File:IterPowPlotT.jpg

#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 "ado.cin"

DB B=2.;
DB F(DB z) { return exp( exp( log(B)*z));}
DB G(DB z) { return log( log(z) )/log(B);}

DB T(DB z) { return exp(B*log(z));}
DB U(DB z) { return exp(log(z)/B);}

int main(){ int m,n; double x,y,t; FILE *o;
o=fopen("IterPowPlot.eps","w"); ado(o,1010,1010);
fprintf(o,"1 1 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);

M(0,0)L(10,10)fprintf(o,"1 setlinecap 1 setlinejoin .03 W 0 0 1 RGB S\n");

M(0,0)L(.995,.01)L(1.013,10)
fprintf(o,"1 setlinecap 1 setlinejoin .03 W 0 .8 0 RGB S\n");

M(0,0)L(.01,.995)L(10,1.013)
fprintf(o,"1 setlinecap 1 setlinejoin .03 W .8 0 .8 RGB S\n");

for(m=0;m<11;m++) {M(m,0)L(m,10)}
for(m=0;m<11;m++) {M(0,m)L(10,m)}
fprintf(o,"2 setlinecap .01 W 0 0 0 RGB S\n");

//DO(m,42){x=0.001+.1*m; y=exp(2.*log(x)); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 0 1 0 RGB S\n");
//DO(m,1002){x=0.001+.01*m; y=exp(.5*log(x)); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 1 0 1 RGB S\n");

DO(m,42){x=0.001+.1*m; y=T(T(T(x))); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 0 1 0 RGB S\n");
DO(m,42){x=0.001+.1*m; y=T(T(x)); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 0 1 0 RGB S\n");
DO(m,42){x=0.001+.1*m; y=T(x); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 0 1 0 RGB S\n");
DO(m,1002){x=0.001+.01*m; y=U(x); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 1 0 1 RGB S\n");
DO(m,1002){x=0.001+.01*m; y=U(U(x)); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 1 0 1 RGB S\n");
DO(m,1002){x=0.001+.01*m; y=U(U(U(x))); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 1 0 1 RGB S\n");

for(n=-20;n<21;n++){t=.1*n; DO(m,92){x=1+.1*m; y=F(t+G(x)); if(m==0) M(x,y) else L(x,y); if(y>10.1)break;} }
fprintf(o,"1 setlinecap 1 setlinejoin .02 W 0 0 0 RGB S\n");

 fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
       system("epstopdf IterPowPlot.eps");
       system( "open IterPowPlot.pdf");
       getchar(); system("killall Preview");
 }

\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{graphicx}
\usepackage{rotating}
\paperwidth 1008pt
\paperheight 1008pt
\topmargin -94pt
\oddsidemargin -81pt
\textwidth 1100pt
\textheight 1100pt
\pagestyle {empty}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\parindent 0pt
\pagestyle{empty}
\begin{document}
\begin{picture}(1002,1002)
%\put(10,10){\ing{IterPowPlot}}
%\put(10,10){\ing{PowIte}}
\put(10,10){\ing{IterPowPlot}}
%\put(11,976){\sx{4}{$y\!=\!\mathrm{pow}_2^c(x)$}}
%\put(11,976){\sx{4}{$y\!=\!x^{2^n}$}}
\put(11,976){\sx{4}{$x^{2^n}$}}
\put(11,898){\sx{4}{$9$}}
\put(11,798){\sx{4}{$8$}}
\put(11,698){\sx{4}{$7$}}
\put(11,598){\sx{4}{$6$}}
\put(11,498){\sx{4}{$5$}}
\put(11,398){\sx{4}{$4$}}
\put(11,298){\sx{4}{$3$}}
\put(11,198){\sx{4}{$2$}}
\put(11,098){\sx{4}{$1$}}
 
\put(100,16){\sx{4}{$1$}}
\put(200,16){\sx{4}{$2$}}
\put(301,16){\sx{4}{$3$}}
\put(401,16){\sx{4}{$4$}}
\put(502,16){\sx{4}{$5$}}
\put(602,16){\sx{4}{$6$}}
\put(703,16){\sx{4}{$7$}}
\put(803,16){\sx{4}{$8$}}
\put(903,16){\sx{4}{$9$}}
\put(990,16){\sx{4}{$x$}}
 
\put(112,850){\sx{3.8}{\rot{90}$n\!\rightarrow \infty $\ero}}
\put(152,866){\sx{3.8}{\rot{88}$n\!=\!3$\ero}}
\put(191,870){\sx{3.8}{\rot{87}$n\!=\!2$\ero}}
\put(325,921){\sx{3.8}{\rot{81}$n\!=\!1$\ero}}
\put(461,893){\sx{3.6}{\rot{70}$n\!=\!0.6$\ero}}
\put(509,894){\sx{3.6}{\rot{69}$n\!=\!0.5$\ero}}
\put(563,895){\sx{3.6}{\rot{63}$n\!=\!0.4$\ero}}
\put(630,897){\sx{3.6}{\rot{59}$n\!=\!0.3$\ero}}
\put(713,900){\sx{3.6}{\rot{54}$n\!=\!0.2$\ero}}
\put(826,913){\sx{3.6}{\rot{50}$n\!=\!0.1$\ero}}
 
\put(928,932){\sx{3.8}{\rot{45}$n\!=\!0$\ero}}

\put(894,778){\sx{3.6}{\rot{39}$n\!=\!-0.1$\ero}}
\put(888,676){\sx{3.6}{\rot{33}$n\!=\!-0.2$\ero}}
\put(884,596){\sx{3.6}{\rot{28}$n\!=\!-0.3$\ero}}
\put(877,528){\sx{3.6}{\rot{24}$n\!=\!-0.4$\ero}}
\put(871,476){\sx{3.6}{\rot{19}$n\!=\!-0.5$\ero}}
\put(870,429){\sx{3.6}{\rot{17}$n\!=\!-0.6$\ero}}
 
\put(890,297){\sx{3.8}{\rot{8}$n\!=\!-1$\ero}}
\put(884,172){\sx{3.8}{\rot{1}$n\!=\!-2$\ero}}
\put(881,132){\sx{3.8}{\rot{.3}$n\!=\!-3$\ero}}
\put(852,100){\sx{3.6}{\rot{.1}$n\!\rightarrow - \infty$\ero}}
\end{picture}
\end{document}