Difference between revisions of "File:KellerPlotT.png"

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Explicit plot of various iterations $t$ the [[Keller function]]
Importing image file
 
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: $ y=\mathrm{Keller}^t(x)=\mathrm{Shoka}\Big( t + \mathrm{ArcShoka}(x)\Big)$
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To plot this graphic, the iterations of the [[Keller function]] are implemented through the [[Shoka function]] and the [[ArcShoka]] function.
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==C++ generator of curves]]==
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// File [[ado.cin]] shold be loaded to the working directory in order to compile the [[C++]] code below.
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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#define DB double
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#define DO(x,y) for(x=0;x<y;x++)
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using namespace std;
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#include <complex>
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typedef complex<double> z_type;
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#define Re(x) x.real()
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#define Im(x) x.imag()
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#define I z_type(0.,1.)
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#include"ado.cin"
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z_type Shoka(z_type z) { return z + log(exp(-z)+(M_E-1.)); }
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z_type ArcShoka(z_type z){ return z + log((1.-exp(-z))/(M_E-1.)) ;}
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#define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
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#define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);
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main(){ int j,k,m,n; DB x,y, a;
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FILE *o;o=fopen("KellerPlot.eps","w");ado(o,408,412);
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fprintf(o,"4 4 translate\n 100 100 scale 2 setlinecap 1 setlinejoin\n");
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for(m=0;m<5;m++){ M(m,0)L(m,4)}
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for(n=0;n<5;n++){ M(0,n)L(4,n)}
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M(0,0)L(4,4)
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fprintf(o,".01 W 0 0 0 RGB S\n");
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DO(n,134){x=.005+.01*n;y=Re(Shoka(3.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 .5 RGB S\n");
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DO(n,216){x=.005+.01*n;y=Re(Shoka(2.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 .5 RGB S\n");
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DO(n,154){x=.005+.02*n;y=Re(Shoka(1.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 .5 RGB S\n");
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DO(n,101){x=.005+.04*n;y=Re(Shoka(-1.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W .5 0 0 RGB S\n");
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DO(n,101){x=.005+.04*n;y=Re(Shoka(-2.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W .5 0 0 RGB S\n");
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DO(n,101){x=.005+.04*n;y=Re(Shoka(-3.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W .5 0 0 RGB S\n");
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fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
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system("epstopdf KellerPlot.eps");
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system( "open KellerPlot.pdf"); //these 2 commands may be specific for macintosh
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getchar(); system("killall Preview");// if run at another operational sysetm, may need to modify
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}
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==Latex generator of labels==
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% File [[KellerPlot.pdf]] should be generated with the code above in order to compile the [[Latex]] document below.
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%<poem><nomathjax><nowiki>
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\documentclass[12pt]{article} %<br>
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\usepackage{geometry} %<br>
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\usepackage{graphicx} %<br>
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\usepackage{rotating} %<br>
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\paperwidth 419pt %<br>
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\paperheight 426pt %<br>
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\topmargin -103pt %<br>
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\oddsidemargin -83pt %<br>
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\textwidth 1200pt %<br>
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\textheight 600pt %<br>
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\pagestyle {empty} %<br>
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\newcommand \sx {\scalebox} %<br>
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\newcommand \rot {\begin{rotate}} %<br>
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\newcommand \ero {\end{rotate}} %<br>
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\newcommand \ing {\includegraphics} %<br>
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\begin{document} %<br>
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\sx{1}{ \begin{picture}(810,410) %<br>
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\put(1,9){\ing{KellerPlot}} % <br>
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\put(-12,401){\sx{2.8}{$y$}} % <br>
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\put(-12,303){\sx{2.8}{$3$}} % <br>
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\put(-12,203){\sx{2.8}{$2$}} % <br>
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\put(-12,103){\sx{2.8}{$1$}} % <br>
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\put(0,-9){\sx{2.5}{$0$}} % <br>
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\put(100,-9){\sx{2.5}{$1$}} % <br>
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\put(200,-9){\sx{2.5}{$2$}} % <br>
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\put(300,-9){\sx{2.5}{$3$}} % <br>
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\put(392,-7){\sx{2.6}{$x$}} % <br>
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%\put(560,214){\rot{37}\sx{4}{$y=\mathrm{Tania}(x)$}\ero} % <br>
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\put( 88,354){\rot{53}\sx{2.8}{$t\!=\!3$}\ero} %<br>
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\put(160,354){\rot{50}\sx{2.8}{$t\!=\!2$}\ero} %<br>
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\put(246,354){\rot{48}\sx{2.8}{$t\!=\!1$}\ero} %<br>
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\put(336,350){\rot{45}\sx{2.8}{$t\!=\!0$}\ero} %<br>
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\put(340,218){\rot{44}\sx{2.8}{$t\!=\!-1$}\ero} %<br>
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\put(344,136){\rot{41}\sx{2.7}{$t\!=\!-2$}\ero} %<br>
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\put(338, 68){\rot{34}\sx{2.7}{$t\!=\!-3$}\ero} %<br>
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\end{picture} %<br>
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} %<br>
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\end{document}
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%</nowiki></nomathjax></poem>
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==Copyleft status==
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Copyleft 2012 by Dmitrii Kouznetsov.
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The image and the generators above may be used for free; attribute the source.
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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:Keller function]]
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[[Category:Transfer function]]
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[[Category:Shoka function]]
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[[Category:ArcShoka]]
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[[Category:Laser science]]
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[[Category:Explicit plot]]
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[[Category:C++]]
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[[Category:Latex]]

Latest revision as of 08:39, 1 December 2018

Explicit plot of various iterations $t$ the Keller function

$ y=\mathrm{Keller}^t(x)=\mathrm{Shoka}\Big( t + \mathrm{ArcShoka}(x)\Big)$

To plot this graphic, the iterations of the Keller function are implemented through the Shoka function and the ArcShoka function.

C++ generator of curves]]

// File ado.cin shold be loaded to the working directory 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++)
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"
z_type Shoka(z_type  z)  { return z + log(exp(-z)+(M_E-1.)); }
z_type ArcShoka(z_type z){ return z + log((1.-exp(-z))/(M_E-1.)) ;}  
#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);
main(){ int j,k,m,n; DB x,y, a;
FILE *o;o=fopen("KellerPlot.eps","w");ado(o,408,412);
fprintf(o,"4 4 translate\n 100 100 scale 2 setlinecap 1 setlinejoin\n");
for(m=0;m<5;m++){ M(m,0)L(m,4)}
for(n=0;n<5;n++){ M(0,n)L(4,n)}
M(0,0)L(4,4)
fprintf(o,".01 W 0 0 0 RGB S\n");
DO(n,134){x=.005+.01*n;y=Re(Shoka(3.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 .5 RGB S\n");
DO(n,216){x=.005+.01*n;y=Re(Shoka(2.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 .5 RGB S\n");
DO(n,154){x=.005+.02*n;y=Re(Shoka(1.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W 0 0 .5 RGB S\n");
DO(n,101){x=.005+.04*n;y=Re(Shoka(-1.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W .5 0 0 RGB S\n");
DO(n,101){x=.005+.04*n;y=Re(Shoka(-2.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W .5 0 0 RGB S\n");
DO(n,101){x=.005+.04*n;y=Re(Shoka(-3.+ArcShoka(x)));if(n==0)M(x,y)else L(x,y)} fprintf(o,".02 W .5 0 0 RGB S\n");
fprintf(o,"showpage\n%cTrailer",'%'); fclose(o);
    system("epstopdf KellerPlot.eps");
    system(    "open KellerPlot.pdf"); //these 2 commands may be specific for macintosh
getchar(); system("killall Preview");// if run at another operational sysetm, may need to modify
}


Latex generator of labels

% File KellerPlot.pdf should be generated with the code above in order to compile the Latex document below.

%



\documentclass[12pt]{article} %<br>
\usepackage{geometry} %<br>
\usepackage{graphicx} %<br>
\usepackage{rotating} %<br>
\paperwidth 419pt %<br>
\paperheight 426pt %<br>
\topmargin -103pt %<br>
\oddsidemargin -83pt %<br>
\textwidth 1200pt %<br>
\textheight 600pt %<br>
\pagestyle {empty} %<br>
\newcommand \sx {\scalebox} %<br>
\newcommand \rot {\begin{rotate}} %<br>
\newcommand \ero {\end{rotate}} %<br>
\newcommand \ing {\includegraphics} %<br>
\begin{document} %<br>
\sx{1}{ \begin{picture}(810,410) %<br>
\put(1,9){\ing{KellerPlot}} % <br>
\put(-12,401){\sx{2.8}{$y$}} % <br>
\put(-12,303){\sx{2.8}{$3$}} % <br>
\put(-12,203){\sx{2.8}{$2$}} % <br>
\put(-12,103){\sx{2.8}{$1$}} % <br>
\put(0,-9){\sx{2.5}{$0$}} % <br>
\put(100,-9){\sx{2.5}{$1$}} % <br>
\put(200,-9){\sx{2.5}{$2$}} % <br>
\put(300,-9){\sx{2.5}{$3$}} % <br>
\put(392,-7){\sx{2.6}{$x$}} % <br>
 %\put(560,214){\rot{37}\sx{4}{$y=\mathrm{Tania}(x)$}\ero} % <br>
\put( 88,354){\rot{53}\sx{2.8}{$t\!=\!3$}\ero} %<br>
\put(160,354){\rot{50}\sx{2.8}{$t\!=\!2$}\ero} %<br>
\put(246,354){\rot{48}\sx{2.8}{$t\!=\!1$}\ero} %<br>
\put(336,350){\rot{45}\sx{2.8}{$t\!=\!0$}\ero} %<br>
\put(340,218){\rot{44}\sx{2.8}{$t\!=\!-1$}\ero} %<br>
\put(344,136){\rot{41}\sx{2.7}{$t\!=\!-2$}\ero} %<br>
\put(338, 68){\rot{34}\sx{2.7}{$t\!=\!-3$}\ero} %<br>
\end{picture} %<br>
} %<br>
\end{document}
%


Copyleft status

Copyleft 2012 by Dmitrii Kouznetsov. The image and the generators above may be used for free; attribute the source.

References

File history

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