Difference between revisions of "File:QfacMapT500a.jpg"

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([[Complex map of function square root of factorial, or $\sqrt{!}$, or halfiteration of factorial $h=\mathrm{Factorial}^{1/2}$ is such function that $ h(h(z)) = z!$ in wide range of values of $z$. Levels $u=\Re(h(z))=\rm const$ and Leve...)
 
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==C++ generator of curves==
  
==C++ generator of curves==
  +
<poem>
  +
#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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using namespace std;
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#include <complex>
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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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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 "facp.cin"
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#include "afacc.cin"
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#include "superfac.cin"
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#include "arcsuperfac.cin"
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//#include "superex.cin"
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//#include "superlo.cin"
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DB xL=0.31813150520476413;
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DB yL=1.3372357014306895;
  +
  +
#include "conto.cin"
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  +
int main(){ int j,k,m,n,n1; DB x,y, p,q, t; z_type z,c,d;
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int M=400,M1=M+1;
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int N=401,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("qfacMap.eps","w");ado(o,402,402);
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fprintf(o,"201 201 translate\n 20 20 scale\n");
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DO(m,M1) X[m]=-8.+.04*m;
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DO(n,N1){ y=-8.+.04*n; if(y<-.011) Y[n]=y; else break;}
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Y[n]= -.01; n++;
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Y[n]= +.01; n++;
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for(j=n;j<N1;j++){y=-8.+.04*(j-1); Y[j]=y;}
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for(m=-8;m<9;m++){if(m==0){M(m,-8.5)L(m,8.5)} else{M(m,-8)L(m,8)}}
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for(n=-8;n<9;n++){ M( -8,n)L(8,n)}
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fprintf(o,".008 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(c);
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c=arcsuperfac(z);
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c=superfac(.5+c);
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// c=FSLOG(z);
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// c=FSEXP(.5+c);
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// d=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>-999 && p<999) g[m*N1+n]=p;
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if(q>-999 && q<999 && fabs(q)> 1.e-14) f[m*N1+n]=q;
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}}
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fprintf(o,"1 setlinejoin 1 setlinecap\n"); //p=6.;q=6.;
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//#include"plofu.cin"
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p=1;q=.5;
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for(m=-2;m<2;m++) for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M-20,N,(m+.1*n),-q, q); fprintf(o,".02 W 0 .6 0 RGB S\n");
  +
for(m= 0;m<2;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M-20,N,-(m+.1*n),-q, q); fprintf(o,".02 W .9 0 0 RGB S\n");
  +
for(m= 0;m<2;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M-20,N, (m+.1*n),-q, q); fprintf(o,".02 W 0 0 .9 RGB S\n");
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for(m=1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".04 W .9 0 0 RGB S\n");
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for(m=1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 .9 RGB S\n");
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conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".04 W .6 0 .6 RGB S\n");
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for(m=-4;m<5;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 0 RGB S\n");
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fprintf(o,"0 setlinejoin 0 setlinecap\n");
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x=.85;
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M(x,0)L(-8.1,0) fprintf(o,".07 W 1 1 1 RGB S\n");
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DO(m,22){ M(x-.4*m,0) L(x-.4*(m+.5),0) } fprintf(o,".1 W 0 0 0 RGB S\n");
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fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
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system("epstopdf qfacMap.eps");
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system( "open qfacMap.pdf"); // for mac
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// getchar(); system("killall Preview"); //for macintosh
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//return 0;
  +
}
  +
</poem>
   
 
==Latex generator of labels==
  
==Latex generator of labels==

Revision as of 16:36, 11 July 2013

[[Complex map of function square root of factorial, or $\sqrt{!}$, or halfiteration of factorial

$h=\mathrm{Factorial}^{1/2}$

is such function that $ h(h(z)) = z!$ in wide range of values of $z$.

Levels $u=\Re(h(z))=\rm const$ and Levels $u=\Im(h(z))=\rm const$ are shown in the plane $z=x+\mathrm i y$.

C++ generator of curves

 #include <math.h>
 #include <stdio.h>
 #include <stdlib.h>
 using namespace std;
 #include <complex>
 #define DB double
 #define DO(x,y) for(x=0;x<y;x++)
 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 "facp.cin"
 #include "afacc.cin"
 #include "superfac.cin"
 #include "arcsuperfac.cin"
 //#include "superex.cin"
 //#include "superlo.cin"
 DB xL=0.31813150520476413;
 DB yL=1.3372357014306895;

 #include "conto.cin"

 int main(){ int j,k,m,n,n1; DB x,y, p,q, t; z_type z,c,d;
 int M=400,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("qfacMap.eps","w");ado(o,402,402);
 fprintf(o,"201 201 translate\n 20 20 scale\n");
 DO(m,M1) X[m]=-8.+.04*m;
 DO(n,N1){ y=-8.+.04*n; if(y<-.011) Y[n]=y; else break;}
        Y[n]= -.01; n++;
        Y[n]= +.01; n++;
 for(j=n;j<N1;j++){y=-8.+.04*(j-1); Y[j]=y;}
 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(c);
        c=arcsuperfac(z);
        c=superfac(.5+c);
 // c=FSLOG(z);
 // c=FSEXP(.5+c);
 // d=z;
 // p=abs(c-d)/(abs(c)+abs(d)); p=-log(p)/log(10.)-1.;
        p=Re(c);q=Im(c);
        if(p>-999 && p<999) g[m*N1+n]=p;
        if(q>-999 && q<999 && fabs(q)> 1.e-14) f[m*N1+n]=q;
                        }}
 fprintf(o,"1 setlinejoin 1 setlinecap\n"); //p=6.;q=6.;
 //#include"plofu.cin"
 p=1;q=.5;
 for(m=-2;m<2;m++) for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M-20,N,(m+.1*n),-q, q); fprintf(o,".02 W 0 .6 0 RGB S\n");
 for(m= 0;m<2;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M-20,N,-(m+.1*n),-q, q); fprintf(o,".02 W .9 0 0 RGB S\n");
 for(m= 0;m<2;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M-20,N, (m+.1*n),-q, q); fprintf(o,".02 W 0 0 .9 RGB S\n");
 for(m=1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".04 W .9 0 0 RGB S\n");
 for(m=1;m<5;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 .9 RGB S\n");
                  conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".04 W .6 0 .6 RGB S\n");
 for(m=-4;m<5;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".04 W 0 0 0 RGB S\n");
 fprintf(o,"0 setlinejoin 0 setlinecap\n");
 x=.85;
 M(x,0)L(-8.1,0) fprintf(o,".07 W 1 1 1 RGB S\n");
 DO(m,22){ M(x-.4*m,0) L(x-.4*(m+.5),0) } fprintf(o,".1 W 0 0 0 RGB S\n");
 fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf qfacMap.eps");
        system( "open qfacMap.pdf"); // for mac
 // getchar(); system("killall Preview"); //for macintosh
 //return 0;
 }

Latex generator of labels

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