Difference between revisions of "File:SuperFacZoomT.png"
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+ | Zoom-in of the central part of the [[complex map]] of the [[SuperFactorial]] function. |
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− | Importing image file |
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+ | |||
+ | $u\!+\!\mathrm i = \mathrm{SuperFactorial}(x\!+\!\mathrm i y))$ |
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+ | |||
+ | ==[[C++]] generator of curves== |
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+ | |||
+ | // Files [[fac.cin]], [[facp.cin]], [[afacc.cin]], [[suerfactorial.cin]], [[ado.cin]] and [[conto.cin]] shoulr be loaded to the working directory in order to compile the [[C++]] code below. |
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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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+ | |||
+ | |||
+ | ==[[Latex]] generator of labels== |
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+ | |||
+ | % file [[SuperFacZoom.pdf]] should be generated with the code above in order to compile the [[Latex]] document below. |
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+ | %<nowiki> |
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+ | % Gerenator of SuperFacMapT.png %<br> |
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+ | % Copyleft 2012 by Dmitrii Kouznetsov %<br> |
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+ | \documentclass[12pt]{article} %<br> |
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+ | \usepackage{geometry} %<br> |
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+ | \usepackage{graphicx} %<br> |
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+ | \usepackage{rotating} %<br> |
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+ | % \paperwidth 340pt %<br> |
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+ | % \paperheight 336pt %<br> |
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+ | \paperwidth 1110pt %<br> |
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+ | \paperheight 448pt %<br> |
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+ | %\topmargin -96pt %<br> |
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+ | %\oddsidemargin -98pt %<br> |
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+ | \topmargin -101pt %<br> |
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+ | \oddsidemargin -80pt %<br> |
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+ | \textwidth 1100pt %<br> |
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+ | \textheight 1100pt %<br> |
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+ | \pagestyle {empty} %<br> |
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+ | \newcommand \sx {\scalebox} %<br> |
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+ | \newcommand \rot {\begin{rotate}} %<br> |
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+ | \newcommand \ero {\end{rotate}} %<br> |
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+ | \newcommand \ing {\includegraphics} %<br> |
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+ | \parindent 0pt |
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+ | \pagestyle{empty} |
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+ | \begin{document}%<br> |
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+ | \sx{2}{ \begin{picture}(362,220) %<br> |
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+ | \put(0,0){\ing{SuperFacZoom}} %<br> |
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+ | |||
+ | \put(4,216){\sx{1.8}{$y$}} %<br> |
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+ | \put(4,194){\sx{1.8}{$2$}} %<br> |
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+ | \put(4,095){\sx{1.8}{$1$}} %<br> |
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+ | \put(097,3){\sx{1.8}{$1$}} %<br> |
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+ | \put(197,3){\sx{1.8}{$2$}} %<br> |
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+ | \put(297,3){\sx{1.8}{$3$}} %<br> |
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+ | \put(397,3){\sx{1.8}{$4$}} %<br> |
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+ | \put(497,3){\sx{1.8}{$5$}} %<br> |
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+ | \put(540,3){\sx{1.8}{$x$}} %<br> |
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+ | |||
+ | \put(360,210){\sx{1.2}{$u\!=\!0.8856031944$}} %<br> |
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+ | %\put(316,178){\sx{1.3}{$u\!=\!0.8$}} %<br> |
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+ | \put(311,198){\sx{1.3}{\rot{-51}$u\!=\!0.8$\ero}} %<br> |
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+ | \put(146,159){\sx{2}{ \rot{62}$u\!=\!1$\ero }} %<br> |
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+ | \put(172,117){\sx{2}{ \rot{1}$u\!=\!0$\ero }} %<br> |
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+ | \put(020,163){\sx{2}{ \rot{-37}$u\!=\!2$\ero }} %<br> |
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+ | \put(018,053){\sx{2}{ \rot{ 22}$u\!=\!3$\ero }} %<br> |
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+ | \put(051,06){\sx{2}{ \rot{ 53}$u\!=\!4$\ero }} %<br> |
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+ | %<br> |
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+ | \put(082,183){\sx{2}{ \rot{2}$v\!=\!1$\ero }} %<br> |
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+ | \put(081,083){\sx{2}{ \rot{46}$v\!=\!2$\ero }} %<br> |
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+ | \put(306,148){\sx{2}{ \rot{0.}$v\!=\!0$\ero }} %<br> |
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+ | \put(406,148){\sx{2}{ \rot{0.}$v\!=\!0$\ero }} %<br> |
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+ | \end{picture} %<br> |
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+ | } %<br> |
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+ | \end{document} %<br> |
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+ | %</nowiki> |
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+ | |||
+ | % [[Category:SuperFactorial]] |
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+ | % [[Category:Superfunction]] |
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+ | % [[Category:Complex map]] |
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+ | % [[Category:C++]] |
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+ | %[[Category:Latex]] |
Latest revision as of 09:43, 21 June 2013
Zoom-in of the central part of the complex map of the SuperFactorial function.
$u\!+\!\mathrm i = \mathrm{SuperFactorial}(x\!+\!\mathrm i y))$
C++ generator of curves
// Files fac.cin, facp.cin, afacc.cin, suerfactorial.cin, ado.cin and conto.cin shoulr 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 }
Latex generator of labels
% file SuperFacZoom.pdf should be generated with the code above in order to compile the Latex document below. % % Gerenator of SuperFacMapT.png %<br> % Copyleft 2012 by Dmitrii Kouznetsov %<br> \documentclass[12pt]{article} %<br> \usepackage{geometry} %<br> \usepackage{graphicx} %<br> \usepackage{rotating} %<br> % \paperwidth 340pt %<br> % \paperheight 336pt %<br> \paperwidth 1110pt %<br> \paperheight 448pt %<br> %\topmargin -96pt %<br> %\oddsidemargin -98pt %<br> \topmargin -101pt %<br> \oddsidemargin -80pt %<br> \textwidth 1100pt %<br> \textheight 1100pt %<br> \pagestyle {empty} %<br> \newcommand \sx {\scalebox} %<br> \newcommand \rot {\begin{rotate}} %<br> \newcommand \ero {\end{rotate}} %<br> \newcommand \ing {\includegraphics} %<br> \parindent 0pt \pagestyle{empty} \begin{document}%<br> \sx{2}{ \begin{picture}(362,220) %<br> \put(0,0){\ing{SuperFacZoom}} %<br> \put(4,216){\sx{1.8}{$y$}} %<br> \put(4,194){\sx{1.8}{$2$}} %<br> \put(4,095){\sx{1.8}{$1$}} %<br> \put(097,3){\sx{1.8}{$1$}} %<br> \put(197,3){\sx{1.8}{$2$}} %<br> \put(297,3){\sx{1.8}{$3$}} %<br> \put(397,3){\sx{1.8}{$4$}} %<br> \put(497,3){\sx{1.8}{$5$}} %<br> \put(540,3){\sx{1.8}{$x$}} %<br> \put(360,210){\sx{1.2}{$u\!=\!0.8856031944$}} %<br> %\put(316,178){\sx{1.3}{$u\!=\!0.8$}} %<br> \put(311,198){\sx{1.3}{\rot{-51}$u\!=\!0.8$\ero}} %<br> \put(146,159){\sx{2}{ \rot{62}$u\!=\!1$\ero }} %<br> \put(172,117){\sx{2}{ \rot{1}$u\!=\!0$\ero }} %<br> \put(020,163){\sx{2}{ \rot{-37}$u\!=\!2$\ero }} %<br> \put(018,053){\sx{2}{ \rot{ 22}$u\!=\!3$\ero }} %<br> \put(051,06){\sx{2}{ \rot{ 53}$u\!=\!4$\ero }} %<br> %<br> \put(082,183){\sx{2}{ \rot{2}$v\!=\!1$\ero }} %<br> \put(081,083){\sx{2}{ \rot{46}$v\!=\!2$\ero }} %<br> \put(306,148){\sx{2}{ \rot{0.}$v\!=\!0$\ero }} %<br> \put(406,148){\sx{2}{ \rot{0.}$v\!=\!0$\ero }} %<br> \end{picture} %<br> } %<br> \end{document} %<br> %
% % % % %
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