Difference between revisions of "File:Sfaczoo300.png"

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{{oq|Sfaczoo300.png|Original file ‎(1,142 × 453 pixels, file size: 302 KB, MIME type: image/png)}}
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Importing image file
  
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Zoom-in of the [[complex map]] of [[SuperFactorial]]
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Copyleft 1011 by Dmitrii Kouznetsov
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==C++ generator of curves==
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Sorry, have misplaced the original generator. I load the code that does almost the same picture.
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Files
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[[SuperFactorial.cin]]
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[[ado.cin]]
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[[conto.cin]]
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should be loaded to the working directory in order to compile the [[C++]] code below:
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<pre>
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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#define DB double
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#define DO(x,y) for(x=0;x<y;x++)
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using namespace std;
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#include <complex>
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typedef complex<double> z_type;
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#define Re(x) x.real()
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#define Im(x) x.imag()
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#define I z_type(0.,1.)
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#include "fac.cin"
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//#include "sinc.cin"
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#include "facp.cin"
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#include "afacc.cin"
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#include "superfactorial.cin"
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#include "conto.cin"
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main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
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int M=551,M1=M+1;
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int N=221,N1=N+1;
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DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
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char v[M1*N1]; // v is working array
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FILE *o;o=fopen("SuperFacZoom.eps","w");ado(o,552,222);
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fprintf(o,"1 1 translate\n 100 100 scale\n");
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DO(m,M1)X[m]=.01*(m-.5);
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DO(n,N1)Y[n]=.01*(n-.5);
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for(m=0;m<6;m++){M(m,0)L(m,2)}
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for(n=0;n<3;n++){M( 0,n)L(5,n)}
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fprintf(o,".004 W 0 0 0 RGB S\n");
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DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
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DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
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DO(n,N1){y=Y[n]; z=z_type(x,y);
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// c=afacc(z);
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// c=fac(z);
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c=superfac(z);
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// p=abs(c-d)/(abs(c)+abs(d)); p=-log(p)/log(10.)-1.;
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p=Re(c);q=Im(c);
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if(p>-20 && p<20 &&
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// (fabs(y)>.034 ||x>-.9 ||fabs(x-int(x))>1.e-3) &&
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q>-20 && q<20 && fabs(q)> 1.e-16
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)
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{g[m*N1+n]=p;f[m*N1+n]=q;}
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}}
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//fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=1.8;q=.7;
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fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=1.4;q=.8;
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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");
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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");
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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");
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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");
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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");
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conto(o,f,w,v,X,Y,M,N, (0. ),-9,9); fprintf(o,".01 W .5 0 .5 RGB S\n");
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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");
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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");
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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");
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//#include"plofu.cin"
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// x=0.8856031944;
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conto(o,g,w,v,X,Y,M,N,0.8856031944,-p,p); fprintf(o,".004 W .2 .2 0 RGB S\n");
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/*
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M(x,-8)L(x,8) fprintf(o,"0 setlinejoin 0 setlinecap 0.004 W 0 0 0 RGB S\n");
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M(x,0)L(-8.1,0) fprintf(o," .05 W 1 1 1 RGB S\n");
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DO(m,23){ M(x-.4*m,0)L(x-.4*(m+.5),0);} fprintf(o,".09 W .3 .3 0 RGB S\n");
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//M(x,0)L(-8.1,0) fprintf(o,"[.19 .21]0 setdash .05 W 0 0 0 RGB S\n");
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// May it be, that, some printers do not interpret well the dashing ?
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*/
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fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
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system("epstopdf SuperFacZoom.eps");
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system( "open SuperFacZoom.pdf"); //for LINUX
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// getchar(); system("killall Preview");//for mac
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}
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</pre>
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==Generator of labels==
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Sorry, the generator of labels is lost
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==References==
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{{ref}}
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http://www.springerlink.com/content/qt31671237421111/fulltext.pdf?page=1<br>
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http://mizugadro.mydns.jp/PAPERS/2010superfae.pdf reprint, English version<br>
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http://mizugadro.mydns.jp/PAPERS/2010superfar.pdf reprint, Russian version<br>
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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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{{fer}}
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==Keywords==
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«[[SuFac]]»,
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«[[SuperFactorial]]»,
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«[[]]»,
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[[Category:Book]]
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[[Category:BookMap]]
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[[Category:C++]]
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[[Category:SuFac]]
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[[Category:SuperFactorial]]
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[[Category:Complex maps]]
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[[Category:SuperFunctions]]

Latest revision as of 00:12, 29 February 2024


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
 }

Generator of labels

Sorry, the generator of labels is lost

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)

Keywords

«SuFac», «SuperFactorial», «[[]]»,

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