Difference between revisions of "File:Superpower2plot.jpg"

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Explicit plot of two [[superfunction]]s of the quadratic function, $T(z)\!=\!z^2$:
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Importing image file
  
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$y\!=\!F(x)\!=\! \exp(2^x)~$, blue curve, shows the [[SuPow]] function
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  +
$y\!=\!F(x)\!=\! \exp(-2^x)~$, red curve, shows the [[SdPow]] function
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  +
The transfer function $T$ is shown with thin black curve.
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[[Superfunction]]s $F$ are solutions of the [[transfer equation]]
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$T(F(z))=F(z\!+\!1)$
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==[[C++]] generator of curves==
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  +
<poem><nomathjax><nowiki>
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#include<stdio.h>
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#include<stdlib.h>
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#include<math.h>
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#define DB double
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void ado(FILE *O, int X, int Y)
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{ fprintf(O,"%c!PS-Adobe-2.0 EPSF-2.0\n",'%');
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fprintf(O,"%c%cBoundingBox: 0 0 %d %d\n",'%','%',X,Y);
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fprintf(O,"/M {moveto} bind def\n");
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fprintf(O,"/L {lineto} bind def\n");
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fprintf(O,"/S {stroke} bind def\n");
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fprintf(O,"/s {show newpath} bind def\n");
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fprintf(O,"/C {closepath} bind def\n");
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fprintf(O,"/F {fill} bind def\n");
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fprintf(O,"/o {.1 0 360 arc C S} bind def\n");
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fprintf(O,"/times-Roman findfont 20 scalefont setfont\n");
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fprintf(O,"/W {setlinewidth} bind def\n");
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fprintf(O,"/RGB {setrgbcolor} bind def\n");}
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DB F(DB x){ return exp(pow(2.,x));}
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DB f(DB x){ return exp(-pow(2.,x));}
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int main(){ FILE * o; int m,n; DB x,y;
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o=fopen("superpower2plo.eps","w"); ado(o,720,720);
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fprintf(o,"510 10 translate 100 100 scale 1 setlinejoin 2 setlinecap\n");
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#define M(x,y) fprintf(o,"%7.4f %7.4f M\n",0.+x, 0.+y);
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#define L(x,y) fprintf(o,"%7.4f %7.4f L\n",0.+x, 0.+y);
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for(m=-5;m<3;m++) {M(m,0)L(m,7)}
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for(n=0;n<8;n++) {M(-5,n)L(2,n)} fprintf(o,".01 W 0 0 0 RGB S\n");
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for(m=0;m<48;m++){x=-2.66+.1*m; y=x*x; if(m==0) M(x,y) else L(x,y) }
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fprintf(o,".01 W 0 0 0 RGB S\n");
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for(m=0;m<73;m++){x=-5.1+.1*m; y=F(x); if(m==0) M(x,y) else L(x,y) }
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fprintf(o,".03 W 0 0 1 RGB S\n");
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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;}
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fprintf(o,".03 W 1 0 0 RGB S\n");
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fprintf(o,"showpage\n"); fclose(o);
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system("epstopdf superpower2plo.eps");
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system("open superpower2plo.pdf");
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}
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</nowiki></nomathjax></poem>
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==[[Latex]] generator of labels==
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  +
<poem><nomathjax><nowiki>
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\documentclass[12pt]{article}
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\usepackage{graphicx}
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\usepackage{geometry}
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%\usepackage{rotate}
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%\usepackage{rotation}
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\usepackage{rotating}
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\paperwidth 718px
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\paperheight 726px
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\topmargin -98px
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\oddsidemargin -90px
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\textwidth 900px
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\textheight 900px
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\newcommand \ing {\includegraphics}
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\newcommand \sx {\scalebox}
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\newcommand \rot {\begin{rotate}}
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\newcommand \ero {\end{rotate}}
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\begin{document}
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\begin{picture}(704,704) \normalsize
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\put(0,0){\ing{"superpower2plo"}}
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\put(494,696){\sx{2.6}{$y$}}
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\put(494,602){\sx{2.6}{$6$}}
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\put(494,502){\sx{2.6}{$5$}}
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\put(494,402){\sx{2.6}{$4$}}
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\put(494,302){\sx{2.6}{$3$}}
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\put(494,202){\sx{2.6}{$2$}}
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\put(494,102){\sx{2.6}{$1$}}
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\put(94,-12){\sx{2.3}{$-4$}}
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\put(194,-12){\sx{2.3}{$-3$}}
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\put(294,-12){\sx{2.3}{$-2$}}
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\put(394,-12){\sx{2.3}{$-1$}}
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\put(506,-12){\sx{2.3}{$0$}}
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\put(606,-12){\sx{2.3}{$1$}}
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\put(704,-11){\sx{2.4}{$x$}}
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\put(212,424){\rot{0.}{ \sx{3}{$y\!=\!x^2$}} \ero}
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\put(124,128){\rot{5}{ \sx{3}{$y\!=\!\exp(2^x)$}} \ero}
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\put(114,78){\rot{-5}\sx{3}{$y\!=\!\exp(-2^x)$} \ero}
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\end{picture}
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\end{document}
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</nowiki></nomathjax></poem>
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  +
==References==
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<references/>
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[[Category:Book]]
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[[Category:BookPlot]]
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[[Category:Explicit plot]]
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[[Category:Power function]]
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[[Category:SdPow]]
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[[Category:SuPow]]
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[[Category:Superfunction]]
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[[Category:Superfunctions]]
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[[Category:Superpower]]

Latest revision as of 08:53, 1 December 2018

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


#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#define DB double
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");
#define M(x,y) fprintf(o,"%7.4f %7.4f M\n",0.+x, 0.+y);
#define L(x,y) fprintf(o,"%7.4f %7.4f L\n",0.+x, 0.+y);
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");
}

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}

References

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