File:IterEq2plotT.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"

 #include "F45E.cin"
 #include "F45L.cin"

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

int main(){ int m,n; double x,y,t; FILE *o;
 o=fopen("IterEq2plot.eps","w"); ado(o,1420,1420);
 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(0,1.99)L(3.995,2.01)L(4.02,24)
fprintf(o,"1 setlinecap 1 setlinejoin .03 W 0 .8 0 RGB S\n");
M(1.99,0)L(2.01,3.995)L(14,4.02)
fprintf(o,"1 setlinecap 1 setlinejoin .03 W .8 0 .8 RGB S\n");
M(0,0)L(14,14)
fprintf(o,"1 setlinecap 1 setlinejoin .04 W 0 0 1 RGB S\n");

 for(m=0;m<15;m++) {M(m,0)L(m,14)}
 for(m=0;m<15;m++) {M(0,m)L(14,m)}
 fprintf(o,"2 setlinecap .01 W 0 0 0 RGB S\n");
 DO(m,82){x=0.001+.1*m;y=exp(log(B)*x); y=exp(log(B)*y); y=exp(log(B)*y); y=exp(log(B)*y); if(m==0)M(x,y) else L(x,y); if(y>15.1) break;}
 DO(m,82){x=0.001+.1*m; y=exp(log(B)*x);y=exp(log(B)*y); y=exp(log(B)*y); if(m==0) M(x,y) else L(x,y);if(y>15.1) break;} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 0 1 0 RGB S\n");
 DO(m,82){x=0.001+.1*m; y=exp(log(B)*x); y=exp(log(B)*y); 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,82){x=0.001+.1*m; y=exp(log(B)*x); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W 0 .9 0 RGB S\n");
 DO(m,141){x=0.001+.1*m; y=log(x)/log(B); if(m==0)M(x,y) else L(x,y);} fprintf(o,"1 setlinecap 1 setlinejoin .04 W .9 0 .9 RGB S\n");
 DO(m,131){x=1.41+.1*m;y=log(x)/log(B);y=log(y)/log(B); if(m==0)M(x,y) else L(x,y);}
 DO(m,131){x=1.63+.1*m;y=log(x)/log(B);y=log(y)/log(B);y=log(y)/log(B); if(m==0)M(x,y) else L(x,y);}
 DO(m,131){x=1.75+.1*m;y=log(x)/log(B);y=log(y)/log(B);y=log(y)/log(B);y=log(y)/log(B); 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; M(2,2); DO(m,122){x=2.05+.1*m; y=Re(F45E(t+F45L(x+1.e-14*I))); L(x,y); if(y>14.1)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 IterEq2plot.eps");
       system( "open IterEq2plot.pdf");
       getchar(); system("killall Preview");
 }

//

\documentclass[12pt]{article}
\usepackage{geometry}
\usepackage{graphicx}
\usepackage{rotating}
\paperwidth 1408pt
\paperheight 1408pt
\topmargin -103pt
\oddsidemargin -73pt
\textwidth 1604pt
\textheight 1604pt
\pagestyle {empty}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\parindent 0pt% <br>
\pagestyle{empty}
\begin{document}
\begin{picture}(1402,1402)
%\put(10,10){\ing{IterPowPlot}}
\put(1,1){\ing{IterEq2plot}}
%\put(0,0){\ing{ZexIte}}
\put(11,1384){\sx{4.4}{$y$}}
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\put(1380,6){\sx{4.4}{$x$}}

\put(416,1158){\sx{5}{\rot{90}$n\!\rightarrow \! \infty$\ero}}
\put(518,1250){\sx{5}{\rot{88}$n\!=\!3$\ero}}
\put(590,1250){\sx{5}{\rot{84}$n\!=\!2$\ero}} %
\put(750,1250){\sx{5}{\rot{78}$n\!=\!1$\ero}} %
\put(800,1240){\sx{5}{\rot{74}$n\!=\!0.8$\ero}} %
\put(872,1240){\sx{5}{\rot{71}$n\!=\!0.6$\ero}} %
\put(961,1240){\sx{5}{\rot{64}$n\!=\!0.4$\ero}} %
\put(1084,1240){\sx{5}{\rot{54}$n\!=\!0.2$\ero}} %
\put(1172,1152){\sx{5.5}{\rot{44}$n\!=\!0$\ero}}
\put(1230,1040){\sx{5}{\rot{34}$n\!=\!-0.2$\ero}} %
\put(1210, 912){\sx{5}{\rot{26}$n\!=\!-0.4$\ero}} %
\put(1204, 824){\sx{5}{\rot{19}$n\!=\!-0.6$\ero}} %
\put(1200, 758){\sx{5}{\rot{15}$n\!=\!-0.8$\ero}} %
\put(1210, 707){\sx{5}{\rot{11}$n\!=\!-1$\ero}} %
\put(1234, 558){\sx{5}{\rot{4}$n\!=\!-2$\ero}} %
\put(1234, 492){\sx{5}{\rot{2}$n\!=\!-3$\ero}} %
%\put(560, 1032){\sx{6.4}{\rot{83}$y\!=\!b^{b^x}$\ero}} %
\put(694, 1032){\sx{6.6}{\rot{72}$y\!=\!b^x$\ero}} %
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\put(825,510){\sx{6}{\rot{6}$y\!=\!\log_b^{~2}(x)$\ero}} %
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