File:Sfaczoo300.png
Original file (1,142 × 453 pixels, file size: 302 KB, MIME type: image/png)
Zoom-in of the complex map of SuperFactorial
Copyleft 1011 by Dmitrii Kouznetsov
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:
#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
}
References
http://www.springerlink.com/content/qt31671237421111/fulltext.pdf?page=1
http://mizugadro.mydns.jp/PAPERS/2010superfae.pdf reprint, English version
http://mizugadro.mydns.jp/PAPERS/2010superfar.pdf reprint, Russian version
D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12. (Russian version: p.8-14)
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 17:50, 20 June 2013 | 1,142 × 453 (302 KB) | Maintenance script (talk | contribs) | Importing image file |
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