File:ExpQ2plotT.png - Revision history

T: $ -> \(

2025-10-09T02:00:34Z

$ -> \(

Maintenance script at 23:35, 30 November 2018

2018-11-30T23:35:44Z

Show changes

Maintenance script at 00:43, 21 June 2013

2013-06-21T00:43:50Z

Maintenance script: Importing image file

2013-06-20T08:50:19Z

Importing image file

New page

Importing image file

@@ Line 1: / Line 1: @@
 <ref>
 http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html <br>
@@ Line 17: / Line 19: @@
 D.Kouznetsov, H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
 </ref>.
 ==References==
 http://en.wikipedia.org/wiki/Square_root_of_2
 http://en.wikipedia.org/wiki/Exponential_function
 ==C++ generator of curves==
  #include<math.h>
  #include<stdio.h>
@@ Line 50: / Line 69: @@
    getchar(); system("killall Preview");//for mac
+ }
 ==[[Latex]] generator of labels==
 % file ExpQ2plot.pdf should be generated with the code above in order to compile the Latex document below.<br>
 % Copyleft 2012 by Dmitrii Kouznetsov<br>
 \documentclass[12pt]{article}
 \usepackage{geometry}
@@ Line 100: / Line 119: @@
 \end{picture}}
 \end{document}
 [[Category:Book]]
 [[Category:BookPlot]]

← Older revision		Revision as of 00:43, 21 June 2013
Line 1:		Line 1:
		+	[[Explicit plot]] of [[exponential]] to base $b\!=\!\sqrt{2} \approx 1.414213562373095$
−	Importing image file
		+
		+	The thick curve: $y=\exp_b(x)$.
		+
		+	The thin line shows the identical funciton, $y\!=\!x$.
		+
		+	The [[fixed point]]s $L\!=\!2$ and $L\!=\!4$ are solutions of the equation
		+
		+	: $\exp_b(L)=L$
		+
		+	for $b=\sqrt{2}$.
		+
		+	Any of these fixed points can be used to construct a [[superexponential]] to base $\sqrt{2}~$
		+	<ref>
		+	http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html <br>
		+	http://tori.ils.uec.ac.jp/PAPERS/2010sqrt2.pdf
		+	D.Kouznetsov, H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
		+	</ref>.
		+
		+	==References==
		+	<references/>
		+
		+	http://en.wikipedia.org/wiki/Square_root_of_2
		+
		+	http://en.wikipedia.org/wiki/Exponential_function
		+
		+	==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 "ado.cin"
		+
		+	DB B=sqrt(2.);
		+
		+	main(){ int m,n; double x,y; FILE *o;
		+	o=fopen("ExpQ2plot.eps","w"); ado(o,1204,804);
		+	fprintf(o,"602 2 translate 100 100 scale\n");
		+	#define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
		+	#define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);
		+	for(m=-6;m<7;m++) {M(m,0)L(m,8)}
		+	for(m=0;m<9;m++) {M(-6,m)L(6,m)}
		+	fprintf(o,"2 setlinecap .01 W S\n 2 setlinecap 1 setlinejoin \n");
		+	for(m=0;m<123;m++){x=-6.1+.1m; y=exp(log(B)x); if(m==0)M(x,y) else L(x,y);} fprintf(o,".04 W .8 0 0 RGB S\n");
		+	M(-.1,-.1)L(6.1,6.1) fprintf(o,".016 W 0 0 0 RGB S\n\n");
		+	fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
		+	system("epstopdf ExpQ2plot.eps");
		+	system( "open ExpQ2plot.pdf");
		+	getchar(); system("killall Preview");//for mac
		+	}
		+
		+	==[[Latex]] generator of labels==
		+
		+	%<nowiki> %<br>
		+	% file IterPowPlot.pdf should be generated with the code above in order to compile the Latex document below. %<br>
		+	% Copyleft 2012 by Dmitrii Kouznetsov <br> %
		+	\documentclass[12pt]{article} % <br>
		+	\usepackage{geometry} % <br>
		+	\usepackage{graphicx} % <br>
		+	\usepackage{rotating} % <br>
		+	\paperwidth 1210pt % <br>
		+	\paperheight 840pt % <br>
		+	\topmargin -96pt % <br>
		+	\oddsidemargin -81pt % <br>
		+	\textwidth 1200pt % <br>
		+	\textheight 1100pt % <br>
		+	\pagestyle {empty} % <br>
		+	\newcommand \sx {\scalebox} % <br>
		+	\newcommand \rot {\begin{rotate}} % <br>
		+	\newcommand \ero {\end{rotate}} % <br>
		+	\newcommand \ing {\includegraphics} % <br>
		+	\parindent 0pt% <br>
		+	\pagestyle{empty} % <br>
		+	\begin{document} % <br>
		+	\begin{picture}(1202,804) % <br>
		+	%\put(10,10){\ing{ExpQ2plot}} % <br>
		+	\put(590,792){\sx{4.2}{$y$}} % <br>
		+	\put(590,698){\sx{4.2}{$7$}} % <br>
		+	\put(590,598){\sx{4.2}{$6$}} % <br>
		+	\put(590,498){\sx{4.2}{$5$}} % <br>
		+	\put(590,398){\sx{4.2}{$4$}} % <br>
		+	\put(590,298){\sx{4.2}{$3$}} % <br>
		+	\put(590,198){\sx{4.2}{$2$}} % <br>
		+	\put(590,098){\sx{4.2}{$1$}} % <br>
		+	% <br>
		+	\put(080,-22){\sx{4}{$-5$}} % <br>
		+	\put(180,-22){\sx{4}{$-4$}} % <br>
		+	\put(281,-22){\sx{4}{$-3$}} % <br>
		+	\put(381,-22){\sx{4}{$-2$}} % <br>
		+	\put(482,-22){\sx{4}{$-\!1$}} % <br>
		+	%
		+	\put(603.6,-22){\sx{4}{$0$}} % <br>
		+	\put(703.7,-22){\sx{4}{$1$}} % <br>
		+	\put(803.8,-22){\sx{4}{$2$}} % <br>
		+	\put(903.9,-22){\sx{4}{$3$}} % <br>
		+	\put(1004.0,-22){\sx{4}{$4$}} % <br>
		+	\put(1104.1,-22){\sx{4}{$5$}} % <br>
		+	\put(1192.2,-22){\sx{4.3}{$x$}} % <br>
		+	% <br>
		+	\put(1034,490){\sx{5.6}{\rot{66}$y\!=\!\exp_{_{\!\!\sqrt{2}}}(x)$\ero}} % <br>
		+	\put(1094,444){\sx{5.7}{\rot{45}$y\!=\!x$\ero}} % <br>
		+	%\put(890,316){\sx{4.5}{\rot{45}$y\!=\!x$\ero}} % <br>
		+	%\put(830,164){\sx{4.5}{\rot{44}$y\!=\!\exp_{\sqrt{2}}(x)$\ero}} % <br>
		+
		+	%\put(670,125){\sx{6}{\rot{24}$y\!=\!(\sqrt{2})^x$\ero}} % <br>
		+	%\put(630,164){\sx{6}{\rot{33}$y\!=\!\exp_{\sqrt{2}}(x)$\ero}} % <br>
		+	%\put(690,36){\sx{6}{\rot{45}$y\!=\!x$\ero}} % <br>
		+	\put(10,10){\ing{ExpQ2plot}} % <br>
		+	\end{picture} % <br>
		+	\end{document} % <br>
		+	%</nowiki>
		+
		+	[[Category:Exponential]]
		+	[[Category:Fixed point]]
		+	[[Category:Transfer function]]
		+	[[Category:SuperFunctions]]
		+	[[Category:AbelFunctions]]
		+	[[Category:Explicit plot]]
		+	[[Category:C++]]
		+	[[Category:Latex]]