Difference between revisions of "File:Tetreal10bx10d.png"

From TORI
Jump to navigation Jump to search
 
(2 intermediate revisions by the same user not shown)
Line 22: Line 22:
 
This image is used as figure 17.2 of book
  
This image is used as figure 17.2 of book
 
[[Superfunctions]]
  
[[Superfunctions]]
  +
<ref>https://www.morebooks.de/store/gb/book/superfunctions/isbn/978-620-2-67286-3 <br>
−
<ref>
  
−
http://mizugadro.mydns.jp/BOOK/444.pdf
 +
http://mizugadro.mydns.jp/BOOK/466.pdf
−
D.Kouznetsov. Superfunctions.
+
D.Kouznetsov. Superfunctions. [[Lambert Academic Publishing]], 2020.
 
</ref>.
  
</ref>.
   
Line 204: Line 204:
   
 
http://mizugadro.mydns.jp/BOOK/466.pdf
  
http://mizugadro.mydns.jp/BOOK/466.pdf
−
D.Kouznetoov. Superfunctions. 2015-2014.
 +
D.Kouznetoov. Superfunctions. [[Lambert Academic Publishing]], 2020.
   
 
[[Category:Book]]
  
[[Category:Book]]

Latest revision as of 13:56, 5 August 2020

Plot of Tetration: $y=\mathrm{tet}_b(x)$ versus $x$ for

$b \rightarrow 1$,
$b = 1.1$,
$b = 1.2$,
$b = 1.3$,
$b = 1.4$,
$b = \sqrt{2}\approx 1.41,$
$b = \exp(1/ \mathrm e) \approx 1.44,$
$b = 1.5$,
$b = 1.6$,
$b = 1.7$,
$b = 1.8$,
$b = 1.9$,
$b = 2$,
$b = \mathrm e \approx 2.71$,
$b = 10$,
$b \rightarrow \infty$.

The fit is used, that provides several decimal digits, that seems to be sufficient to provide the "camera-ready copy"; the errors of the fitting are not seen even at the zooming-in.

This image is used as figure 17.2 of book Superfunctions [1].

Copyleft 2010 by Dmitrii Kouznetsov: Please attribute the source at the reuse: it helps to trace mistakes, if any

C++ generator of curves

// Files GLxw2048.inc, f2048ten.inc, f4ten.cin, fit1.cin should be loaded to the working directory in order to compile the C++ code below: 

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
using namespace std;
#include <complex>
typedef complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)

//b=10
#include "f4ten.cin"

#include "fit1.cin"

void ado(FILE *O, int X, int Y)
{      fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
       fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
       fprintf(O,"/M {moveto} bind def\n");
       fprintf(O,"/L {lineto} bind def\n");
       fprintf(O,"/S {stroke} bind def\n");
       fprintf(O,"/s {show newpath} bind def\n");
       fprintf(O,"/C {closepath} bind def\n");
       fprintf(O,"/F {fill} bind def\n");
       fprintf(O,"/o {.1 0 360 arc C S} bind def\n");
       fprintf(O,"/times-Roman findfont 20 scalefont setfont\n");
       fprintf(O,"/W {setlinewidth} bind def\n");
       fprintf(O,"/RGB {setrgbcolor} bind def\n");}
 //#include "ado.cin"

#define M(x,y) fprintf(o,"%6.4f %6.4f M\n",0.+x,0.+y);
#define L(x,y) fprintf(o,"%6.4f %6.4f L\n",0.+x,0.+y);
#define o(x,y) fprintf(o,"%6.4f %6.4f o\n",0.+x,0.+y);

main(){ int j,k,m,n; DB p,q,t1,t3,u,v,w,x,y; z_type z,c,d;
FILE *o;o=fopen("tet10bx.eps","w");ado(o,134,124);
fprintf(o,"22 22 translate\n 10 10 scale\n");
fprintf(o,"2 setlinecap\n");
for(m=-2;m<12;m++){if(m!=0){M(m,-2)L(m,10)}} 
for(n= -2;n<11;n++){if(n!=0){M(-2,n)L(11,n)}}  fprintf(o,".006 W 0 0 0 RGB S\n");
M(-2,0)L(11.1,0) M(0, -2)L(0,10.1)             fprintf(o,".03  W 0 0 0 RGB S\n");
M(0,M_E)L(11.,M_E)                             fprintf(o,".006  W 0 0 0 RGB S\n"); 
fprintf(o,"1 setlinejoin 1 setlinecap\n");

//DO(m,400){x=-1.99+.008*m;y=Re(FIT1(log(10.),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W .5 0 .5 RGB S\n");
DO(m,400){x=-1.80+.02*m; y=Re(FIT1(log(2.),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W .5 0 .5 RGB S\n");
DO(m,400){x=-1.78+.02*m; y=Re(FIT1(log(1.9),x)); if(y>10.33) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.77+.02*m; y=Re(FIT1(log(1.8),x)); if(y>10.33) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.74+.02*m; y=Re(FIT1(log(1.7),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.72+.03*m; y=Re(FIT1(log(1.6),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.68+.04*m; y=Re(FIT1(log(1.5),x)); if(y>10.3) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.64+.04*m; y=Re(FIT1(log(1.4),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.58+.04*m; y=Re(FIT1(log(1.3),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.52+.04*m; y=Re(FIT1(log(1.2),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
DO(m,400){x=-1.42+.04*m; y=Re(FIT1(log(1.1),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 .5 0 RGB S\n");
//
DO(m,400){x=-1.65+.04*m; y=Re(FIT1(1./M_E,x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W 0 0 .7 RGB S\n");
DO(m,400){x=-1.64+.04*m; y=Re(FIT1(log(sqrt(2.)),x)); if(x>11.1) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".03 W .8 0 0 RGB S\n");
DO(m,400){x=-1.873+.01*m; y=Re(FIT1(1.,x)); if(y>11) break; if(m==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 0 RGB S\n");
//
DO(m,401){x=-1.987+.01*m;y=Re(F4TEN(x));if(m==0)M(x,y)else L(x,y)}fprintf(o,".02 W .5 0 .5 RGB S\n");
//DO(m,39){x=-1.89+.098*m; y=Re(FSEXP(x));if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
//DO(m,48){x=-1.82+.0973*m; y=Re(F2(x));       if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
//DO(m,126){x=-1.72+.1*m; y=Re(F15(x));        if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
//DO(m,130){x=-1.65+.1*m; y=Re(E1ETF(x));      if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
//DO(m,130){x=-1.64+.1*m; y=Re(f21E(x));       if(m==0)M(x,y)else L(x,y)} fprintf(o,".01 W 0 0 0 RGB S\n");
M(-1.998,-2)L(-1.992,-.01)L(-1,0)L(-.01,.01)L(0,1)L(.012,10.1)  fprintf(o,".02 W .4 0 .8 RGB S\n");
M(-1.01,-2)L(-1,0)L(-.99,.99)L(0,1)L(10.97,1.01)        fprintf(o,".02 W .2 .4 0 RGB S\n");
fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
       system("epstopdf tet10bx.eps");
       system(    "open tet10bx.pdf"); //mac
//     system(    "xpdf tet10bx.pdf"); // linux
getchar(); system("killall Preview");// mac
}

Latex generator of labels

% File tet10bx.pdf sould be generated with code above in order to compile the Latex document below %

%


\documentclass[12pt]{article} % <br>
\usepackage{geometry} % See geometry.pdf % <br>
\geometry{letterpaper} % ... or a4paper or a5paper or ... ??% <br>
\usepackage{graphicx}% <br>
\usepackage{amssymb}% <br>
\usepackage{hyperref}% <br>
\usepackage{rotating}% <br>
\usepackage[utf8x]{inputenc}% <br>
\usepackage[english,russian]{babel}% <br>
\usepackage{color}% <br>
\definecolor{red}{rgb}{1,0.1,0.1}% <br>
\definecolor{black}{rgb}{0,0,0}% <br>
\definecolor{white}{rgb}{1,1,1}% <br>
\definecolor{yellow}{rgb}{1,.93,0}% <br>
\definecolor{bluedark}{rgb}{0,0,.87}% <br>
\paperwidth 528pt% <br>
\paperheight 488pt% <br>
\topmargin -102pt% <br>
\oddsidemargin -78pt% <br>
\textwidth 610pt% <br>
\textheight 570pt% <br>
% <br>
\newcommand \sx {\scalebox}% <br>
\newcommand \ing {\includegraphics}% <br>
\newcommand \tet {\mathrm{tet}}% <br>
\newcommand \pen {\mathrm{pen}}% <br>
\newcommand \bC {\mathbb C}% <br>
\newcommand \fac {\mathrm {Factorial}}% <br>
\newcommand \rme {\mathrm e}% <br>
\newcommand \rmi {\mathrm i}% <br>
\newcommand \ds {\displaystyle}% <br>
\newcommand \rot {\begin{rotate}}% <br>
\newcommand \ero {\end{rotate}}% <br>
% <br>
\begin{document}% <br>
\parindent 0pt% <br>
\sx{4}% <br>
{\normalsize% <br>
\begin{picture}(155,122)% <br>
\put(0,0){\ing{tet10bx}}% <br>
%\put(-2,125){\sx{.7}{$y\!=\!{\rm tet}_{b}(x)$ ~as solution of~ $F(z\!+\!1)=\exp_b(F(z))$ ~,~ $F(0)\!=\!1$}}% <br>
%\put( 0,125){\sx{.55}{$y\!=\!F(x)$ ~as solution of~ $F(z\!+\!1)\!=\!\exp_b(F(z))$ ,~ $F(0)\!=\!1$}}% <br>
\put( 17,120){\sx{.6}{$y$}}% <br>
\put( 17,100){\sx{.6}{$8$}}% <br>
\put( 17,80){\sx{.6}{$6$}}% <br>
\put( 17,60){\sx{.6}{$4$}}% <br>
\put( 18,48){\sx{.6}{e}}% <br>
\put( 17,40){\sx{.6}{$2$}}% <br>
\put( 17,20){\sx{.6}{$0$}}% <br>
\put( 20.4,16){\sx{.6}{$0$}}% <br>
\put( 40.4,16){\sx{.6}{$2$}}% <br>
\put( 60.4,16){\sx{.6}{$4$}}% <br>
\put( 80.4,16){\sx{.6}{$6$}}% <br>
\put(100.4,16){\sx{.6}{$8$}}% <br>
\put(119,16){\sx{.6}{$10$}}% <br>
\put(128.6,16.2){\sx{.6}{$x$}}% <br>
%\put(2,90){\sx{.9}{$y\!=\!e\!\big(F_{1}(x\!+\!\rmi o)\big)$}}% <br>
%\put(183,105){\sx{1.}{$y\!=\!F_{3}(x)$}}% <br>
%\put(193,52){\sx{1.}{$y\!=\!\rme$}}% <br>
\put(26.6,86){\sx{.5}{\rot{90} $b\!\rightarrow\!\infty$ \ero } }% <br>
\put(31,106){\sx{.5}{\rot{88} $b\!=\!10$ \ero } }% <br>
%\put(39.2,106){\sx{.5}{\rot{86} $b\!=\! 3$ \ero } }% <br>
\put(42,87){\sx{.5}{\rot{87} $b\!=\! \rme$ \ero } }% <br>
\put(48.4,106){\sx{.5}{\rot{86} $b\!=\!2$ \ero } }% <br>
\put(53.3,106){\sx{.45}{\rot{85} $b\!=\!1.9$ \ero } }% <br>
\put(60.3,106){\sx{.45}{\rot{85} $b\!=\!1.8$ \ero } }% <br>
\put(68.4,106){\sx{.45}{\rot{84} $b\!=\!1.7$ \ero } }% <br>
\put(83,106){\sx{.45}{\rot{83} $b\!=\!1.6$ \ero } }% <br>
\put(128,106){\sx{.47}{\rot{80} $b\!=\!1.5$ \ero } }% <br>
%\put(55,88){\sx{1.3}{$y\!=\!\tet_b(x)$ } }% <br>
%\put(124,106){\sx{.6}{$b\!=\!1.5$}}% <br>
\put(109,46){\sx{.4}{\rot{2}$b\!=\!\exp(1/\rme)$\ero}}% <br>
\put(120,41.8){\sx{.34}{$b\!=\!\sqrt{2}$}}% <br>
\put(120,38){\sx{.36}{$b\!=\!1.4$}}% <br>
\put(120,33.6){\sx{.36}{$b\!=\!1.2$}}% <br>
%\put(115,29.6){\sx{.36}{$b\!=\!1.1$}}% <br>
\put(123,29){\sx{.36}{$b\!\rightarrow\!1$}}% <br>
\end{picture}}% <br>
\end{document}

References

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. Суперфункции. Lambert Academic Publishing, 2014. (In Russian), Figure 17.1.

http://mizugadro.mydns.jp/BOOK/466.pdf D.Kouznetoov. Superfunctions. Lambert Academic Publishing, 2020.

  1. ↑ https://www.morebooks.de/store/gb/book/superfunctions/isbn/978-620-2-67286-3
    http://mizugadro.mydns.jp/BOOK/466.pdf D.Kouznetsov. Superfunctions. Lambert Academic Publishing, 2020.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current17:50, 20 June 2013Thumbnail for version as of 17:50, 20 June 20132,192 × 2,026 (436 KB)Maintenance script (talk | contribs)Importing image file

You cannot overwrite this file.

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Retrieved from "https://mizugadro.mydns.jp/t/index.php?title=File:Tetreal10bx10d.png&oldid=34913"