imported>Dmitrii Kouznetsov |
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| == Summary == | | == Summary == |
| {{Image_Details|user
| | Importing file |
| |description = [[Complex map]] of [[tetration]] to base <math>b=\sqrt{2}</math>
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| | |
| <math>u+\mathrm i v=\mathrm{tet}_b(x\!+\!\mathrm i y)$
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| </math>
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| |author = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
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| |date-created = August 2014
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| |pub-country = Japan
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| |notes = I plan to use this image in the article
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| D.Kouznetsov. Holomorphic ackermann. 2015, in preparation.
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| |versions = http://mizugadro.mydns.jp/t/index.php/File:Ack3a600.jpg
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| The real-real plot of this function is one of curves at http://en.citizendium.org/wiki/File:Tetreal10bx10d.png
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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
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| [[ado.cin]],
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| [[conto.cin]],
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| [[sqrt2f21e.cin]]
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| should be loaded to the working directory in order to compile the code below.
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| | |
| <nowiki>
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| #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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| #define z_type std::complex<double>
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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 "sqrt2f21e.cin"
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| #include "conto.cin"
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| | |
| int main(){ int j,k,m,m1,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
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| | |
| int M=601,M1=M+1;
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| int N=461,N1=N+1;
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| | |
| DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1];
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| char v[M1*N1]; // v is working array
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| FILE *o;o=fopen("tetqma.eps","w");ado(o,602,202);
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| fprintf(o,"301 101 translate\n 10 10 scale\n");
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| DO(m,M1)X[m]=-30.+.1*(m);
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| DO(n,200)Y[n]=-10.+.05*n;
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| Y[200]=-.01;
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| Y[201]= .01;
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| for(n=202;n<N1;n++) Y[n]=-10.+.05*(n-1.);
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| for(m=-30;m<31;m++){if(m==0){M(m,-10.2)L(m,10.2)} else{M(m,-10)L(m,10)}}
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| for(n=-10;n<11;n++){ M( -30,n)L(30,n)}
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| fprintf(o,".008 W 0 0 0 RGB S\n");
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| DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
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| | |
| DO(n,N1){y=Y[n];
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| for(m=295;m<305;m++)
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| {x=X[m]; //printf("%5.2f\n",x);
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| z=z_type(x,y);
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| c=F21E(z);
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| p=Re(c);q=Im(c);
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| if(p>-99. && p<99. && q>-99. && q<99. ){ g[m*N1+n]=p;f[m*N1+n]=q;}
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| d=c;
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| for(k=1;k<31;k++)
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| { m1=m+k*10; if(m1>M) break;
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| d=exp(d*(.5*log(2.)));
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| p=Re(d);q=Im(d);
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| if(p>-99. && p<99. && q>-99. && q<99. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;}
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| }
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| d=c;
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| for(k=1;k<31;k++)
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| { m1=m-k*10; if(m1<0) break;
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| d=log(d)*(2./log(2.));
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| p=Re(d);q=Im(d);
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| if(p>-99. && p<99. && q>-99. && q<99. ){ g[m1*N1+n]=p;f[m1*N1+n]=q;}
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| }
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| }}
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| | |
| fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=1;q=.5;
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| for(m=-10;m<10;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".02 W 0 .6 0 RGB S\n");
| |
| for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".02 W .9 0 0 RGB S\n");
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| for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".02 W 0 0 .9 RGB S\n");
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| for(m=1;m<10;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".08 W .9 0 0 RGB S\n");
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| for(m=1;m<10;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".08 W 0 0 .9 RGB S\n");
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| conto(o,f,w,v,X,Y,M,N, (0. ),-p,p); fprintf(o,".08 W .6 0 .6 RGB S\n");
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| for(m=-9;m<10;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".08 W 0 0 0 RGB S\n");
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| | |
| fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
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| system("epstopdf tetqma.eps");
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| system( "open tetqma.pdf");
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| getchar(); system("killall Preview");
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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{amsproc}
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| \usepackage{graphicx}
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| \usepackage{rotating}
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| \usepackage{hyperref}
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| \newcommand \be {\begin{eqnarray}}
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| \newcommand \ee {\end{eqnarray} }
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| \newcommand \sx {\scalebox}
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| \newcommand \rme {{\rm e}}
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| \newcommand \rmi {{\rm i}}
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| \newcommand \ds {\displaystyle}
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| \newcommand \bN {\mathbb{N}}
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| \newcommand \bC {\mathbb{C}}
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| \newcommand \bR {\mathbb{R}}
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| \newcommand \cO {\mathcal{O}}
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| \newcommand \cF {\mathcal{F}}
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| \newcommand \rot {\begin{rotate}}
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| \newcommand \ero {\end{rotate}}
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| \newcommand \nS {\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!}
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| \newcommand \pS {{~}~{~}}
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| \newcommand \fac {\mathrm{Factorial}}
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| \newcommand {\rf}[1] {(\ref{#1})}
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| \newcommand{\iL}[1] {~\label{#1}\pS \rm[#1]\nS} %make the labels visible
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| \newcommand \eL[1] {\iL{#1}\ee}
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| \newcommand \ing \includegraphics
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| \newcommand \tet {\mathrm{tet}}
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| | |
| \usepackage{geometry}
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| \topmargin -94pt
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| \oddsidemargin -87pt
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| \paperwidth 618pt
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| \paperheight 216pt
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| | |
| \begin{document}
| |
| | |
| \newcommand \mapax {
| |
| \put(2,206){\sx{1.2}{$y$}}
| |
| \put(2,188){\sx{1.2}{$8$}}
| |
| \put(2,168){\sx{1.2}{$6$}}
| |
| \put(2,148){\sx{1.2}{$4$}}
| |
| \put(2,128){\sx{1.2}{$2$}}
| |
| \put(2,108){\sx{1.2}{$0$}}
| |
| \put(-6,88){\sx{1.2}{$-2$}}
| |
| \put(-6,68){\sx{1.2}{$-4$}}
| |
| \put(-6,48){\sx{1.2}{$-6$}}
| |
| \put(-6,28){\sx{1.2}{$-8$}}
| |
| \put(-1,1){\sx{1.2}{$-30$}}
| |
| \put( 49,1){\sx{1.2}{$-25$}}
| |
| \put( 99,1){\sx{1.2}{$-20$}}
| |
| \put(149,1){\sx{1.2}{$-15$}}
| |
| \put(199,1){\sx{1.2}{$-10$}}
| |
| \put(252,1){\sx{1.2}{$-5$}}
| |
| \put(309,1){\sx{1.2}{$0$}}
| |
| \put(329,1){\sx{1.2}{$2$}}
| |
| \put(349,1){\sx{1.2}{$4$}}
| |
| \put(369,1){\sx{1.2}{$6$}}
| |
| \put(389,1){\sx{1.2}{$8$}}
| |
| \put(407,1){\sx{1.2}{$10$}}
| |
| \put(457,1){\sx{1.2}{$15$}}
| |
| \put(507,1){\sx{1.2}{$20$}}
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| \put(557,1){\sx{1.2}{$25$}}
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| \put(607,1){\sx{1.2}{$x$}}
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| }
| |
| | |
| {\begin{picture}(620,216) \mapax \put(10,10){\ing{tetqma}}
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| \put(22,194){\sx{1.4}{$v\!=\!0$}}
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| \put(254,206){\sx{1.4}{$v\!=\!-0.2$}}
| |
| \put(262,182){\sx{1.4}{$v\!=\!0.2$}}
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| \put(262,170){\sx{1.4}{$v\!=\!0.4$}}
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| \put(266,148){\sx{1.4}{$v\!=\!1$}}
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| \put(261,69){\sx{1.4}{$v\!=\!-1$}}
| |
| | |
| \put(308,158){\sx{1.4}{\rot{66}$u\!=\!2.4$\ero}}
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| \put(324,158){\sx{1.4}{\rot{53}$u\!=\!2.2$\ero}}
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| \put(314,138){\sx{1.4}{\rot{-33}$u\!=\!1.8$\ero}}
| |
| | |
| \put(318,61){\sx{1.4}{\rot{-56}$u\!=\!2.2$\ero}}
| |
| \put(214,12){\sx{1.4}{\rot{80}$u\!=\!3.8$\ero}}
| |
| \put(240,12){\sx{1.4}{\rot{83}$u\!=\!3.6$\ero}}
| |
| \put(256,12){\sx{1.4}{\rot{85}$u\!=\!3.4$\ero}}
| |
| \put(282,16){\sx{1.4}{\rot{90}$u\!=\!3$\ero}}
| |
| \put(294,12){\sx{1.4}{\rot{90}$u\!=\!2.8$\ero}}
| |
| \put(22, 145.6){\sx{1.4}{$u\!=\!4$}} \put(502, 151){\sx{1.4}{$u\!=\!2$}}
| |
| \put(25,108.4){\sx{1.4}{\bf cut}} \put(502,108.4){\sx{1.4}{$v\!=\!0$}}
| |
| \put(22, 70.4){\sx{1.4}{$u\!=\!4$}} \put(502, 64.6){\sx{1.4}{$u\!=\!2$}}
| |
| \put(22, 21){\sx{1.4}{$v\!=\!0$}}
| |
| \end{picture}}
| |
| \end{document}
| |
| </nowiki>
| |
| | |
| ==References==
| |
| | |
| http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html<br>
| |
| http://www.ils.uec.ac.jp/~dima/PAPERS/2010q2.pdf<br>
| |
| http://mizugadro.mydns.jp/PAPERS/2010q2.pdf
| |
| D.Kouznetsov, H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
| |
| | |
| 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 Publishing, 2014. (In Russian)
| |
| | |
| D.Kouznetsov. Holomorphic [[ackermann]]s. 2015, in preparation.
| |
| | |
| [[Category:Complex map]]
| |
| [[Category:Superfunction]]
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| [[Category:Tetration]]
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| [[Category:TORI]]
| |
