Difference between revisions of "File:SdPow2map.jpg"

From TORI
Jump to navigation Jump to search
(Importing image file)
 
 
Line 1: Line 1:
  +
[[Complex map]] of function [[SdPow]]$_2$ ;
−
Importing image file
  
  +
  +
$F(z)=$[[SdPow]]$_2(z)=\exp(-2^z)$
  +
  +
is shown with lines of constant real part and lines of constant imaginary part:
  +
  +
$u\!+\mathrm i v=F(x\!+\mathrm i y)$
  +
  +
== Superpower ==
  +
  +
[[Superpower]] function $F$ is [[superfunction]] for the quadratic transfer function $T(z)\!=\!z^2$,
  +
which is in its turn, interpreted as [[power function]] to base 2.
  +
  +
[[Superpower]] function $F$ is solution of the transfer equation
  +
  +
$F(z\!+\!1)=T(F(z))$
  +
  +
==[[C++]] generator of map==
  +
Files [[ado.cin]] and [[conto.cin]] should be loaded in order to compile the [[C++]] code below.
  +
<poem><nomathjax><nowiki>
  +
#include <math.h>
  +
#include <stdio.h>
  +
#include <stdlib.h>
  +
#define DB double
  +
#define DO(x,y) for(x=0;x<y;x++)
  +
#include <complex>
  +
typedef std::complex<double> z_type;
  +
#define Re(x) x.real()
  +
#define Im(x) x.imag()
  +
#define I z_type(0.,1.)
  +
#include "conto.cin"
  +
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
  +
int M=501,M1=M+1;
  +
int N=501,N1=N+1;
  +
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
  +
char v[M1*N1]; // v is working array
  +
//FILE *o;o=fopen("superpower2ma.eps","w");ado(o,1020,1020);
  +
FILE *o;o=fopen("sdpow2ma.eps","w");ado(o,1020,1020);
  +
fprintf(o,"510 510 translate\n 100 100 scale\n");
  +
DO(m,M1) X[m]=-5.+.02*(m-.5);
  +
DO(n,N1) Y[n]=-5.+.02*(n-.5);
  +
for(m=-5;m<6;m++){if(m==0){M(m,-5.1)L(m,5.1)} else{M(m,-5)L(m,5)}}
  +
for(n=-5;n<6;n++){ M( -5,n)L(5,n)}
  +
fprintf(o,".01 W 0 0 0 RGB S\n");
  +
DO(m,M1)DO(n,N1){g[m*N1+n]=1.e15; f[m*N1+n]=1.e15;}
  +
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
  +
DO(n,N1){y=Y[n]; z=z_type(x,y);
  +
c=exp(-pow(2.,z));
  +
p=Re(c);
  +
q=Im(c);
  +
if(p>-2.e15 && p<1.e15
  +
&& q>-1.e15 && q<1.e15
  +
)
  +
{g[m*N1+n]=p;
  +
f[m*N1+n]=q;
  +
}
  +
}}
  +
fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=10;q=.4;
  +
for(m=-10;m<10;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".013 W 0 .6 0 RGB S\n");
  +
for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".011 W .9 0 0 RGB S\n");
  +
for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".011 W 0 0 .9 RGB S\n");
  +
for(m=1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".028 W .9 0 0 RGB S\n");
  +
for(m=1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".028 W 0 0 .9 RGB S\n");
  +
conto(o,f,w,v,X,Y,M,N, (0. ),-1.e14,1.e14); fprintf(o,".028 W .6 0 .6 RGB S\n");
  +
for(m=-10;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".024 W 0 0 0 RGB S\n");
  +
m=0; conto(o,g,w,v,X,Y,M,N, (0.+m),-1.e14,1.e14); fprintf(o,".024 W 0 0 0 RGB S\n");
  +
for(m=1;m<11;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".024 W 0 0 0 RGB S\n");
  +
  +
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
  +
system("epstopdf sdpow2ma.eps");
  +
system( "open sdpow2ma.pdf");
  +
getchar(); system("killall Preview");//for mac
  +
}
  +
</nowiki></nomathjax></poem>
  +
  +
==[[Latex]] generator of labels==
  +
  +
<poem><nomathjax><nowiki>
  +
\documentclass[12pt]{article}
  +
\usepackage{graphicx}
  +
\usepackage{geometry}
  +
%\usepackage{rotate}
  +
%\usepackage{rotation}
  +
\usepackage{rotating}
  +
\paperwidth 1044px
  +
\paperheight 1036px
  +
\topmargin -98px
  +
\oddsidemargin -90px
  +
\textwidth 2000px
  +
\textheight 2000px
  +
\newcommand \ing {\includegraphics}
  +
\newcommand \sx {\scalebox}
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
\begin{document}
  +
\begin{picture}(1030,1026) \normalsize
  +
\put(30,20){\ing{"sdpow2ma"}}
  +
%\put(30,20){\ing{"superpower2ma"}}
  +
\put(16,1016){\sx{3}{$y$}}
  +
\put(16,918){\sx{3}{$4$}}
  +
\put(16,818){\sx{3}{$3$}}
  +
\put(16,718){\sx{3}{$2$}}
  +
\put(16,618){\sx{3}{$1$}}
  +
\put(16,518){\sx{3}{$0$}}
  +
\put(-10,418){\sx{3}{$-1$}}
  +
\put(-10,318){\sx{3}{$-2$}}
  +
\put(-10,218){\sx{3}{$-3$}}
  +
\put(-10,118){\sx{3}{$-4$}}
  +
\put(-10,18){\sx{3}{$-5$}}
  +
\put(10,-1){\sx{3}{$-5$}}
  +
\put(110,-1){\sx{3}{$-4$}}
  +
\put(210,-1){\sx{3}{$-3$}}
  +
\put(310,-1){\sx{3}{$-2$}}
  +
\put(410,-1){\sx{3}{$-1$}}
  +
\put(534,-1){\sx{3}{$0$}}
  +
\put(634,-1){\sx{3}{$1$}}
  +
\put(734,-1){\sx{3}{$2$}}
  +
\put(834,-1){\sx{3}{$3$}}
  +
\put(934,-1){\sx{3}{$4$}}
  +
\put(1028,-1){\sx{3.1}{$x$}}
  +
\put(150,978){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}
  +
\put(150,756){\rot{1}{ \sx{3}{$u\!=\!1$}} \ero}
  +
\put(150,522){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}
  +
\put(150,290){\rot{-1}{ \sx{3}{$u\!=\!1$}} \ero}
  +
\put(150,68){\rot{0.}{ \sx{3}{$v\!=\!0$}} \ero}
  +
%
  +
\put(336,484){\rot{90}{ \sx{3}{$u\!=\!0.8$}} \ero}
  +
\put(454,484){\rot{90}{ \sx{3}{$u\!=\!0.6$}} \ero}
  +
\put(538,484){\rot{90}{ \sx{3}{$u\!=\!0.4$}} \ero}
  +
\put(618,484){\rot{90}{ \sx{3}{$u\!=\!0.2$}} \ero}
  +
%\put(530,489){\rot{90}{ \sx{3}{$u\!=\!2$}} \ero}
  +
%
  +
\put(780,564){\rot{-11}{ \sx{3}{$u\!=\!0$}} \ero}
  +
\put(790,522){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}
  +
\put(782,482){\rot{10}{ \sx{3}{$u\!=\!0$}} \ero}
  +
%
  +
\put(310,926){\rot{90}{ \sx{3}{$u\!=\!1.2$}} \ero}
  +
\put(400,926){\rot{90}{ \sx{3}{$u\!=\!1.4$}} \ero}
  +
\put(442,926){\rot{90}{ \sx{3}{$u\!=\!1.6$}} \ero}
  +
\put(476,926){\rot{90}{ \sx{3}{$u\!=\!1.8$}} \ero}
  +
\put(502,936){\rot{90}{ \sx{3}{$u\!=\!2$}} \ero}
  +
%
  +
\put(800,978){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}%%%
  +
\put(788,938){\rot{12}{ \sx{3}{$u\!=\!0$}} \ero} %
  +
\put(816,906){\rot{24}{ \sx{3}{$v\!=\!0$}} \ero} %
  +
\put(820,870){\rot{32}{ \sx{3}{$u\!=\!0$}} \ero}
  +
%
  +
\put(310,26){\rot{90}{ \sx{3}{$u\!=\!1.2$}} \ero}
  +
\put(400,26){\rot{90}{ \sx{3}{$u\!=\!1.4$}} \ero}
  +
\put(442,26){\rot{90}{ \sx{3}{$u\!=\!1.6$}} \ero}
  +
\put(476,26){\rot{90}{ \sx{3}{$u\!=\!1.8$}} \ero}
  +
\put(502,36){\rot{90}{ \sx{3}{$u\!=\!2$}} \ero}
  +
%
  +
\put(658,172){\rot{-31}{ \sx{3}{$u\!=\!0$}} \ero}
  +
%
  +
%
  +
\put(508,800){\rot{-33}{ \sx{3}{$v\!=\!-1$}} \ero}
  +
%\put(480,748){\rot{-16}{ \sx{3}{$v\!=\!-0.8$}} \ero}
  +
\put(476,730){\rot{-17}{ \sx{3}{$v\!=\!-0.6$}} \ero}
  +
\put(478,670){\rot{-6}{ \sx{3}{$v\!=\!-0.4$}} \ero}
  +
\put(480,602){\rot{0}{ \sx{3}{$v\!=\!-0.2$}} \ero}
  +
  +
\put(480,446){\rot{2}{ \sx{3}{$v\!=\!0.2$}} \ero}%%
  +
\put(482,372){\rot{9}{ \sx{3}{$v\!=\!0.4$}} \ero}%%
  +
\put(500,320){\rot{16}{ \sx{3}{$v\!=\!0.6$}} \ero}
  +
\put(528,262){\rot{28}{ \sx{3}{$v\!=\!1$}} \ero}
  +
%\put(508,348){\rot{-33}{ \sx{3}{$v\!=\!-1$}} \ero}
  +
%\put(480,268){\rot{-12}{ \sx{3}{$v\!=\!-0.6$}} \ero}
  +
%\put(480,210){\rot{-4}{ \sx{3}{$v\!=\!-0.4$}} \ero}
  +
%\put(480,150){\rot{0}{ \sx{3}{$v\!=\!-0.2$}} \ero}
  +
\end{picture}
  +
\end{document}
  +
</nowiki></nomathjax></poem>
  +
  +
==References==
  +
<references/>
  +
  +
[[Category:Book]]
  +
[[Category:BookMap]]
  +
[[Category:Complex map]]
  +
[[Category:Power function]]
  +
[[Category:SdPow]]
  +
[[Category:Superfunction]]
  +
[[Category:Superpower]]

Latest revision as of 08:51, 1 December 2018

Complex map of function SdPow$_2$ ;

$F(z)=$SdPow$_2(z)=\exp(-2^z)$

is shown with lines of constant real part and lines of constant imaginary part:

$u\!+\mathrm i v=F(x\!+\mathrm i y)$

Superpower

Superpower function $F$ is superfunction for the quadratic transfer function $T(z)\!=\!z^2$, which is in its turn, interpreted as power function to base 2.

Superpower function $F$ is solution of the transfer equation

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

C++ generator of map

Files ado.cin and conto.cin should be loaded in order to compile the C++ code below.


#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include <complex>
typedef std::complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"
int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=501,M1=M+1;
int N=501,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
//FILE *o;o=fopen("superpower2ma.eps","w");ado(o,1020,1020);
FILE *o;o=fopen("sdpow2ma.eps","w");ado(o,1020,1020);
fprintf(o,"510 510 translate\n 100 100 scale\n");
DO(m,M1) X[m]=-5.+.02*(m-.5);
DO(n,N1) Y[n]=-5.+.02*(n-.5);
for(m=-5;m<6;m++){if(m==0){M(m,-5.1)L(m,5.1)} else{M(m,-5)L(m,5)}}
for(n=-5;n<6;n++){ M( -5,n)L(5,n)}
fprintf(o,".01 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){g[m*N1+n]=1.e15; f[m*N1+n]=1.e15;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
       c=exp(-pow(2.,z));
      p=Re(c);
      q=Im(c);
      if(p>-2.e15 && p<1.e15
       && q>-1.e15 && q<1.e15
      )
 {g[m*N1+n]=p;
  f[m*N1+n]=q;
 }
                      }}
fprintf(o,"1 setlinejoin 1 setlinecap\n"); p=10;q=.4;
for(m=-10;m<10;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".013 W 0 .6 0 RGB S\n");
for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".011 W .9 0 0 RGB S\n");
for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".011 W 0 0 .9 RGB S\n");
for(m=1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".028 W .9 0 0 RGB S\n");
for(m=1;m<11;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".028 W 0 0 .9 RGB S\n");
                conto(o,f,w,v,X,Y,M,N, (0. ),-1.e14,1.e14); fprintf(o,".028 W .6 0 .6 RGB S\n");
for(m=-10;m<0;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".024 W 0 0 0 RGB S\n");
             m=0; conto(o,g,w,v,X,Y,M,N, (0.+m),-1.e14,1.e14); fprintf(o,".024 W 0 0 0 RGB S\n");
for(m=1;m<11;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".024 W 0 0 0 RGB S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
      system("epstopdf sdpow2ma.eps");
      system( "open sdpow2ma.pdf");
      getchar(); system("killall Preview");//for mac
}

Latex generator of labels


\documentclass[12pt]{article}
\usepackage{graphicx}
\usepackage{geometry}
%\usepackage{rotate}
%\usepackage{rotation}
\usepackage{rotating}
\paperwidth 1044px
\paperheight 1036px
\topmargin -98px
\oddsidemargin -90px
\textwidth 2000px
\textheight 2000px
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\begin{document}
\begin{picture}(1030,1026) \normalsize
\put(30,20){\ing{"sdpow2ma"}}
%\put(30,20){\ing{"superpower2ma"}}
\put(16,1016){\sx{3}{$y$}}
\put(16,918){\sx{3}{$4$}}
\put(16,818){\sx{3}{$3$}}
\put(16,718){\sx{3}{$2$}}
\put(16,618){\sx{3}{$1$}}
\put(16,518){\sx{3}{$0$}}
\put(-10,418){\sx{3}{$-1$}}
\put(-10,318){\sx{3}{$-2$}}
\put(-10,218){\sx{3}{$-3$}}
\put(-10,118){\sx{3}{$-4$}}
\put(-10,18){\sx{3}{$-5$}}
\put(10,-1){\sx{3}{$-5$}}
\put(110,-1){\sx{3}{$-4$}}
\put(210,-1){\sx{3}{$-3$}}
\put(310,-1){\sx{3}{$-2$}}
\put(410,-1){\sx{3}{$-1$}}
\put(534,-1){\sx{3}{$0$}}
\put(634,-1){\sx{3}{$1$}}
\put(734,-1){\sx{3}{$2$}}
\put(834,-1){\sx{3}{$3$}}
\put(934,-1){\sx{3}{$4$}}
\put(1028,-1){\sx{3.1}{$x$}}
\put(150,978){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}
\put(150,756){\rot{1}{ \sx{3}{$u\!=\!1$}} \ero}
\put(150,522){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}
\put(150,290){\rot{-1}{ \sx{3}{$u\!=\!1$}} \ero}
\put(150,68){\rot{0.}{ \sx{3}{$v\!=\!0$}} \ero}
%
\put(336,484){\rot{90}{ \sx{3}{$u\!=\!0.8$}} \ero}
\put(454,484){\rot{90}{ \sx{3}{$u\!=\!0.6$}} \ero}
\put(538,484){\rot{90}{ \sx{3}{$u\!=\!0.4$}} \ero}
\put(618,484){\rot{90}{ \sx{3}{$u\!=\!0.2$}} \ero}
%\put(530,489){\rot{90}{ \sx{3}{$u\!=\!2$}} \ero}
%
\put(780,564){\rot{-11}{ \sx{3}{$u\!=\!0$}} \ero}
\put(790,522){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}
\put(782,482){\rot{10}{ \sx{3}{$u\!=\!0$}} \ero}
%
\put(310,926){\rot{90}{ \sx{3}{$u\!=\!1.2$}} \ero}
\put(400,926){\rot{90}{ \sx{3}{$u\!=\!1.4$}} \ero}
\put(442,926){\rot{90}{ \sx{3}{$u\!=\!1.6$}} \ero}
\put(476,926){\rot{90}{ \sx{3}{$u\!=\!1.8$}} \ero}
\put(502,936){\rot{90}{ \sx{3}{$u\!=\!2$}} \ero}
%
\put(800,978){\rot{0}{ \sx{3}{$v\!=\!0$}} \ero}%%%
\put(788,938){\rot{12}{ \sx{3}{$u\!=\!0$}} \ero} %
\put(816,906){\rot{24}{ \sx{3}{$v\!=\!0$}} \ero} %
\put(820,870){\rot{32}{ \sx{3}{$u\!=\!0$}} \ero}
%
\put(310,26){\rot{90}{ \sx{3}{$u\!=\!1.2$}} \ero}
\put(400,26){\rot{90}{ \sx{3}{$u\!=\!1.4$}} \ero}
\put(442,26){\rot{90}{ \sx{3}{$u\!=\!1.6$}} \ero}
\put(476,26){\rot{90}{ \sx{3}{$u\!=\!1.8$}} \ero}
\put(502,36){\rot{90}{ \sx{3}{$u\!=\!2$}} \ero}
%
\put(658,172){\rot{-31}{ \sx{3}{$u\!=\!0$}} \ero}
%
%
\put(508,800){\rot{-33}{ \sx{3}{$v\!=\!-1$}} \ero}
%\put(480,748){\rot{-16}{ \sx{3}{$v\!=\!-0.8$}} \ero}
\put(476,730){\rot{-17}{ \sx{3}{$v\!=\!-0.6$}} \ero}
\put(478,670){\rot{-6}{ \sx{3}{$v\!=\!-0.4$}} \ero}
\put(480,602){\rot{0}{ \sx{3}{$v\!=\!-0.2$}} \ero}

\put(480,446){\rot{2}{ \sx{3}{$v\!=\!0.2$}} \ero}%%
\put(482,372){\rot{9}{ \sx{3}{$v\!=\!0.4$}} \ero}%%
\put(500,320){\rot{16}{ \sx{3}{$v\!=\!0.6$}} \ero}
\put(528,262){\rot{28}{ \sx{3}{$v\!=\!1$}} \ero}
%\put(508,348){\rot{-33}{ \sx{3}{$v\!=\!-1$}} \ero}
%\put(480,268){\rot{-12}{ \sx{3}{$v\!=\!-0.6$}} \ero}
%\put(480,210){\rot{-4}{ \sx{3}{$v\!=\!-0.4$}} \ero}
%\put(480,150){\rot{0}{ \sx{3}{$v\!=\!-0.2$}} \ero}
\end{picture}
\end{document}

References

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current06:14, 1 December 2018Thumbnail for version as of 06:14, 1 December 20182,175 × 2,158 (1.47 MB)Maintenance script (talk | contribs)Importing image file

You cannot overwrite this file.

The following 2 pages use this file:

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Retrieved from "https://mizugadro.mydns.jp/t/index.php?title=File:SdPow2map.jpg&oldid=21359"