File:Penmap.jpg

Summary

Title / Description	Complex map of the natural pentation pen is shown with lines ${\displaystyle u=\Re (\mathrm {pen} (x\!+\!\mathrm {i} y)=\mathrm {const} }$ and lines ${\displaystyle v=\Im (\mathrm {pen} (x\!+\!\mathrm {i} y)=\mathrm {const} }$ in the ${\displaystyle x,y}$ plane
Citizendium author & Copyright holder	Copyright © Dmitrii Kouznetsov. See below for licence/re-use information.
Date created	year 2014
Country of first publication	Japan, Germany
Notes	Description of this image is available in Russian in book Суперфункции [1].
Other versions	http://mizugadro.mydns.jp/t/images/e/ea/Penmap.jpg
Using this image on CZ	Please click here to add the credit line, then copy the code below to add this image to a Citizendium article, changing the size, alignment, and caption as necessary. {{Image|Penmap.jpg|right|350px|Add image caption here.}}

Licensing

   

This media, Penmap.jpg, is licenced under the Creative Commons Attribution 3.0 Unported License

You are free: To Share — To copy, distribute and transmit the work; To Remix — To adapt the work.
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For any reuse or distribution, you must make clear to others the licence terms of this work (the best way to do this is with a link to this licence's web page). Any of the above conditions can be waived if you get permission from the copyright holder. Nothing in this licence impairs or restricts the author's moral rights.
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C++ generator of map

Files ado.cin, conto.cin fsexp.cin, fslog.cin should be loaded 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++) #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=-.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"); M(-4,L)L(0,L) 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"); }

Latex generator of labels

\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(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(446,370){\sx{3.9}{\rot{70}$y\!=\!\mathrm{pen}(x)$\ero}} \put(8,236){\sx{3.3}{$y=10\,\delta(x)$}} \put(312, 9){\sx{3.2}{$y\!=\!L$}} \end{picture} \end{document}

References