z); //    p=abs(c-d)/(abs(c)+abs(d));  p=-log(p)/log(10.)-1.; p=Re(c);q=Im(c); if(p>-20 && p<20 && //      (fabs(y)>.034 ||x>-.9 ||fabs(x-int(x))>1.e-3) &&           q>-20 && q<20 && fabs(q)> 1.e-16        ) {g[m*N1+n]=p;f[m*N1+n]=q;} }} //fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=1.8;q=.7; fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.4;q=.8; for(m=-4;m<4;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".004 W 0 .5 0 RGB S\n"); for(m=0;m<4;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".004 W .8 0 0 RGB S\n"); for(m=0;m<4;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".004 W 0 0 .8 RGB S\n"); for(m=1;m<15;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".01 W .8 0 0 RGB S\n"); for(m=1;m<15;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".01 W 0 0 .8 RGB S\n"); conto(o,f,w,v,X,Y,M,N, (0. ),-9,9); fprintf(o,".01 W .5 0 .5 RGB S\n"); for(m=-14;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".01 W 0 0 0 RGB S\n"); m=0;    conto(o,g,w,v,X,Y,M,N, (0.+m),-9,9); fprintf(o,".01 W 0 0 0 RGB S\n"); for(m=1;m<17;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".01 W 0 0 0 RGB S\n"); //#include"plofu.cin" // x=0.8856031944; conto(o,g,w,v,X,Y,M,N,0.8856031944,-p,p); fprintf(o,".004 W .2 .2 0 RGB S\n"); /* M(x,-8)L(x,8) fprintf(o,"0 setlinejoin 0 setlinecap 0.004 W 0 0 0 RGB S\n"); M(x,0)L(-8.1,0) fprintf(o,"                  .05 W  1 1 1 RGB S\n"); DO(m,23){ M(x-.4*m,0)L(x-.4*(m+.5),0);} fprintf(o,".09 W .3 .3 0 RGB S\n"); //M(x,0)L(-8.1,0) fprintf(o,"[.19 .21]0 setdash .05 W 0 0 0 RGB S\n"); // May it be, that, some printers do not interpret well the dashing ? */ fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); system("epstopdf SuperFacZoom.eps"); system(   "open SuperFacZoom.pdf");    //for LINUX //    getchar; system("killall Preview");//for mac }

Latex generator of labels
% file SuperFacZoom.pdf should be generated with the code above in order to compile the Latex document below. % % Gerenator of SuperFacMapT.png % % Copyleft 2012 by Dmitrii Kouznetsov % \documentclass[12pt]{article} % \usepackage{geometry} % \usepackage{graphicx} % \usepackage{rotating} % % \paperwidth 340pt % % \paperheight 336pt % \paperwidth 1110pt % \paperheight 448pt % %\topmargin -96pt % %\oddsidemargin -98pt % \topmargin -101pt % \oddsidemargin -80pt % \textwidth 1100pt % \textheight 1100pt % \pagestyle {empty} % \newcommand \sx {\scalebox} % \newcommand \rot {\begin{rotate}} % \newcommand \ero {\end{rotate}} % \newcommand \ing {\includegraphics} % \parindent 0pt \pagestyle{empty} \begin{document}% \sx{2}{ \begin{picture}(362,220) % \put(0,0){\ing{SuperFacZoom}} % \put(4,216){\sx{1.8}{$y$}} % \put(4,194){\sx{1.8}{$2$}} % \put(4,095){\sx{1.8}{$1$}} % \put(097,3){\sx{1.8}{$1$}} % \put(197,3){\sx{1.8}{$2$}} % \put(297,3){\sx{1.8}{$3$}} % \put(397,3){\sx{1.8}{$4$}} % \put(497,3){\sx{1.8}{$5$}} % \put(540,3){\sx{1.8}{$x$}} %

\put(360,210){\sx{1.2}{$u\!=\!0.8856031944$}} % %\put(316,178){\sx{1.3}{$u\!=\!0.8$}} % \put(311,198){\sx{1.3}{\rot{-51}$u\!=\!0.8$\ero}} % \put(146,159){\sx{2}{ \rot{62}$u\!=\!1$\ero }} % \put(172,117){\sx{2}{ \rot{1}$u\!=\!0$\ero }} % \put(020,163){\sx{2}{ \rot{-37}$u\!=\!2$\ero }} % \put(018,053){\sx{2}{ \rot{ 22}$u\!=\!3$\ero }} % \put(051,06){\sx{2}{ \rot{ 53}$u\!=\!4$\ero }} % % \put(082,183){\sx{2}{ \rot{2}$v\!=\!1$\ero }} % \put(081,083){\sx{2}{ \rot{46}$v\!=\!2$\ero }} % \put(306,148){\sx{2}{ \rot{0.}$v\!=\!0$\ero }} % \put(406,148){\sx{2}{ \rot{0.}$v\!=\!0$\ero }} % \end{picture} % } % \end{document} % %

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