File:Sqrt23uplot.jpg

Explicit plot of the growing superexponential to base $\sqrt{2}$, thick curve, and the exponential to this base, thin curve:

$y=\mathrm{SuExp}_{\sqrt{2},5}(x)$

and

$y=\exp_{\sqrt{2}}(x)$

Usage
This image is used as figure 9.4 of books Суперфункции (Russian version) and Superfunctions .

C++ generator of curves
typedef std::complex z_type; //#include "superex.cin" //#include "slog14128.cin" //#include "difapro.cin" int main{ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; // FILE *o;o=fopen("rearea1.eps","w");  ado(o,202,148); FILE *o;o=fopen("sqrt23uplo.eps","w"); ado(o,808,2208); fprintf(o,"404 4 translate\n 100 100 scale\n"); M(0,-.06)L(0,20.4) M(-4.,0)L(4.01,0) fprintf(o,"2 setlinecap .03 W S\n"); for(m=-4;m<5;m++){if(m!=0){M(m,0)L(m,20)}} for(n= 0;n<21;n++){if(n!=0){M(-4,n)L(4,n)}} fprintf(o,".003 W S\n"); //M(-2,-4)L(-2,0) //M(0,2)L(10,2) //M(-2,2)L(4,-4) //M(-5,4)L(0,4) //fprintf(o,".01 W S\n");
 * 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.)
 * 4) include "ado.cin"
 * 5) include "sqrt2f21e.cin"
 * 6) include "sqrt2f23e.cin"
 * 7) include "sqrt2f43e.cin"
 * 8) include "sqrt2f45e.cin"
 * 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< 84;   m+=4) { x=-1.84+.01*m; z=x;  y=Re(F21E(z)); if(m==0) M(x,y) else L(x,y)} for(m=0;m<511;  m+=10){ x=-1. +.01*m; z=x; y=Re(F21E(z)); L(x,y)} for(m=520;m<1101;m+=20){ x=-1. +.01*m; z=x; y=Re(F21E(z)); L(x,y)} fprintf(o,".05 W 0 0 1 RGB S\n");

//for(m=0;m<201;m+=5) { x=-10+.1*m; z=x; y=Re(F23E(z)); if(m==0) M(x,y) else L(x,y)} //fprintf(o,".05 W 0 .8 0 RGB S\n");

// //for(m=0;m<201;m+=5) { x=-10+.1*m; z=x; y=Re(F43E(z)); if(m==0) M(x,y) else L(x,y)} // //fprintf(o,".02 W .5 0 .5 RGB S\n");

//for(m=0;m<300;m++) { x=-4.1+sqrt(1.+m); z=x; y=Re(F45E(z)); if(m==0) M(x,y) else L(x,y) for(m=0;m<100;m++){ x=-5.+.1*m; z=x; y=Re(F45E(z)); if(m==0) M(x,y) else L(x,y) if(y>22.) break;} fprintf(o,".07 W 0 0 .5 RGB S\n");

for(m=0;m<100;m++){ x=-5.+.1*m; y=exp(log(sqrt(2.))*x); if(m==0) M(x,y) else L(x,y) if(y>22.) break;} fprintf(o,".02 W .5 0 0 RGB S\n");

// //for(m=0;m<386;m+=5) { x=-1.984+.01*m; z=x; y=Re(FSEXP(z)); if(m==0) M(x,y) else L(x,y)} // //fprintf(o,".07 W 0 1 1 RGB S\n");

// //for(m=0;m<145;m+=2) { y=-4+.1*m; z=z_type(y,0.); x=Re(FSLOG(z)); if(m==0) M(x,y) else L(x,y)} // //fprintf(o,".012 W 0 0 0 RGB S\n");

/* DO(m,502){     x=-10.+.04*m; z=z_type(x,0.); c=difapro(z); y=Re(c)*1.e24; if(m==0) M(x,y) else L(x,y)} fprintf(o,".02 W .6 0 .6 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o); system("epstopdf sqrt23uplo.eps"); system(   "open sqrt23uplo.pdf"); getchar; system("killall Preview"); // For macintosh }

Latex generator of labels
\documentclass[12pt]{article} \usepackage{geometry} \usepackage{graphicx} \usepackage{rotating} \paperwidth 810pt \paperheight 2262pt \topmargin -103pt \oddsidemargin -72pt \textwidth 1064pt \textheight 2440pt \pagestyle {empty} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \ing {\includegraphics} \parindent 0pt \pagestyle{empty} \begin{document} %\begin{picture}(808,1408) \begin{picture}(808,2210) \put(0,0){\ing{sqrt23uplo}} \put(368,2090){\sx{4.4}{$y$}} \put(350,1992){\sx{4.4}{$20$}} \put(350,1892){\sx{4.4}{$19$}} \put(350,1792){\sx{4.4}{$18$}} \put(350,1692){\sx{4.4}{$17$}} \put(350,1592){\sx{4.4}{$16$}} \put(350,1492){\sx{4.4}{$15$}} \put(350,1392){\sx{4.4}{$14$}} \put(350,1292){\sx{4.4}{$13$}} \put(350,1192){\sx{4.4}{$12$}} \put(350,1092){\sx{4.4}{$11$}} \put(350,992){\sx{4.4}{$10$}} \put(370,892){\sx{4.4}{$9$}} \put(370,792){\sx{4.4}{$8$}} \put(370,692){\sx{4.4}{$7$}} \put(370,592){\sx{4.4}{$6$}} \put(370,491){\sx{4.4}{$5$}} \put(370,391){\sx{4.4}{$4$}} \put(370,290){\sx{4.4}{$3$}} \put(370,190){\sx{4.4}{$2$}} \put(370,90){\sx{4.4}{$1$}} \put(64,-36){\sx{4.4}{$-3$}} \put(164,-36){\sx{4.4}{$-2$}} \put(264,-36){\sx{4.4}{$-1$}} \put(394,-36){\sx{4.4}{$0$}} \put(494,-36){\sx{4.4}{$1$}} \put(594,-36){\sx{4.4}{$2$}} \put(694,-36){\sx{4.4}{$3$}} \put(782,-36){\sx{4.4}{$x$}}%\put(546,654){\sx{4.5}{\rot{72}$y\!=\!\mathrm{SuExp}_{\sqrt{2},5}(x)$\ero}} \put(644,644){\sx{4.5}{\rot{76}$y\!=\!\mathrm{SuExp}_{\sqrt{2},5}(x)$\ero}} \put(564,194){\sx{5.4}{\rot{45}$y\!=\!\exp_{\sqrt{2}}(x)$\ero}} \end{picture} \end{document}