Difference between revisions of "File:Sqrt27t.jpg"

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[[Explicit plot]] of [[tetration]] to base $\sqrt{2}$
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Importing image file
  
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$y=\mathrm{tet}_{\sqrt{2}}(x)$
  +
  +
Usage: this is figure 16.1 of the book [[Суперфункции]] (2014, In Russian) <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 Publishing]], 2014.
  +
</ref>; the English version is in preparation in 2015.
  +
  +
This image is used also as figure 7a in the article
  +
<ref>
  +
http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html <br>
  +
http://mizugadro.mydns.jp/PAPERS/2010sqrt2.pdf offprint
  +
D.Kouznetsov, H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
  +
</ref>.
  +
  +
  +
==Refereces==
  +
<references/>
  +
  +
  +
==[[C++]] generator of the First map==
  +
Files [[ado.cin]],
  +
[[conto.cin]],
  +
[[sqrt2f21e.cin]]
  +
should be loaded in order to compile the code below.
  +
  +
<poem><nomathjax><nowiki>
  +
#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 "conto.cin"
  +
#include "ado.cin"
  +
// #include "tq2e.cin"
  +
//#include "f21E.cin"
  +
#include "sqrt2f21e.cin"
  +
  +
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
  +
//FILE *o;o=fopen("tq2Ereal.eps","w"); ado(o,0,0,620,620);
  +
// FILE *o;o=fopen("figreal.eps","w"); ado(o,0,0,620,620);
  +
// FILE *o;o=fopen("fig8a.eps","w"); ado(o,0,0,620,620);
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FILE *o;o=fopen("sqrt27a.eps","w"); ado(o,0,0,620,620);
  +
fprintf(o,"210 410 translate\n 100 100 scale\n");
  +
#define M(x,y) fprintf(o,"%7.4f %7.4f M\n",0.+x,0.+y);
  +
#define L(x,y) fprintf(o,"%7.4f %7.4f L\n",0.+x,0.+y);
  +
M(0,-4.06)L(0,2.06)
  +
M(-2.06,0)L(4.06,0)
  +
fprintf(o,".03 W S\n");
  +
for(n=-2;n<5;n++){if(n!=0){M(n,0)L(n,-.1)}}
  +
for(n=-4;n<3;n++){if(n!=0){M(0,n)L(-.1,n)}}
  +
fprintf(o,".03 W S\n");
  +
M(-2,-4)L(-2,2)L(4,2)
  +
M(-2,2)L(4,-4)
  +
fprintf(o,".01 W S\n");
  +
  +
fprintf(o,"1 setlinejoin 0 setlinecap\n");
  +
  +
  +
for(m=0;m<684;m+=4) { x=-1.84+.01*m; z=x;
  +
y=Re(F21E(z));
  +
if(m==0) M(x,y) else L(x,y)}
  +
fprintf(o,".03 W 0 0 1 RGB S\n");
  +
  +
/*
  +
for(m=0;m<684;m+=4) { x=-1.84+.01*m; z=x;
  +
y=Re(F21E(z));
  +
if(m==0) M(-y,-x) else L(-y,-x)}
  +
fprintf(o,".004 W 0 0 0 RGB S\n");
  +
*/
  +
  +
// c=TQ2E(z);
  +
// p=Re(c);
  +
// #include "plof.cin"
  +
  +
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
  +
system("epstopdf sqrt27a.eps");
  +
system( "open sqrt27a.pdf"); //for LINUX
  +
// getchar(); system("killall Preview"); // For macintosh
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of the labels==
  +
  +
<poem><nomathjax><nowiki>
  +
\documentclass[12pt,a4paper,oneside]{book}
  +
%\newcommand \EN[1] {{#1}} % make the English version
  +
\newcommand \EN[1] {{}} % suppress the English version
  +
\newcommand \RU[1] {{#1}} % make the Russian version (in this document not supported)
  +
%\newcommand \RU[1] {{}} % suppress the Russian version
  +
%The Japanese version is not yet supported. While \JP is used to suppress several lines at once.
  +
\newcommand \JP[1] {{}} % ореsuppress some text
  +
%\usepackage[space]{cite }% If exist.
  +
\usepackage[utf8]{inputenc}
  +
\usepackage[T2A]{fontenc}
  +
\usepackage[russian]{babel}
  +
\usepackage{latexsym,amsmath,amssymb,amsbsy,graphicx}
  +
  +
\usepackage{rotating}
  +
\usepackage{hyperref}
  +
\usepackage{wrapfig}
  +
\usepackage{geometry}
  +
\paperwidth 216mm
  +
\paperheight 216mm
  +
\textwidth 550mm
  +
\oddsidemargin -76pt
  +
\topmargin -92pt
  +
\textheight 457mm
  +
\pagestyle{empty}
  +
  +
\newcommand \sx {\scalebox}
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
\newcommand \ing {\includegraphics}
  +
\parindent 0pt
  +
\begin{document}
  +
  +
\begin{picture}(610,610)
  +
\put(0,0){\ing{sqrt27a}}
  +
\put(172,599){\sx{4}{$y$}}
  +
\put(172,499){\sx{4}{$1$}}
  +
\put(140,298){\sx{4}{$-1$}}
  +
\put(140,198){\sx{4}{$-2$}}
  +
\put(140, 98){\sx{4}{$-3$}}
  +
%\put(160, 0){\sx{3.8}{$-4$}}
  +
\put( -9,366){\sx{4}{$-2$}}
  +
\put( 89,366){\sx{4}{$-1$}}
  +
\put(300,366){\sx{4}{$1$}}
  +
\put(401,366){\sx{4}{$2$}}
  +
\put(502,366){\sx{4}{$3$}}
  +
\put(592,370){\sx{4.2}{$x$}}
  +
%\put(600,420){\sx{4.2}{$x$}}
  +
\put(340,530){\sx{4.3}{\rot{5}$y\!=\!\mathrm{tet}_{\sqrt{2}}(x)$\ero}}
  +
\put(380,200){\sx{4.2}{\rot{-45}$y\!=\!-x$\ero}}
  +
\end{picture}
  +
  +
\end{document}
  +
  +
</nowiki></nomathjax></poem>
  +
  +
[[Category:Base sqrt2]]
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[[Category:Book]]
  +
[[Category:BookPlot]]
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[[Category:C++]]
  +
[[Category:Explicit plot]]
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[[Category:Exp]]
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[[Category:Generator]]
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[[Category:Latex]]
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[[Category:Superfunction]]
  +
[[Category:Tetration]]

Latest revision as of 08:52, 1 December 2018

Explicit plot of tetration to base $\sqrt{2}$

$y=\mathrm{tet}_{\sqrt{2}}(x)$

Usage: this is figure 16.1 of the book Суперфункции (2014, In Russian) [1]; the English version is in preparation in 2015.

This image is used also as figure 7a in the article [2].


Refereces

  1. ↑ https://www.morebooks.de/store/ru/book/Суперфункции/isbn/978-3-659-56202-0
    http://www.ils.uec.ac.jp/~dima/BOOK/202.pdf
    http://mizugadro.mydns.jp/BOOK/202.pdf Д.Кузнецов. Суперфункции. Lambert Academic Publishing, 2014.
  2. ↑ http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html
    http://mizugadro.mydns.jp/PAPERS/2010sqrt2.pdf offprint D.Kouznetsov, H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.


C++ generator of the First map

Files ado.cin, conto.cin, sqrt2f21e.cin should be loaded in order to compile the 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 "conto.cin"
#include "ado.cin"
// #include "tq2e.cin"
//#include "f21E.cin"
#include "sqrt2f21e.cin"

int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
 //FILE *o;o=fopen("tq2Ereal.eps","w"); ado(o,0,0,620,620);
// FILE *o;o=fopen("figreal.eps","w"); ado(o,0,0,620,620);
// FILE *o;o=fopen("fig8a.eps","w"); ado(o,0,0,620,620);
  FILE *o;o=fopen("sqrt27a.eps","w"); ado(o,0,0,620,620);
 fprintf(o,"210 410 translate\n 100 100 scale\n");
#define M(x,y) fprintf(o,"%7.4f %7.4f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%7.4f %7.4f L\n",0.+x,0.+y);
M(0,-4.06)L(0,2.06)
M(-2.06,0)L(4.06,0)
fprintf(o,".03 W S\n");
for(n=-2;n<5;n++){if(n!=0){M(n,0)L(n,-.1)}}
for(n=-4;n<3;n++){if(n!=0){M(0,n)L(-.1,n)}}
fprintf(o,".03 W S\n");
M(-2,-4)L(-2,2)L(4,2)
M(-2,2)L(4,-4)
fprintf(o,".01 W S\n");

fprintf(o,"1 setlinejoin 0 setlinecap\n");


for(m=0;m<684;m+=4) { x=-1.84+.01*m; z=x;
                        y=Re(F21E(z));
                        if(m==0) M(x,y) else L(x,y)}
fprintf(o,".03 W 0 0 1 RGB S\n");

/*
for(m=0;m<684;m+=4) { x=-1.84+.01*m; z=x;
                        y=Re(F21E(z));
                        if(m==0) M(-y,-x) else L(-y,-x)}
fprintf(o,".004 W 0 0 0 RGB S\n");
*/

// c=TQ2E(z);
// p=Re(c);
// #include "plof.cin"

 fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf sqrt27a.eps");
        system( "open sqrt27a.pdf"); //for LINUX
// getchar(); system("killall Preview"); // For macintosh
}

Latex generator of the labels


\documentclass[12pt,a4paper,oneside]{book}
%\newcommand \EN[1] {{#1}} % make the English version
\newcommand \EN[1] {{}} % suppress the English version
\newcommand \RU[1] {{#1}} % make the Russian version (in this document not supported)
%\newcommand \RU[1] {{}} % suppress the Russian version
%The Japanese version is not yet supported. While \JP is used to suppress several lines at once.
\newcommand \JP[1] {{}} % ореsuppress some text
%\usepackage[space]{cite }% If exist.
\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage[russian]{babel}
\usepackage{latexsym,amsmath,amssymb,amsbsy,graphicx}

\usepackage{rotating}
\usepackage{hyperref}
\usepackage{wrapfig}
\usepackage{geometry}
\paperwidth 216mm
\paperheight 216mm
\textwidth 550mm
\oddsidemargin -76pt
\topmargin -92pt
\textheight 457mm
\pagestyle{empty}

\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\parindent 0pt
\begin{document}

\begin{picture}(610,610)
\put(0,0){\ing{sqrt27a}}
\put(172,599){\sx{4}{$y$}}
\put(172,499){\sx{4}{$1$}}
\put(140,298){\sx{4}{$-1$}}
\put(140,198){\sx{4}{$-2$}}
\put(140, 98){\sx{4}{$-3$}}
%\put(160, 0){\sx{3.8}{$-4$}}
\put( -9,366){\sx{4}{$-2$}}
\put( 89,366){\sx{4}{$-1$}}
\put(300,366){\sx{4}{$1$}}
\put(401,366){\sx{4}{$2$}}
\put(502,366){\sx{4}{$3$}}
\put(592,370){\sx{4.2}{$x$}}
%\put(600,420){\sx{4.2}{$x$}}
\put(340,530){\sx{4.3}{\rot{5}$y\!=\!\mathrm{tet}_{\sqrt{2}}(x)$\ero}}
\put(380,200){\sx{4.2}{\rot{-45}$y\!=\!-x$\ero}}
\end{picture}

\end{document}

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