Difference between revisions of "File:FacitT.jpg"

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(Iterates of Factorial: $y=\mathrm{Factorial}^n(x)$ versus $x$ for various $n$. ==C++ generator of curves== ==Latex generator of labels== Category:Factorial Category:Iterate Category:Superfactorial [[Category:AbelFactoria...)
 
(C++)
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==[[C++]] generator of curves==
  
==[[C++]] generator of curves==
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// Do not forget to load all the *.cin mentioned below in the end of the first paragraph of the code!
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<poem><nomathjax><nowiki>
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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 "facp.cin"
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#include "afacc.cin"
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#include "superfac.cin"
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#include "abelfac.cin"
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#include "ado.cin"
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int main(){ int m,n; DB x,y, p,q, t; z_type z,c,d;
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#define M(x,y) fprintf(o,"%5.3f %5.3f M\n",0.+x,0.+y);
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#define L(x,y) fprintf(o,"%5.3f %5.3f L\n",0.+x,0.+y);
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FILE *o;o=fopen("facit.eps","w");ado(o,1002,1002);
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fprintf(o,"1 1 translate\n 100 100 scale\n");
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fprintf(o,"1 setlinejoin 2 setlinecap\n");
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DO(m,11){M(m,0)L(m,10)}
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DO(n,11){M(0,n)L(10, n)}
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fprintf(o,".01 W S\n");
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DO(n,2001){x=.004*n; z=x; c=fac(z); y=Re(c); if(y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W 0 .9 0 RGB S\n");
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DO(n,2001){x=.002*n; z=x; c=fac(fac(z)); y=Re(c); if(y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W 0 .9 0 RGB S\n");
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DO(n,2001){x=.002*n; z=x; c=fac(fac(fac(z))); y=Re(c); if(y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W 0 .9 0 RGB S\n");
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M(0,1)L(2,1)L(2,10)fprintf(o,".03 W 0 .8 0 RGB S\n");
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DO(n,1001){x=.88+.01*n;z=x; c=afacc(z); y=Re(c); if(x>10.02||y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W .9 0 .9 RGB S\n");
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DO(n,1001){x=.95+.01*n;z=x; c=afacc(afacc(z)); y=Re(c); if(x>10.02||y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W .9 0 .9 RGB S\n");
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DO(n,1001){x=.98+.01*n;z=x; c=afacc(afacc(afacc(z))); y=Re(c); if(x>10.02||y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W .9 0 .9 RGB S\n");
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M(1,.48)L(1,2)L(10,2) fprintf(o,".03 W .9 0 .9 RGB S\n");
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DO(m,41){ t=-2.+.1*m;
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M(1,1);DO(n,1901){x=1.0005+.005*n; c=abelfac(x); c=superfac(t+c); y=Re(c);if(y>10.06) break; L(x,y);}fprintf(o,".012 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 facit.eps");
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system( "open facit.pdf"); // macintosh
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getchar(); system("killall Preview"); // macintosh
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}
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</nowiki></nomathjax></poem>
   
 
==[[Latex]] generator of labels==
  
==[[Latex]] generator of labels==
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<poem><nomathjax><nowiki>
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</nowiki></nomathjax></poem>
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[[Category:Factorial]]
  
[[Category:Factorial]]

Revision as of 20:21, 26 September 2013

Iterates of Factorial:

$y=\mathrm{Factorial}^n(x)$ versus $x$ for various $n$.

C++ generator of curves

// Do not forget to load all the *.cin mentioned below in the end of the first paragraph of the code!


#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 "facp.cin"
#include "afacc.cin"
#include "superfac.cin"
#include "abelfac.cin"
#include "ado.cin"

int main(){ int m,n; DB x,y, p,q, t; z_type z,c,d;
#define M(x,y) fprintf(o,"%5.3f %5.3f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%5.3f %5.3f L\n",0.+x,0.+y);
FILE *o;o=fopen("facit.eps","w");ado(o,1002,1002);
fprintf(o,"1 1 translate\n 100 100 scale\n");
fprintf(o,"1 setlinejoin 2 setlinecap\n");

DO(m,11){M(m,0)L(m,10)}
DO(n,11){M(0,n)L(10, n)}
fprintf(o,".01 W S\n");

DO(n,2001){x=.004*n; z=x; c=fac(z); y=Re(c); if(y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W 0 .9 0 RGB S\n");
DO(n,2001){x=.002*n; z=x; c=fac(fac(z)); y=Re(c); if(y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W 0 .9 0 RGB S\n");
DO(n,2001){x=.002*n; z=x; c=fac(fac(fac(z))); y=Re(c); if(y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W 0 .9 0 RGB S\n");
M(0,1)L(2,1)L(2,10)fprintf(o,".03 W 0 .8 0 RGB S\n");
DO(n,1001){x=.88+.01*n;z=x; c=afacc(z); y=Re(c); if(x>10.02||y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W .9 0 .9 RGB S\n");
DO(n,1001){x=.95+.01*n;z=x; c=afacc(afacc(z)); y=Re(c); if(x>10.02||y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W .9 0 .9 RGB S\n");
DO(n,1001){x=.98+.01*n;z=x; c=afacc(afacc(afacc(z))); y=Re(c); if(x>10.02||y>10.06) break; if(n==0)M(x,y) else L(x,y);} fprintf(o,".05 W .9 0 .9 RGB S\n");
M(1,.48)L(1,2)L(10,2) fprintf(o,".03 W .9 0 .9 RGB S\n");

DO(m,41){ t=-2.+.1*m;
M(1,1);DO(n,1901){x=1.0005+.005*n; c=abelfac(x); c=superfac(t+c); y=Re(c);if(y>10.06) break; L(x,y);}fprintf(o,".012 W 0 0 0 RGB S\n");}

fprintf(o,"showpage\n\%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf facit.eps");
        system( "open facit.pdf"); // macintosh
        getchar(); system("killall Preview"); // macintosh
}

Latex generator of labels

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current20:14, 26 September 2013Thumbnail for version as of 20:14, 26 September 20132,092 × 2,092 (891 KB)T (talk | contribs)Iterates of Factorial: $y=\mathrm{Factorial}^n(x)$ versus $x$ for various $n$. ==C++ generator of curves== ==Latex generator of labels== Category:Factorial Category:Iterate Category:Superfactorial [[Category:AbelFactoria...
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