imported>Dmitrii Kouznetsov |
|
| (3 intermediate revisions by one other user not shown) |
| Line 1: |
Line 1: |
| == Summary == | | == Summary == |
| {{Image_Details|user
| | Importing file |
| |description = [[Complex map]] of [[natural tetration]] tet, id est, [[tetration]] to natural base <math>b=\mathrm e\approx 1.71</math> ; <math>u</math> has sense of the real part, and <math>v</math> ha sense of imaginary part of <nath>\mathrm{tet}(x\!+\!\mathrm i y)</math>
| |
| |author = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
| |
| |date-created = year 2014
| |
| |pub-country = Japan, Germany
| |
| |notes = Similar map is used at the cover of the Russian book [[Суперфункции]] <ref>
| |
| https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0 <br>
| |
| http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf <br>
| |
| http://mizugadro.mydns.jp/BOOK/202.pdf
| |
| Д. Кузнецов. Суперфункции. Lambert Academic Press, 2014 (in Russian)
| |
| </ref>.
| |
| | |
| The format of this map is adjisted to that of the natural [[pentation]] at http://en.citizendium.org/wiki/File:Penmap.jpg
| |
| in order to simplify the comparison
| |
| |versions = http://mizugadro.mydns.jp/t/index.php/File:B271t3T.png
| |
| }}
| |
| == Licensing ==
| |
| {{CC|by|3.0}}
| |
| | |
| ==[[C++]] generator of map==
| |
| Files [[fsexp.cin]], [[ado.cin]] and [[conto.cin]] should be loaded to the working directory in order to compile the [[C++]] code below
| |
| | |
| <nowiki>
| |
| #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 "conto.cin"
| |
| #include "fsexp.cin"
| |
| //#include "fslog.cin"
| |
| main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
| |
| int M=801,M1=M+1;
| |
| int N=401,N1=N+1;
| |
| DB X[M1],Y[N1];
| |
| DB *g, *f, *w; // w is working array.
| |
| g=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
| |
| f=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
| |
| w=(DB *)malloc((size_t)((M1*N1)*sizeof(DB)));
| |
| char v[M1*N1]; // v is working array
| |
| FILE *o;o=fopen("b271tMap3.eps","w"); ado(o,802,802);
| |
| fprintf(o,"401 401 translate\n 100 100 scale\n");
| |
| fprintf(o,"1 setlinejoin 2 setlinecap\n");
| |
| DO(m,M1) X[m]=-4.+.01*(m-.5);
| |
| for(n=0;n<N1;n++) Y[n]=sinh((2./200.)*(n-200.5));
| |
| for(m=-4;m<5;m++) {M(m,-4)L(m,4)}
| |
| for(n=-4;n<5;n++) {M( -4,n)L(4,n)} fprintf(o,".006 W 0 0 0 RGB S\n");
| |
| DO(m,M1)DO(n,N1){ g[m*N1+n]=999;
| |
| f[m*N1+n]=999;}
| |
| DB b=sqrt(2);
| |
| DO(m,M1){x=X[m]; printf("x=%6.3f\n",x);
| |
| DO(n,N1){y=Y[n]; z=z_type(x,y); //if(abs(z+2.)>.019)
| |
| {
| |
| c=FSEXP(z);
| |
| p=Re(c); q=Im(c);
| |
| if(p>-12 && p<12 && fabs(q)>1.e-12) g[m*N1+n]=p;
| |
| if(q>-12 && q<12 && fabs(q)>1.e-12) f[m*N1+n]=q;
| |
| }
| |
| }}
| |
| fprintf(o,"1 setlinejoin 1 setlinecap\n");
| |
| p=1.;q=.3;
| |
| for(m=-8;m<8;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q,q);fprintf(o,".007 W 0 .6 0 RGB S\n");
| |
| for(m=0;m<8;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q);fprintf(o,".007 W .9 0 0 RGB S\n");
| |
| for(m=0;m<8;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q);fprintf(o,".007 W 0 0 .9 RGB S\n");
| |
| for(m= 1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);fprintf(o,".02 W .8 0 0 RGB S\n");
| |
| for(m= 1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);fprintf(o,".02 W 0 0 .8 RGB S\n");
| |
| conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".02 W .5 0 .5 RGB S\n");
| |
| for(m=-10;m<11;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".02 W 0 0 0 RGB S\n");
| |
| M(-2,0)L(-4,0)fprintf(o,"0 setlinecap .03 W 1 1 1 RGB S\n");
| |
| for(n=0;n<11;n++){ M(-2-.2*(n+.2),0) L(-2-.2*(n+.45),0) } fprintf(o,".04 W 1 .5 0 RGB S\n");
| |
| for(n=0;n<21;n++){ M(-2-.2*(n+.7),0) L(-2-.2*(n+.95),0) } fprintf(o,".04 W 0 .5 1 RGB S\n");
| |
| fprintf(o,"0 setlinejoin 0 setlinecap\n");
| |
| fprintf(o,"showpage\n");
| |
| fprintf(o,"%c%cTrailer\n",'%','%');
| |
| fclose(o);
| |
| free(f);
| |
| free(g);
| |
| free(w);
| |
| system("epstopdf b271tMap3.eps");
| |
| system( "open b271tMap3.pdf"); //for macintosh
| |
| getchar(); system("killall Preview"); // For macintosh
| |
| }
| |
| </nowiki>
| |
| ==[[Latex]] generator of labels==
| |
| | |
| % <nowiki>
| |
| \documentclass[12pt]{article}
| |
| \paperheight 828px
| |
| \paperwidth 836px
| |
| \textwidth 1294px
| |
| \textheight 1100px
| |
| \topmargin -104px
| |
| \oddsidemargin -78px
| |
| \usepackage{graphics}
| |
| \usepackage{rotating}
| |
| \newcommand \sx {\scalebox}
| |
| \newcommand \rot {\begin{rotate}}
| |
| \newcommand \ero {\end{rotate}}
| |
| \newcommand \ing {\includegraphics}
| |
| \newcommand \rmi {\mathrm{i}}
| |
| \begin{document}
| |
| \newcommand \zoomax {
| |
| \put(18, 806){\sx{3.3}{$y$}}
| |
| \put(18, 713){\sx{3}{$3$}}
| |
| \put(18, 613){\sx{3}{$2$}}
| |
| \put(18, 513){\sx{3}{$1$}}
| |
| \put(18, 413){\sx{3}{$0$}}
| |
| \put(-6, 313){\sx{3}{$-1$}}
| |
| \put(-6, 213){\sx{3}{$-2$}}
| |
| \put(-6, 113){\sx{3}{$-3$}}
| |
| \put(014, -5){\sx{3}{$-4$}}
| |
| \put(114, -5){\sx{3}{$-3$}}
| |
| \put(214, -5){\sx{3}{$-2$}}
| |
| \put(314, -5){\sx{3}{$-1$}}
| |
| \put(435, -5){\sx{3}{$0$}}
| |
| \put(535, -5){\sx{3}{$1$}}
| |
| \put(635, -5){\sx{3}{$2$}}
| |
| \put(735, -5){\sx{3}{$3$}}
| |
| \put(827,-4){\sx{3}{$x$}}
| |
| }
| |
| \parindent 0pt
| |
| \sx{1}{\begin{picture}(852,820) \put(40,20){\ing{b271tMap3}}
| |
| \zoomax
| |
| \put(60,415){\sx{2.8}{\bf cut}}
| |
| \put(340,548){\sx{3}{$v\!=\!1$}}
| |
| \put(360,414){\sx{3}{$v\!=\!0$}}
| |
| \put(760,414){\sx{3}{$v\!=\!0$}}
| |
| \put(340,280){\sx{3}{$v\!=\!-1$}}
| |
| \put(70,800){\sx{2.5}{$f\approx L\approx0.318+1.337i$}}
| |
| \put(60,60){\sx{2.5}{$f\approx L^*\approx0.318-1.337i$}}
| |
| \put(100,638){\sx{2.5}{$v\!=\!1.4$}}
| |
| \put(552,745){\sx{2.5}{$v\!=\!1.4$}}
| |
| \put(100,198){\sx{2.5}{$v\!=\!-\!1.4$}}
| |
| \put(540,90){\sx{2.5}{$v\!=\!-\!1.4$}}
| |
| \put(666,726){\sx{2.5}{$u\!=\!0.2$}}
| |
| \put(216,616){\sx{2.5}{$u\!=\!0.2$}}
| |
| \put(660,642){\sx{3}{$u\!=\!0$}}
| |
| \put(210,536){\sx{3}{$u\!=\!0$}}
| |
| \put(410,700){\sx{2.5}{$u\!=\!0.4$}}
| |
| \put(217,213){\sx{2.5}{$u\!=\!0.2$}}
| |
| \put(410,130){\sx{2.5}{$u\!=\!0.4$}}
| |
| \end{picture}}
| |
| \end{document}
| |
| %</nowiki>
| |
| | |
| ==References==
| |
| <references/>
| |
| | |
| [[Category:Superfunction]]
| |
| [[Category:Tetration]]
| |
| [[Category:Complex map]]
| |
| [[Category:TORI]]
| |
