Difference between revisions of "File:Sqrt23uplot.jpg"

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Explicit plot of the growing superexponential to base $\sqrt{2}$ , thick curve,
−
Importing image file
  
  +
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]]
  +
<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. Суперфунцкии. Lambert Academic Publishing,
  +
2014.
  +
</ref><ref>
  +
http://www.ils.uec.ac.jp/~dima/BOOK/437.pdf<br>
  +
http://mizugadro.mydns.jp/BOOK/437.pdf
  +
Dmitrii Kouznetsov. Superfunctions. 2015, in preparation
  +
</ref>.
  +
  +
==References==
  +
<references/>
  +
==[[C++]] generator of curves==
  +
<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 "ado.cin"
  +
#include "sqrt2f21e.cin"
  +
#include "sqrt2f23e.cin"
  +
#include "sqrt2f43e.cin"
  +
#include "sqrt2f45e.cin"
  +
//#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");
  +
#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,-.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");
  +
  +
/*
  +
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
  +
}
  +
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of labels==
  +
<poem><nomathjax><nowiki>
  +
\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}
  +
  +
</nowiki></nomathjax></poem>
  +
  +
[[Category:Book]]
  +
[[Category:C++]]
  +
[[Category:Explicit plot]]
  +
[[Category:Superfunction]]
  +
[[Category:Base sqrt2]]
  +
[[Category:BookPlot]]

Latest revision as of 08:52, 1 December 2018

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 [1][2].

References

  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. Суперфунцкии. Lambert Academic Publishing, 2014.
  2. ↑ http://www.ils.uec.ac.jp/~dima/BOOK/437.pdf
    http://mizugadro.mydns.jp/BOOK/437.pdf Dmitrii Kouznetsov. Superfunctions. 2015, in preparation

C++ generator of curves


 #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 "ado.cin"
#include "sqrt2f21e.cin"
#include "sqrt2f23e.cin"
#include "sqrt2f43e.cin"
#include "sqrt2f45e.cin"
//#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");
#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,-.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");

/*
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}

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