File:Sqrt27t.jpg

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) ; the English version is in preparation in 2015.

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

C++ generator of the First map
Files ado.cin, conto.cin, sqrt2f21e.cin should be loaded in order to compile the code below.

typedef std::complex z_type; // #include "conto.cin" // #include "tq2e.cin" //#include "f21E.cin"
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 6) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)
 * 1) include "ado.cin"
 * 1) 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"); 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");
 * 1) define M(x,y) fprintf(o,"%7.4f %7.4f M\n",0.+x,0.+y);
 * 2) define L(x,y) fprintf(o,"%7.4f %7.4f L\n",0.+x,0.+y);

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]   	% make the English version \newcommand \EN[1] –     	% suppress the English version \newcommand \RU[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}