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.

#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 "fac.cin"
//#include "sinc.cin"
#include "facp.cin"
#include "afacc.cin"
#include "superfactorial.cin"
#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 %<br> % Copyleft 2012 by Dmitrii Kouznetsov %<br> \documentclass[12pt]{article} %<br> \usepackage{geometry} %<br> \usepackage{graphicx} %<br> \usepackage{rotating} %<br> % \paperwidth 340pt %<br> % \paperheight 336pt %<br> \paperwidth 1110pt %<br> \paperheight 448pt %<br> %\topmargin -96pt %<br> %\oddsidemargin -98pt %<br> \topmargin -101pt %<br> \oddsidemargin -80pt %<br> \textwidth 1100pt %<br> \textheight 1100pt %<br> \pagestyle {empty} %<br> \newcommand \sx {\scalebox} %<br> \newcommand \rot {\begin{rotate}} %<br> \newcommand \ero {\end{rotate}} %<br> \newcommand \ing {\includegraphics} %<br> \parindent 0pt \pagestyle{empty} \begin{document}%<br> \sx{2}{ \begin{picture}(362,220) %<br> \put(0,0){\ing{SuperFacZoom}} %<br> \put(4,216){\sx{1.8}{$y$}} %<br> \put(4,194){\sx{1.8}{$2$}} %<br> \put(4,095){\sx{1.8}{$1$}} %<br> \put(097,3){\sx{1.8}{$1$}} %<br> \put(197,3){\sx{1.8}{$2$}} %<br> \put(297,3){\sx{1.8}{$3$}} %<br> \put(397,3){\sx{1.8}{$4$}} %<br> \put(497,3){\sx{1.8}{$5$}} %<br> \put(540,3){\sx{1.8}{$x$}} %<br> \put(360,210){\sx{1.2}{$u\!=\!0.8856031944$}} %<br> %\put(316,178){\sx{1.3}{$u\!=\!0.8$}} %<br> \put(311,198){\sx{1.3}{\rot{-51}$u\!=\!0.8$\ero}} %<br> \put(146,159){\sx{2}{ \rot{62}$u\!=\!1$\ero }} %<br> \put(172,117){\sx{2}{ \rot{1}$u\!=\!0$\ero }} %<br> \put(020,163){\sx{2}{ \rot{-37}$u\!=\!2$\ero }} %<br> \put(018,053){\sx{2}{ \rot{ 22}$u\!=\!3$\ero }} %<br> \put(051,06){\sx{2}{ \rot{ 53}$u\!=\!4$\ero }} %<br> %<br> \put(082,183){\sx{2}{ \rot{2}$v\!=\!1$\ero }} %<br> \put(081,083){\sx{2}{ \rot{46}$v\!=\!2$\ero }} %<br> \put(306,148){\sx{2}{ \rot{0.}$v\!=\!0$\ero }} %<br> \put(406,148){\sx{2}{ \rot{0.}$v\!=\!0$\ero }} %<br> \end{picture} %<br> } %<br> \end{document} %<br> %

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