File:Penzoo25t400.jpg

Complex map of natural pentation, range in vicinity of the origin of coordinates, positive imaginary values of the argument.

$u\!+\!\mathrm i v=\mathrm{pen}(x\!+\!\mathrm i y)$

Usage: FIgure 10.5 of the Book Суперфункции (In Russian) .

The map shown is zoom-in of the central part of map in figure http://mizugadro.mydns.jp/t/index.php/File:Penmap.jpg

C++ generator of curves
Files conto.cin, ado.cin and fsexp.cin should be loaded in order to compile the code below:

typedef std::complex z_type; // #include "fslog.cin"
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x8.) 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; int M=501,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("penzoo25.eps","w"); ado(o,504,204); fprintf(o,"252 2 translate\n 100 100 scale\n"); DO(m,M1) X[m]=-2.5+.01*(m-.5); DO(n,N1) Y[n]=0.+.005*(n-.5); // for(m=1;m<400;m++) {M(-2.5+.01*m,0)L(-2.5+.01*m,2)} // for(n=1;n<200;n++) {M(-2.5, .01*n)L(1.5,.01*n)} fprintf(o,"2 setlinecap .0002 W 0 0 0 RGB S\n"); for(m=0;m<51;m++) {M(-2.5+.1*m,0)L(-2.5+.1*m,2)} for(n=1;n<21;n++) {M(-2.5, .1*n)L(2.5,.1*n)} fprintf(o,"2 setlinecap .002 W 0 0 0 RGB S\n"); M(-2.316,1.683) L(-2.316,0)

M(-2.260,0) L(-2.260,1.384) L(0,1.384)

M(1.057,0) L(1.057,1.546) L(0,1.546) fprintf(o,"0 setlinecap .0022 W 0 0 0 RGB S\n"); for(m=0;m<5;m++) {M(-2+m,0)L(-2+m,2)} for(n=0;n<3;n++) {M(-2.5,n)L(2.5,n)} fprintf(o,"2 setlinecap .006 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]; DO(n,N1){y=Y[n]; z=z_type(x,y); // c=pen0(z); // c=FSEXP(pen0(z-1.)); // c=FSEXP(FSEXP(pen0(z-2.))); c=pen7(z); // d=FSEXP(pen(z-1.)); //     p=abs((c-d)/(c+d));  p=-log(p)/log(10.); p=Re(c); q=Im(c); if(p>-9999 && p<9999 && fabs(p)>1.e-11) g[m*N1+n]=p; if(q>-9999 && q<9999 && fabs(q)>1.e-11) f[m*N1+n]=q; }} // #include "plofu.cin"

fprintf(o,"1 setlinejoin 2 setlinecap\n");

p=2;q=.5; for(m=-19;m<19;m++)for(n=1;n<10;n+=1)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".003 W 0 .6 0 RGB S\n"); for(m=0;m<29;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q); fprintf(o,".003 W .9 0 0 RGB S\n"); for(m=0;m<29;m++) for(n=1;n<10;n+=1)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".003 W 0 0 .9 RGB S\n");

for(m= 1;m<20;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);fprintf(o,".008 W .9 0 0 RGB S\n"); for(m= 1;m<20;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);fprintf(o,".008 W 0 0 .9 RGB S\n"); conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".008 W .6 0 .6 RGB S\n"); for(m=-31;m<32;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".007 W 0 0 0 RGB S\n");

DB t2=M_PI/1.86573322821;

//DB tx=-2.32; DB tx=-2.316;

//M(tx,t2)L(4.1,t2) M(tx,t2)L(2.6,t2) fprintf(o,"0 setlinecap .014 W 1 1 1 RGB S\n"); //DO(n,64){ x=tx+.1*n; M(x,t2) L(x+.04,t2) } //DO(n,64){ x=tx+.1*n; M(x,-t2) L(x+.04,-t2) } //DO(n,34){ x=.1*n; M(x,t2) L(x+.04,t2) } //fprintf(o,"0 setlinecap .004 W 0 0 0 RGB S\n");

//conto(o,g,w,v,X,Y,M,N, ( 1. ),-99,99); fprintf(o,".12 W 1 .5 0 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);

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

system("epstopdf penzoo25.eps"); system(   "open penzoo25.pdf"); }

Latex generator of labels
\documentclass[12pt]{article} \paperheight 212px \paperwidth 510px \textwidth 894px \textheight 800px \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}(512,208) %\put(12,0){\ing{24}} %\put(12,0){\ing{penma}} \put(8,9){\ing{penzoo25}} \put(1,205){\sx{1.2}{$y$}} \put(-.4,176.8){\sx{1.1}{$\frac{P}{2 \rm i}$}} \put(130,177){\sx{1.2}{\bf cut}} \put(1,158){\sx{1.1}{$\frac{3}{2}$}} \put(1,107){\sx{1.2}{$1$}} \put(1,057){\sx{1.17}{$\frac{1}{2}$}} \put(1,7){\sx{1.2}{$0$}} \put(50,0.4){\sx{1.12}{$-2$}} \put(150,0.4){\sx{1.12}{$-1$}} \put(258,0.5){\sx{1.12}{$0$}} \put(358.4,0.5){\sx{1.12}{$1$}} \put(459,0.5){\sx{1.12}{$2$}} \put(505,0.5){\sx{1.12}{$x$}} % \put(392,73){\sx{1.7}{\rot{61}$v\!=\!2$\ero}} \put(212,120){\sx{1.7}{\rot{0}$v\!=\!1$\ero}} \put(195.6,5.8){\sx{1.7}{\rot{0}$v\!=\!0$\ero}} % \put(063,17){\sx{1.7}{\rot{78}$u\!=\!-1$\ero}} \put(166,18){\sx{1.7}{\rot{90}$u\!=\!0$\ero}} \put(265,18){\sx{1.7}{\rot{81}$u\!=\!1$\ero}} \put(334,15){\sx{1.7}{\rot{65}$u\!=\!2$\ero}} % \put(29.5,146){\sx{1.2}{$L$}} \put(361.4,162.3){\sx{1.2}{$L$}} \end{picture} \end{document}