File:Sqrt2sufuplot.png

Four superexponentials to base $\sqrt{2}$

Usage: this is figure 16.10 of the book Суперфункции (2014, In Russian) ; the English version is in preparation in 2015.

This image is used also in article .

C++ generator of the curves
Files ado.cin, conto.cin, sqrt2f21e.cin, sqrt2f23e.cin, sqrt2f43e.cin, sqrt2f45e.cin should be loaded in order to compile the code below.

typedef std::complex z_type; //#include "superex.cin" //#include "slog14128.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("sqrt23.eps","w"); ado(o,202,148); fprintf(o,"101 41 translate\n 10 10 scale\n"); M(0,-4.06)L(0,10.06) M(-10.06,0)L(10.06,0) fprintf(o,".03 W S\n"); for(n=-10;n<11;n++){if(n!=0){M(n,0)L(n,-.1)}} for(n= -4;n<11;n++){if(n!=0){M(0,n)L(-.1,n)}} fprintf(o,".03 W S\n"); M(-2,-4)L(-2,0) M(0,2)L(10,2) //M(-2,2)L(4,-4) M(-10,4)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) include "difapro.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 2 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<166;m+=5) { x=-10+sqrt(1.*m); z=x; y=Re(F45E(z)); if(m==0) M(x,y) else L(x,y)} fprintf(o,".03 W 1 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 sqrt23.eps"); system(   "open sqrt23.pdf"); getchar; system("killall Preview"); // For macintosh }

Latex generator of the labels
\documentclass[12pt]{article} \usepackage{geometry} \usepackage{graphicx} \usepackage{rotating} \paperwidth 424pt \paperheight 302pt \topmargin -106pt \oddsidemargin -73pt \textwidth 1064pt \textheight 1060pt \pagestyle {empty} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \newcommand \ing {\includegraphics} \parindent 0pt \pagestyle{empty} \begin{document} \sx{2.1}{\begin{picture}(146,142) %\put(10,10){\ing{IterPowPlot}} %\put(40,40){\ing{Itereq2tlo}} \put(0,0){\ing{sqrt23}} \put(95,139){\sx{.7}{$y$}} \put(95,119){\sx{.6}{$8$}} \put(95, 99){\sx{.6}{$6$}} \put(95, 79){\sx{.6}{$4$}} \put(95, 59){\sx{.6}{$2$}} \put(91, 19){\sx{.6}{$-2$}} \put( 17,35){\sx{.6}{$-\!8$}} \put( 37,35){\sx{.6}{$-\!6$}} \put( 57,35){\sx{.6}{$-\!4$}} \put( 77,35){\sx{.6}{$-\!2$}} \put(120,35){\sx{.6}{$2$}} \put(140,35){\sx{.6}{$4$}} \put(160,35){\sx{.6}{$6$}} \put(180,35){\sx{.6}{$8$}} \put(197.6,35){\sx{.7}{$x$}} % \put(110,93){\sx{.6}{$y\!=\!F_{4,5}(x)\!=\!\mathrm{SuExp}_{\sqrt{2},5}(x)$}} %\put(116, 88){\sx{.7}{$y\!=\!\mathrm{tet}(x)$}} \put(126, 69){\sx{.6}{$y\!=\!F_{2,3}(x)$, $y\!=\!F_{4,3}(x)$}} \put(126, 54){\sx{.6}{$y\!=\!F_{2,1}(x)\!=\!\mathrm{tet}_{\sqrt{2}}(x)$}} %\put(108, 44){\sx{.7}{$y\!=\!10^{24}w(x)$}} %\enp} \put(126,44){\sx{.6}{$y\!=\!10^{24} d_{42}(x)$}} \end{picture}} \end{document}