imported>Dmitrii Kouznetsov |
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| == Summary == | | == Summary == |
| {{Image_Details|user
| | Importing file |
| |description = [[Complex map]] of the [[natural pentation]] pen is shown with lines <math>u=\Re(\mathrm{pen}(x\!+\!\mathrm i y)=\mathrm{const}</math> and lines <math>v=\Im(\mathrm{pen}(x\!+\!\mathrm i y)=\mathrm{const}</math> in the <math>x,y</math> plane
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| |author = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
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| |date-created = year 2014
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| |pub-country = Japan, Germany
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| |notes = Description of this image is available in Russian in book [[Суперфункции]] <ref>
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| https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0 <br>
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| http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf <br>
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| http://mizugadro.mydns.jp/BOOK/202.pdf Д.Кузнецов. Суперфункции. Lambert Academic Publishing, 2014 (In Russian), page 270, figure 19.21.
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| </ref>.
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| |versions = http://mizugadro.mydns.jp/t/images/e/ea/Penmap.jpg
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| }}
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| == Licensing ==
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| {{CC|by|3.0}}
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| | |
| ==[[C++]] generator of map==
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| Files [[ado.cin]], [[conto.cin]] [[fsexp.cin]], [[fslog.cin]] should be loaded in order to compile the [[C++]] code below
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| | |
| <nowiki>
| |
| #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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| #include <complex>
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| typedef std::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 "ado.cin"
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| #include "fsexp.cin"
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| #include "fslog.cin"
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| | |
| z_type pen0(z_type z){
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| DB Lp=-1.8503545290271812;
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| DB k,a,b;
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| k=1.86573322821; a=-.6263241; b=0.4827;
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| z_type e=exp(k*z);
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| return Lp + e*(1.+e*(a+b*e));
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| }
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| | |
| z_type pen7(z_type z){ DB x; int m,n; z=pen0(z+(2.24817451898-7.));
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| DO(n,7) { if(Re(z)>8.) return 999.; z=FSEXP(z); if(abs(z)<40) goto L1; return 999.; L1: ;}
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| return z; }
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| | |
| z_type pen(z_type z){ DB x; int m,n;
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| x=Re(z); if(x<= -4.) return pen0(z);
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| m=int(x+5.);
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| z-=DB(m);
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| z=pen0(z);
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| DO(n,m) z=FSEXP(z);
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| return z;
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| }
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| | |
| int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
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| FILE *o;o=fopen("penplo.eps","w"); ado(o,608,1008);
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| fprintf(o,"404 204 translate\n 100 100 scale\n");
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| #define M(x,y) fprintf(o,"%8.4f %8.4f M\n",0.+x,0.+y);
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| #define L(x,y) fprintf(o,"%8.4f %8.4f L\n",0.+x,0.+y);
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| for(m=-4;m<3;m++) {M(m,-2)L(m,8)}
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| 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");
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| | |
| 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");
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| | |
| 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");
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| | |
| DB L=-1.8503545290271812;
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| DB K=1.86573322821;
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| DB a=-.6263241;
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| DB b=0.4827;
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| DO(n,80){x=-4.+.04*n; DB e=exp(K*(x+2.24817451898)); y=L+e;
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| if(n==0) M(x,y) else L(x,y); if(y>8.) break;}
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| fprintf(o,".01 W 0 0 1 RGB S\n");
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| | |
| M(-4,L)L(0,L)
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| fprintf(o,".01 W 1 0 0 RGB S\n");
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| | |
| DB t2=M_PI/1.86573322821;
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| DB tx=-2.32;
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| fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
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| | |
| printf("pen7(-1)=%18.14f\n", Re(pen7(-1.)));
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| printf("Pi/1.86573322821=%18.14f %18.14f\n", M_PI/1.86573322821, 2*M_PI/1.86573322821);
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| | |
| system("epstopdf penplo.eps");
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| system( "open penplo.pdf");
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| }
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| </nowiki>
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| ==[[Latex]] generator of labels==
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| | |
| <nowiki>
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| \documentclass[12pt]{article}
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| \paperwidth 608px
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| \paperheight 1008px
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| \textwidth 1394px
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| \textheight 1300px
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| \topmargin -104px
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| \oddsidemargin -90px
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| \usepackage{graphics}
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| \usepackage{rotating}
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| \newcommand \sx {\scalebox}
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| \newcommand \rot {\begin{rotate}}
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| \newcommand \ero {\end{rotate}}
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| \newcommand \ing {\includegraphics}
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| \newcommand \rmi {\mathrm{i}}
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| \begin{document}
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| {\begin{picture}(608,1008)
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| \put(0,0){\ing{penplo}}
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| \put(377,994){\sx{3.2}{$y$}}
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| \put(377,895){\sx{3.2}{$7$}}
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| \put(377,795){\sx{3.2}{$6$}}
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| \put(377,695){\sx{3.2}{$5$}}
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| \put(377,594){\sx{3.2}{$4$}}
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| \put(377,494){\sx{3.2}{$3$}}
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| \put(377,394){\sx{3.2}{$2$}}
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| \put(377,294){\sx{3.2}{$1$}}
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| \put(377,194){\sx{3.2}{$0$}}
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| \put(358, 93){\sx{3.2}{$-1$}}
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| \put(80,174){\sx{3.2}{$-3$}}
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| \put(180,174){\sx{3.2}{$-2$}}
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| \put(280,174){\sx{3.2}{$-1$}}
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| \put(396,174){\sx{3.2}{$0$}}
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| \put(496,174){\sx{3.2}{$1$}}
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| \put(590,174){\sx{3.2}{$x$}}
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| \put(242,406){\sx{3.6}{\rot{85}$y\!=\!L+\exp(k(x\!+\!x_1))$\ero}}
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| \put(446,370){\sx{3.9}{\rot{70}$y\!=\!\mathrm{pen}(x)$\ero}}
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| \put(8,236){\sx{3.3}{$y=10\,\delta(x)$}}
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| \put(312, 9){\sx{3.2}{$y\!=\!L$}}
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| \end{picture}
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| \end{document}
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| </nowiki>
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| | |
| ==References==
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| <references/>
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| | |
| [[Category:Complex map]]
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| [[Category:Tetration]]
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| [[Category:Pentation]]
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| [[Category:Superfunction]]
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| [[Category:Ackermann]]
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| [[Category:TORI]]
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