Difference between revisions of "File:Sqrt27t.jpg"

Fig.16.1 from page 216 of book «Superfinctions» ^[1], 2020.

This figure is used also as Рис.16.1 at page 219 of the Russian version «Суперфункции» ^[2], 2014.

This image is used also as figure 7a of article ^[3] in Mathematics of Computation, 2010.

The image shows the Explicit plot of tetration to base \(\sqrt{2}\)

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

The tеtration to this base is described also in Mathematics of Computation («Portrait of the four regular super-exponentials to base sqrt(2)»)^[3], 2010.

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}

Refereces

Keywords

«Base sqrt2», «Book», «BookPlot», «C++», «Explicit plot», «Exp», «Exponentiation», «Generator», «Latex», «Superfunction», «Superfunctions», «Tetration»,