File:ExpIte4T.jpg - Revision history

T: $ -> \( ; description ; refs ; pre ; keywords

2025-12-15T13:38:08Z

$ -> \( ; description ; refs ; pre ; keywords

Maintenance script at 23:35, 30 November 2018

2018-11-30T23:35:43Z

T at 04:00, 28 July 2013

2013-07-28T04:00:35Z

T at 03:59, 28 July 2013

2013-07-28T03:59:56Z

Maintenance script at 00:44, 21 June 2013

2013-06-21T00:44:02Z

Maintenance script: Importing image file

2013-06-20T08:50:18Z

Importing image file

New page

Importing image file

@@ Line 1: / Line 1: @@
 ==[[C++]] generator of curves==
@@ Line 9: / Line 42: @@
 // Files [[ado.cin]], [[fsexp.cin]], [[fslog.cin]]
 //should be loaded to the working directory in order to compile the code below.
  #include <math.h>
  #include <stdio.h>
@@ Line 62: / Line 95: @@
        getchar(); system("killall Preview"); // For macintosh
+ }
 ==[[Latex]] Generator of labels==
-%<poem><nomathjax><nowiki> %<br>
+%<pre><br>
-% file *.pdf should be generated with the code above in order to compile the Latex document below. %<br>
+% file ExpIte4.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>
@@ Line 136: / Line 167: @@
 \end{picture} % <br>
 \end{document} % <br>
 ==References==
 [[Category:Book]]
@@ Line 166: / Line 212: @@
 [[Category:Arctetration]]
 [[Category:Superfunction]]
 [[Category:Transfer function]]

@@ Line 67: / Line 67: @@
 ==[[Latex]] Generator of labels==
-%<nowiki> %<br>
+%<poem><nomathjax><nowiki> %<br>
-% file PowPlo.pdf should be generated with the code above in order to compile the Latex document below. %<br>
+% file *.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>
@@ Line 136: / Line 136: @@
 \end{picture} % <br>
 \end{document} % <br>
-%</nowiki>
+%</nowiki></nomathjax></poem>
 ==References==
@@ Line 153: / Line 153: @@
 http://reference.wolfram.com/mathematica/ref/Nest.html Nest, Wolfram Mathematica 9 Documentation center, 2013
 [[Category:Exp]]
 [[Category:Log]]
 [[Category:Iteration]]
 [[Category:Iteration of exp]]
@@ Line 162: / Line 167: @@
 [[Category:Superfunction]]
 [[Category:Transfer function]]

@@ Line 137: / Line 137: @@
 \end{document} % <br>
 %</nowiki>
 [[Category:Exp]]

@@ Line 141: / Line 141: @@
 [[Category:Log]]
 [[Category:Iteration]]
 [[Category:Tetration]]
-[[Category:ArcTetration]]
+[[Category:Arctetration]]
 [[Category:Superfunction]]
 [[Category:Transfer function]]

← Older revision		Revision as of 00:44, 21 June 2013
Line 1:		Line 1:
		+	[[iteration]]s of [[exp]]: $y\!=\!\exp^n(x)$ for various values of $n$.
−	Importing image file
		+
		+	For non-integer values of $n$, the evaluation is performed using [[tetration]] and [[ArcTetration]] funcitons,
		+
		+	$y\!=\!\exp^n(x)=\mathrm{tet}\Big(n+\mathrm{ate}(x)\Big)$
		+
		+	==[[C++]] generator of curves==
		+
		+	// Files [[ado.cin]], [[fsexp.cin]], [[fslog.cin]]
		+	//should be loaded to the working directory in order to compile the 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.)
		+
		+	//#include "Tania.cin" // need for LambertW
		+	//#include "LambertW.cin" // need for AuZex
		+	//#include "SuZex.cin"
		+	//#include "AuZex.cin"
		+	#include "fsexp.cin"
		+	#include "fslog.cin"
		+
		+	// z_type tra(z_type z){ return exp(z)+z;}
		+	// z_type F(z_type z){ return log(suzex(z));}
		+	// z_type G(z_type z){ return auzex(exp(z));}
		+
		+	#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);
		+
		+	main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d; FILE *o;o=fopen("ExpIte4.eps","w"); ado(o,804,804);
		+	fprintf(o,"402 402 translate\n 100 100 scale\n");
		+	fprintf(o,"1 setlinejoin 2 setlinecap\n");
		+	for(n=-4;n<5;n++) {M(-4,n)L(4,n)}
		+	for(m=-4;m<5;m++) {M(m,-4)L(m,4)}
		+	// M(M_E,0)L(M_E,1) M(0,M_E)L(1,M_E)
		+	fprintf(o,".004 W S\n");
		+	// DO(m,700){x=.01 +.02*m; y=Re(LambertW(LambertW(x)));if(m==0) M(x,y) else L(x,y) if(x>12.03\|\|y>12.03) break;} fprintf(o,".033 W 1 0 0 RGB S\n");
		+	// DO(m,700){x=.01 +.02*m; y=Re(LambertW(x));if(m==0) M(x,y) else L(x,y) if(x>12.03\|\|y>12.03) break;} fprintf(o,".04 W 1 .5 0 RGB S\n");
		+	// M(0,0) L(12.03,12.03) fprintf(o,".04 W 0 1 0 RGB S\n");
		+	DO(m,700){x=-4.02+.02*m; y=exp(x); if(m==0) M(x,y) else L(x,y) if(x>4.03\|\|y>4.03) break;} fprintf(o,".032 W 0 1 0 RGB S\n");
		+	DO(m,700){x=-4.02+.02*m; y=exp(exp(x)); if(m==0) M(x,y) else L(x,y) if(x>4.03\|\|y>4.03) break;} fprintf(o,".032 W 0 1 0 RGB S\n");
		+	DO(m,700){x=-4.02+.02*m; y=exp(exp(exp(x)));if(m==0) M(x,y) else L(x,y) if(x>4.03\|\|y>4.03) break;} fprintf(o,".032 W 0 1 0 RGB S\n");
		+	DO(m,700){y=-4.02+.02*m; x=exp(y); if(m==0) M(x,y) else L(x,y) if(x>4.03\|\|y>4.03) break;} fprintf(o,".032 W 1 0 1 RGB S\n");
		+	DO(m,700){y=-4.02+.02*m; x=exp(exp(y)); if(m==0) M(x,y) else L(x,y) if(x>4.03\|\|y>4.03) break;} fprintf(o,".032 W 1 0 1 RGB S\n");
		+	DO(m,700){y=-4.02+.02*m; x=exp(exp(exp(y)));if(m==0) M(x,y) else L(x,y) if(x>4.03\|\|y>4.03) break;} fprintf(o,".032 W 1 0 1 RGB S\n");
		+	for(n=0;n<34;n+=1) {DO(m,700){x=-4.01 +.02m; y=Re(FSLOG(x)); y=Re(FSEXP(.1n+y)); if(m==0) M(x,y) else L(x,y) if(x>4.03\|\|y>4.03) break;}}
		+	for(n=-33;n<0;n+=1){t=Re(FSEXP( FSLOG(-4.)-.1*n));
		+	DO(m,700){x=t +.02m; y=Re(FSLOG(x)); y=Re(FSEXP(.1n+y)); if(m==0) M(x,y) else L(x,y) if(x>4.03\|\|y>4.03) break;}}
		+	fprintf(o,".01 W 0 0 0 RGB S\n");
		+	fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%'); fclose(o);
		+	system("epstopdf ExpIte4.eps");
		+	system( "open ExpIte4.pdf"); //for macintosh
		+	getchar(); system("killall Preview"); // For macintosh
		+	}
		+
		+
		+
		+	==[[Latex]] Generator of labels==
		+
		+	%<nowiki> %<br>
		+	% file PowPlo.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 806pt % <br>
		+	\paperheight 806pt % <br>
		+	\topmargin -105pt % <br>
		+	\oddsidemargin -73pt % <br>
		+	\textwidth 1100pt % <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}(802,802) % <br>
		+	%\put(10,10){\ing{PowPlo}} % <br>
		+	%\put(0,0){\ing{TraItu3}} % <br>
		+	\put(0,0){\ing{ExpIte4}} % <br>
		+	\put(411,788){\sx{3}{$y$}} % <br>
		+	\put(411,693.6){\sx{2.9}{$3$}} % <br>
		+	\put(411,593.4){\sx{2.9}{$2$}} % <br>
		+	\put(411,493.2){\sx{2.9}{$1$}} % <br>
		+	\put(411,393){\sx{2.9}{$0$}} % <br>
		+	\put(407,292.8){\sx{2.9}{$-1$}} % <br>
		+	\put(407,192.6){\sx{2.9}{$-2$}} % <br>
		+	\put(407,092.4){\sx{2.9}{$-3$}} % <br>
		+	% <br>
		+	\put(081,408){\sx{2.9}{$-3$}} % <br>
		+	\put(181,408){\sx{2.9}{$-2$}} % <br>
		+	\put(281,408){\sx{2.9}{$-1$}} % <br>
		+	\put(396,408){\sx{2.9}{$0$}} % <br>
		+	\put(497,408){\sx{2.9}{$1$}} % <br>
		+	\put(597,408){\sx{2.9}{$2$}} % <br>
		+	\put(697,408){\sx{2.9}{$3$}} % <br>
		+	\put(787,408){\sx{3}{$x$}} % <br>
		+	% <br>
		+	\put(6,748){\sx{3}{\rot{4}$n\!=\!3.2$\ero}} % <br>
		+	\put(6,708){\sx{3}{\rot{3}$n\!=\!3.1$\ero}} % <br>
		+	\put(6,675){\sx{3}{\rot{3}$n\!=\!3$\ero}} % <br>
		+	\put(5,643){\sx{3}{\rot{3}$n\!=\!2.9$\ero}} % <br>
		+	\put(6,345){\sx{3}{\rot{1}$n\!=\!0.6$\ero}} % <br>
		+	%
		+	\put(7,308){\sx{3}{\rot{4}$n\!=\!0.4$\ero}} % <br>
		+	\put(7,280){\sx{3}{\rot{5}$n\!=\!0.3$\ero}} % <br>
		+	\put(8,242){\sx{3}{\rot{9}$n\!=\!0.2$\ero}} % <br>
		+	\put(9,185){\sx{3}{\rot{11}$n\!=\!0.1$\ero}} % <br>
		+	% <br>
		+	\put(50,36){\sx{3}{\rot{45}$n\!=\!0$\ero}} % <br>
		+	% <br>
		+	\put(202,5){\sx{3}{\rot{76}$n\!=\!-0.1$\ero}} % <br>
		+	\put(263,5){\sx{3}{\rot{82}$n\!=\!-0.2$\ero}} % <br>
		+	\put(299,5){\sx{3}{\rot{84}$n\!=\!-0.3$\ero}} % <br>
		+	\put(691,5){\sx{3}{\rot{84}$n\!=\!-3$\ero}} % <br>
		+	\put(724,5){\sx{3}{\rot{83}$n\!=\!-3.1$\ero}} % <br>
		+	\put(764,5){\sx{3}{\rot{82}$n\!=\!-3.2$\ero}} % <br>
		+	% <br>
		+	\put(480,600){\sx{3.6}{\rot{69}$y\!=\!\exp(x)$\ero}} % <br>
		+	\put(641,630){\sx{3.4}{\rot{44}$y\!=\!x$\ero}} % <br>
		+	\put(650,484){\sx{3.6}{\rot{19}$y\!=\!\ln(x)$\ero}} % <br>
		+
		+	\end{picture} % <br>
		+	\end{document} % <br>
		+	%</nowiki>
		+
		+	[[Category:Exp]]
		+	[[Category:Log]]
		+	[[Category:Iteration]]
		+	[[Category:Tetration]]
		+	[[Category:ArcTetration]]
		+	[[Category:Superfunction]]
		+	[[Category:Transfer function]]
		+	[[Category:Explicit plot]]
		+	[[Category:C++]]
		+	[[Category:Latex]]