File:Superpower2plot.jpg

Explicit plot of two superfunctions of the quadratic function, $T(z)\!=\!z^2$:

$y\!=\!F(x)\!=\! \exp(2^x)~$, blue curve, shows the SuPow function

$y\!=\!F(x)\!=\! \exp(-2^x)~$, red curve, shows the SdPow function

The transfer function $T$ is shown with thin black curve.

Superfunctions $F$ are solutions of the transfer equation

$T(F(z))=F(z\!+\!1)$

C++ generator of curves
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");} DB F(DB x){ return exp(pow(2.,x));} DB f(DB x){ return exp(-pow(2.,x));} int main{ FILE * o; int m,n; DB x,y; o=fopen("superpower2plo.eps","w"); ado(o,720,720); fprintf(o,"510 10 translate 100 100 scale 1 setlinejoin 2 setlinecap\n"); for(m=-5;m<3;m++) {M(m,0)L(m,7)} for(n=0;n<8;n++) {M(-5,n)L(2,n)} fprintf(o,".01 W 0 0 0 RGB S\n"); for(m=0;m<48;m++){x=-2.66+.1*m; y=x*x; if(m==0) M(x,y) else L(x,y) } fprintf(o,".01 W 0 0 0 RGB S\n"); for(m=0;m<73;m++){x=-5.1+.1*m; y=F(x); if(m==0) M(x,y) else L(x,y) } fprintf(o,".03 W 0 0 1 RGB S\n"); for(m=0;m<73;m++){x=-5.1+.1*m; y=f(x); if(m==0) M(x,y) else L(x,y) if(y>7)break;} fprintf(o,".03 W 1 0 0 RGB S\n"); fprintf(o,"showpage\n"); fclose(o); system("epstopdf superpower2plo.eps"); system("open superpower2plo.pdf"); }
 * 1) include
 * 2) include
 * 3) include
 * 4) define DB double
 * 1) define M(x,y) fprintf(o,"%7.4f %7.4f M\n",0.+x, 0.+y);
 * 2) define L(x,y) fprintf(o,"%7.4f %7.4f L\n",0.+x, 0.+y);

Latex generator of labels
\documentclass[12pt]{article} \usepackage{graphicx} \usepackage{geometry} %\usepackage{rotate} %\usepackage{rotation} \usepackage{rotating} \paperwidth 718px \paperheight 726px \topmargin -98px \oddsidemargin -90px \textwidth 900px \textheight 900px \newcommand \ing {\includegraphics} \newcommand \sx {\scalebox} \newcommand \rot {\begin{rotate}} \newcommand \ero {\end{rotate}} \begin{document} \begin{picture}(704,704) \normalsize \put(0,0){\ing{"superpower2plo"}} \put(494,696){\sx{2.6}{$y$}} \put(494,602){\sx{2.6}{$6$}} \put(494,502){\sx{2.6}{$5$}} \put(494,402){\sx{2.6}{$4$}} \put(494,302){\sx{2.6}{$3$}} \put(494,202){\sx{2.6}{$2$}} \put(494,102){\sx{2.6}{$1$}} \put(94,-12){\sx{2.3}{$-4$}} \put(194,-12){\sx{2.3}{$-3$}} \put(294,-12){\sx{2.3}{$-2$}} \put(394,-12){\sx{2.3}{$-1$}} \put(506,-12){\sx{2.3}{$0$}} \put(606,-12){\sx{2.3}{$1$}} \put(704,-11){\sx{2.4}{$x$}} \put(212,424){\rot{0.}{ \sx{3}{$y\!=\!x^2$}} \ero} \put(124,128){\rot{5}{ \sx{3}{$y\!=\!\exp(2^x)$}} \ero} \put(114,78){\rot{-5}\sx{3}{$y\!=\!\exp(-2^x)$} \ero} \end{picture} \end{document}