File:Penplot.jpg

 #include <math.h>
 #include <stdio.h>
 #include <stdlib.h>
 #define DB double
 #define DO(x,y) for(x=0;x<y;x++)
#include <complex>
typedef std::complex<double> z_type;
 #define Re(x) x.real()
 #define Im(x) x.imag()
 #define I z_type(0.,1.)
 #include "ado.cin"
 #include "fsexp.cin"
 #include "fslog.cin"

z_type pen0(z_type z){
DB Lp=-1.8503545290271812;
DB k,a,b;
// k=1.86573322821; a=-.62632418; b=0.4827;
        k=1.86573322821; a=-.6263241; b=0.4827;

z_type e=exp(k*z);
return Lp + e*(1.+e*(a+b*e));
}

z_type pen7(z_type z){ DB x; int m,n; z=pen0(z+(2.24817451898-7.));
DO(n,7) { if(Re(z)>8.) return 999.; z=FSEXP(z); if(abs(z)<40) goto L1; return 999.; L1: ;}
return z; }

z_type pen(z_type z){ DB x; int m,n;
x=Re(z); if(x<= -4.) return pen0(z);
m=int(x+5.);
z-=DB(m);
z=pen0(z);
DO(n,m) z=FSEXP(z);
return z;
}

int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
FILE *o;o=fopen("penplo.eps","w"); ado(o,608,1008);
 fprintf(o,"404 204 translate\n 100 100 scale\n");
#define M(x,y) fprintf(o,"%8.4f %8.4f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%8.4f %8.4f L\n",0.+x,0.+y);
 for(m=-4;m<3;m++) {M(m,-2)L(m,8)}
 for(n=-2;n<11;n++) {M( -4,n)L(2,n)} fprintf(o,"2 setlinecap 1 setlinejoin .004 W 0 0 0 RGB S\n");

DO(n,150){x=-4+.04*n;y=Re(pen7(x)); if(n==0) M(x,y)else L(x,y); if(y>8.)break;} fprintf(o,".02 W 0 0 0 RGB S\n");

DO(n,150){x=-2.2+.04*n;y=10.*(Re(pen7(x))-(1.+x)); if(n==0) M(x,y)else L(x,y); if(y>.3)break;} fprintf(o,".01 W 0 .5 0 RGB S\n");

DB L=-1.8503545290271812;
DB K=1.86573322821;
DB a=-.6263241;
DB b=0.4827;
DO(n,80){x=-4.+.04*n; DB e=exp(K*(x+2.24817451898)); y=L+e;
        if(n==0) M(x,y) else L(x,y); if(y>8.) break;}
fprintf(o,".01 W 0 0 1 RGB S\n");

/*
DO(n,60){x=-4+.04*n; DB e=exp(K*(x+2.24817451898)); y=L+e*(1.+e*(a));
        if(n==0) M(x,y) else L(x,y); if(y>8.||y<-2.) break;}
*/
M(-4,L)L(0,L)
fprintf(o,".01 W 1 0 0 RGB S\n");


/*
DO(n,60){x=-4+.04*n; DB e=exp(K*(x+2.24817451898)); y=L+e*(1.+e*(a+e*b));
        if(n==0) M(x,y) else L(x,y); if(y<-2.) break;}
fprintf(o,".01 W 1 0 0 RGB S\n");
*/

DB t2=M_PI/1.86573322821;
DB tx=-2.32;
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);

printf("pen7(-1)=%18.14f\n", Re(pen7(-1.)));
printf("Pi/1.86573322821=%18.14f %18.14f\n", M_PI/1.86573322821, 2*M_PI/1.86573322821);

        system("epstopdf penplo.eps");
        system( "open penplo.pdf");
}

\documentclass[12pt]{article}
\paperwidth 608px
\paperheight 1008px
\textwidth 1394px
\textheight 1300px
\topmargin -104px
\oddsidemargin -90px
\usepackage{graphics}
\usepackage{rotating}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\newcommand \rmi {\mathrm{i}}
\begin{document}
{\begin{picture}(608,1008)
%\put(12,0){\ing{24}}
%\put(12,0){\ing{penma}}
\put(0,0){\ing{penplo}}
\put(377,994){\sx{3.2}{$y$}}
\put(377,895){\sx{3.2}{$7$}}
\put(377,795){\sx{3.2}{$6$}}
\put(377,695){\sx{3.2}{$5$}}
\put(377,594){\sx{3.2}{$4$}}
\put(377,494){\sx{3.2}{$3$}}
\put(377,394){\sx{3.2}{$2$}}
\put(377,294){\sx{3.2}{$1$}}
\put(377,194){\sx{3.2}{$0$}}
\put(358, 93){\sx{3.2}{$-1$}}
\put(80,174){\sx{3.2}{$-3$}}
\put(180,174){\sx{3.2}{$-2$}}
\put(280,174){\sx{3.2}{$-1$}}
\put(396,174){\sx{3.2}{$0$}}
\put(496,174){\sx{3.2}{$1$}}
\put(590,174){\sx{3.2}{$x$}}
\put(242,406){\sx{3.6}{\rot{85}$y\!=\!L+\exp(k(x\!+\!x_1))$\ero}}
%
%\put(560,510){\sx{3.6}{\rot{84}$y\!=\!L+\exp(k(x\!+\!x_1))$\ero}}
%\put(532,708){\sx{3.6}{\rot{86}$y\!=\!\mathrm{pen}(x)$\ero}}
\put(446,370){\sx{3.9}{\rot{70}$y\!=\!\mathrm{pen}(x)$\ero}}
%\put(366,236){\sx{2.3}{$y\!=\!10(\mathrm{pen}(x)\!-\!1\!-\!x)$}}
%\put(416,239){\sx{3.4}{$y=10\,\delta(x)$}}
\put(8,236){\sx{3.3}{$y=10\,\delta(x)$}}
%\put(366, 8){\sx{3.3}{$L$}}
\put(312, 9){\sx{3.2}{$y\!=\!L$}}
\end{picture}
\end{document}