File:Superfactocomple1.png

Complex map of $f=$SuperFactorial($x\!+\!\mathrm i y$) in the $x,y$ plane.

Levels $u\!=\!\Re(f)=$constant and $u\!=\!\Im(f)=$constant are drawn. Thick lines correspond to the integer values.

C++ generator of curves
Sorry, have misplaced the original generator. I load the code that does almost the same picture.

Files SuperFactorial.cin ado.cin conto.cin should be loaded to the working directory in order to compile the [C++]] code below: // using namespace std; typedef std::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"

int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; int M=403,M1=M+1; int N=401,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("fig2b.eps","w");ado(o,402,402); FILE *o;o=fopen("SuperFacMap.eps","w");ado(o,402,402); fprintf(o,"201 201 translate\n 20 20 scale\n"); // DO(m,M1)X[m]=-8.04+.04*(m+.5); DO(m,M1){t=-1.+.022*m; X[m]=.2+t-1.11*exp(-1.9*t);}

// DO(n,N1)Y[n]=-8.04+.04*(n+.5); DO(n,N1){t=-8.04+.04*(n+.5); t*=.97; Y[n]=t-.25*sin(0.6127874523307*t);}

for(m=-8;m<9;m++){if(m==0){M(m,-8.5)L(m,8.5)} else{M(m,-8)L(m,8)}} for(n=-8;n<9;n++){    M(  -8,n)L(8,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=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,".01 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,".01 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,".01 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,".04 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,".04 W 0 0 .8 RGB S\n"); conto(o,f,w,v,X,Y,M,N, (0. ),-9,9); fprintf(o,".04 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,".04 W 0 0 0 RGB S\n"); m=0;    conto(o,g,w,v,X,Y,M,N, (0.+m),-9,9); fprintf(o,".04 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,".04 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 SuperFacMap.eps"); system(   "open SuperFacMap.pdf");     //for LINUX //    getchar; system("killall Preview");//for mac }

generator of labels
\documentclass[12pt]{article} \paperwidth 342pt \paperheight 338pt \textwidth 500pt \textheight 500pt \topmargin -106pt \oddsidemargin -96pt \parindent 0pt \pagestyle{empty} \usepackage {graphics} \usepackage{rotating} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \ing {\includegraphics} \newcommand \sx {\scalebox} \begin{document} %\begin{picture}(1006,1006) \put(0,0){\ing{facit}} \begin{picture}(362,362) \put(0,0){\ing{SuperFacMap}} \put(30,357){\sx{1.3}{$y$}} \put(30,317){\sx{1.3}{$6$}} \put(30,277){\sx{1.3}{$4$}} \put(30,237){\sx{1.3}{$2$}} \put(29,196){\sx{1.3}{$0$}} \put(20,156){\sx{1.3}{$-2$}} \put(20,116){\sx{1.3}{$-4$}} \put(20,76){\sx{1.3}{$-6$}} \put(20,36){\sx{1.3}{$-8$}} \put(70,29){\sx{1.3}{$-6$}} \put(110,29){\sx{1.3}{$-4$}} \put(150,29){\sx{1.3}{$-2$}} \put(198,29){\sx{1.3}{$0$}} \put(238,29){\sx{1.3}{$2$}} \put(278,29){\sx{1.3}{$4$}} \put(318,29){\sx{1.3}{$6$}} \put(354,29){\sx{1.3}{$x$}} \put(50,344){\sx{1.3}{$u\!=\!2$}} \put(50,306){\sx{1.3}{$v\!=\!0$}} \put(50,255){\sx{1.3}{$u\!=\!2$}} \put(50,204){\sx{1.3}{$v\!=\!0$}} %central \put(50,152){\sx{1.3}{$u\!=\!2$}} \put(50,100){\sx{1.3}{$v\!=\!0$}} \put(50,049){\sx{1.3}{$u\!=\!2$}} % column \put(122,342){\sx{1.2}{$v\!=\!-0.2$}} \put(135,314){\sx{1.2}{$u\!=\!1.8$}} \put(252,314){\sx{1.2}{$u\!=\!1.2$}} \put(136,265){\sx{1.2}{$v\!=\!0.2$}} \put(125,210){\sx{1.2}{$u\!=\!2.2$}} \put(125,130){\sx{1.2}{$v\!=\!-0.2$}} \put(134,084){\sx{1.2}{$u\!=\!1.8$}} \put(252,084){\sx{1.2}{$u\!=\!1.2$}} \put(134,054){\sx{1.2}{$v\!=\!0.2$}} % column \put(322,343){\sx{1.3}{$u\!=\!1$}} \put(322,306){\sx{1.3}{$v\!=\!0$}} \put(322,269){\sx{1.3}{$u\!=\!1$}} \put(266,247){$u\!=\!0.8856031944$} \put(332,231){\sx{1.3}{$v\!=\!0$}} %central \put(329,164){\sx{1.3}{$v\!=\!0$}} %central \put(322,137){\sx{1.3}{$u\!=\!1$}} \put(322,100){\sx{1.3}{$v\!=\!0$}} \put(322, 50){\sx{1.3}{$u\!=\!1$}} \end{picture} \end{document}