Difference between revisions of "File:Itelin125T.jpg"

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(Iterates of the linear function $T(z)=A+B z$ for $A\!=\!1$, $B\!=\!2. $y=T^n(x)$ is plotted versus $x$ for various values of $n$. Category:Linear function Category:Iteration Category:Explicit plot Category:C++ Cateogry:Latex)
 
 
(4 intermediate revisions by one other user not shown)
Line 3: Line 3:
 
$T(z)=A+B z$
  
$T(z)=A+B z$
   
−
for $A\!=\!1$, $B\!=\!2.
 +
for $A\!=\!1$, $B\!=\!2$
   
 
$y=T^n(x)$ is plotted versus $x$ for various values of $n$.
  
$y=T^n(x)$ is plotted versus $x$ for various values of $n$.
   
  +
==[[C++]] Generator of lines==
−
[[Category:Linear function]]
  
  +
// File [[ado.cin]] should be loaded in the working directory in order to compile the [[C++]] code below
−
[[Category:Iteration]]
  
  +
//<nomathjax><poem><nowiki>
−
[[Category:Explicit plot]]
  
  +
#include<math.h>
  +
#include<stdio.h>
  +
#include<stdlib.h>
  +
#define DO(x,y) for(x=0;x<y;x++)
  +
#define DB double
  +
#include"ado.cin"
  +
  +
DB A=1.0000;
  +
DB B=2.000;
  +
DB T(DB c,DB x){ DB Bc=pow(B,c); return A*(Bc-1.)/(B-1.) + Bc*x; }
  +
DB U(DB c,DB x){ DB Bc=pow(B,c); return (x-A*(Bc-1.)/(B-1.))/Bc; }
  +
  +
int main(){ FILE *o; int m,n,k; DB c, x,y,t;
  +
o=fopen("itelin125.eps","w");
  +
ado(o,1002,1002);
  +
#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);
  +
fprintf(o,"501 501 translate 100 100 scale 2 setlinecap\n");
  +
for(n=-5;n<6;n++) { M(-5,n)L(5,n)}
  +
for(m=-5;m<6;m++) { M(m,-5)L(m,5)}
  +
fprintf(o,".004 W S\n");
  +
c= 40.001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 0 1 0 RGB S\n");
  +
c= 4.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 0 1 0 RGB S\n");
  +
c= 3.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 0 1 0 RGB S\n");
  +
c= 2.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 0 1 0 RGB S\n");
  +
c= 1.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 0 1 0 RGB S\n");
  +
c= 0.000001; x=-5.;y=T(c,x); if(y<-7.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".02 W 0 0 0 RGB S\n");
  +
c=-1.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 1 0 1 RGB S\n");
  +
c=-2.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 1 0 1 RGB S\n");
  +
c=-3.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 1 0 1 RGB S\n");
  +
c=-4.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 1 0 1 RGB S\n");
  +
c=-40.0001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 1 0 1 RGB S\n");
  +
DO(n,31){c=-3.000001+.2*n; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);}
  +
fprintf(o,".012 W 0 0 0 RGB S\n");
  +
fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%');
  +
fclose(o);
  +
system("epstopdf itelin125.eps");
  +
system( "open itelin125.pdf");
  +
}
  +
//</nowiki></poem></nomathjax>
  +
  +
  +
==[[Latex]] generator of curves==
  +
%<nomathjax><poem><nowiki>
  +
\documentclass[12pt]{article}
  +
\paperwidth 1006pt
  +
\paperheight 1006pt
  +
\textwidth 1800pt
  +
\textheight 1800pt
  +
\topmargin -108pt
  +
\oddsidemargin -72pt
  +
\parindent 0pt
  +
\pagestyle{empty}
  +
\usepackage {graphics}
  +
\usepackage{rotating}
  +
\newcommand \rot {\begin{rotate}}
  +
\newcommand \ero {\end{rotate}}
  +
\newcommand \ing {\includegraphics}
  +
\newcommand \sx {\scalebox}
  +
\begin{document}
  +
\begin{picture}(1004,1004)
  +
\put(0,0){\ing{itelin125}}
  +
\put(480,984){\sx{3}{$y$}}
  +
\put(480,892){\sx{3}{$4$}}
  +
\put(480,792){\sx{3}{$3$}}
  +
\put(480,692){\sx{3}{$2$}}
  +
\put(480,592){\sx{3}{$1$}}
  +
\put(479,492){\sx{3}{$0$}}
  +
\put(454,391){\sx{3}{$-1$}}
  +
\put(454,291){\sx{3}{$-2$}}
  +
\put(454,191){\sx{3}{$-3$}}
  +
\put(454,91){\sx{3}{$-4$}}
  +
  +
\put(70,475){\sx{3}{$-4$}}
  +
\put(170,475){\sx{3}{$-3$}}
  +
\put(270,475){\sx{3}{$-2$}}
  +
\put(370,475){\sx{3}{$-1$}}
  +
\put(495,475){\sx{3}{$0$}}
  +
\put(595,475){\sx{3}{$1$}}
  +
\put(695,475){\sx{3}{$2$}}
  +
\put(795,475){\sx{3}{$3$}}
  +
\put(895,475){\sx{3}{$4$}}
  +
\put(984,476){\sx{3.1}{$x$}}
  +
  +
\put(410,870){\rot{89}\sx{3.1}{$n\!\rightarrow\!\infty$}\ero}
  +
\put(440,870){\rot{84}\sx{3.1}{$n\!=\!4$}\ero}
  +
\put(470,870){\rot{82}\sx{3.1}{$n\!=\!3$}\ero}
  +
\put(530,870){\rot{74}\sx{3.1}{$n\!=\!2$}\ero}
  +
\put(616,870){\rot{65}\sx{3.1}{$n\!=\!1.2$}\ero}
  +
\put(646,870){\rot{62}\sx{3.1}{$n\!=\!1$}\ero}
  +
\put(682,870){\rot{59}\sx{3.1}{$n\!=\!0.8$}\ero}
  +
\put(724,870){\rot{57}\sx{3.1}{$n\!=\!0.6$}\ero}
  +
\put(768,870){\rot{53}\sx{3.1}{$n\!=\!0.4$}\ero}
  +
\put(822,870){\rot{48}\sx{3.1}{$n\!=\!0.2$}\ero}
  +
\put(880,867){\rot{45}\sx{3.1}{$n\!=\!0$}\ero}
  +
\put(890,813){\rot{41}\sx{3.1}{$n\!=\!-0.2$}\ero}
  +
\put(889,760){\rot{36}\sx{3.1}{$n\!=\!-0.4$}\ero}
  +
\put(889,712){\rot{32}\sx{3.1}{$n\!=\!-0.6$}\ero}
  +
\put(889,671){\rot{29}\sx{3.1}{$n\!=\!-0.8$}\ero}
  +
\put(889,633){\rot{26}\sx{3.1}{$n\!=\!-1$}\ero}
  +
\put(905,518){\rot{13}\sx{3.1}{$n\!=\!-2$}\ero}
  +
\put(900,422){\rot{4}\sx{3.1}{$n\!=\!-4$}\ero}
  +
\put(874,392){\rot{.01}\sx{3.1}{$n\!\rightarrow\!-\infty$}\ero}
  +
\end{picture}
  +
\end{document}
  +
  +
%</nowiki></poem></nomathjax>
  +
  +
==References==
  +
  +
[[Category:Book]]
  +
[[Category:BookPlot]]
 
[[Category:C++]]
  
[[Category:C++]]
  +
[[Category:Explicit plot]]
−
[[Cateogry:Latex]]
  
  +
[[Category:Iteration]]
  +
[[Category:Latex]]
  +
[[Category:Linear function]]

Latest revision as of 08:38, 1 December 2018

Iterates of the linear function

$T(z)=A+B z$

for $A\!=\!1$, $B\!=\!2$

$y=T^n(x)$ is plotted versus $x$ for various values of $n$.

C++ Generator of lines

// File ado.cin should be loaded in the working directory in order to compile the C++ code below

//


#include<math.h>
#include<stdio.h>
#include<stdlib.h>
#define DO(x,y) for(x=0;x<y;x++)
#define DB double
#include"ado.cin"

DB A=1.0000;
DB B=2.000;
DB T(DB c,DB x){ DB Bc=pow(B,c); return A*(Bc-1.)/(B-1.) + Bc*x; }
DB U(DB c,DB x){ DB Bc=pow(B,c); return (x-A*(Bc-1.)/(B-1.))/Bc; }

int main(){ FILE *o; int m,n,k; DB c, x,y,t;
o=fopen("itelin125.eps","w");
ado(o,1002,1002);
#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);
fprintf(o,"501 501 translate 100 100 scale 2 setlinecap\n");
for(n=-5;n<6;n++) { M(-5,n)L(5,n)}
for(m=-5;m<6;m++) { M(m,-5)L(m,5)}
fprintf(o,".004 W S\n");
c= 40.001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 0 1 0 RGB S\n");
c= 4.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 0 1 0 RGB S\n");
c= 3.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 0 1 0 RGB S\n");
c= 2.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 0 1 0 RGB S\n");
c= 1.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 0 1 0 RGB S\n");
c= 0.000001; x=-5.;y=T(c,x); if(y<-7.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".02 W 0 0 0 RGB S\n");
c=-1.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 1 0 1 RGB S\n");
c=-2.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 1 0 1 RGB S\n");
c=-3.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 1 0 1 RGB S\n");
c=-4.000001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 1 0 1 RGB S\n");
c=-40.0001; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);fprintf(o,".03 W 1 0 1 RGB S\n");
DO(n,31){c=-3.000001+.2*n; x=-5.;y=T(c,x); if(y<-5.){y=-5.;x=U(c,y);} M(x,y);x=5.;y=T(c,x); if(y>5.){y=5.;x=U(c,y);}L(x,y);}
fprintf(o,".012 W 0 0 0 RGB S\n");
fprintf(o,"showpage\n"); fprintf(o,"%c%cTrailer\n",'%','%');
fclose(o);
system("epstopdf itelin125.eps");
system( "open itelin125.pdf");
}
//


Latex generator of curves

%


\documentclass[12pt]{article}
\paperwidth 1006pt
\paperheight 1006pt
\textwidth 1800pt
\textheight 1800pt
\topmargin -108pt
\oddsidemargin -72pt
\parindent 0pt
\pagestyle{empty}
\usepackage {graphics}
\usepackage{rotating}
\newcommand \rot {\begin{rotate}}
\newcommand \ero {\end{rotate}}
\newcommand \ing {\includegraphics}
\newcommand \sx {\scalebox}
\begin{document}
\begin{picture}(1004,1004)
\put(0,0){\ing{itelin125}}
\put(480,984){\sx{3}{$y$}}
\put(480,892){\sx{3}{$4$}}
\put(480,792){\sx{3}{$3$}}
\put(480,692){\sx{3}{$2$}}
\put(480,592){\sx{3}{$1$}}
\put(479,492){\sx{3}{$0$}}
\put(454,391){\sx{3}{$-1$}}
\put(454,291){\sx{3}{$-2$}}
\put(454,191){\sx{3}{$-3$}}
\put(454,91){\sx{3}{$-4$}}

\put(70,475){\sx{3}{$-4$}}
\put(170,475){\sx{3}{$-3$}}
\put(270,475){\sx{3}{$-2$}}
\put(370,475){\sx{3}{$-1$}}
\put(495,475){\sx{3}{$0$}}
\put(595,475){\sx{3}{$1$}}
\put(695,475){\sx{3}{$2$}}
\put(795,475){\sx{3}{$3$}}
\put(895,475){\sx{3}{$4$}}
\put(984,476){\sx{3.1}{$x$}}

\put(410,870){\rot{89}\sx{3.1}{$n\!\rightarrow\!\infty$}\ero}
\put(440,870){\rot{84}\sx{3.1}{$n\!=\!4$}\ero}
\put(470,870){\rot{82}\sx{3.1}{$n\!=\!3$}\ero}
\put(530,870){\rot{74}\sx{3.1}{$n\!=\!2$}\ero}
\put(616,870){\rot{65}\sx{3.1}{$n\!=\!1.2$}\ero}
\put(646,870){\rot{62}\sx{3.1}{$n\!=\!1$}\ero}
\put(682,870){\rot{59}\sx{3.1}{$n\!=\!0.8$}\ero}
\put(724,870){\rot{57}\sx{3.1}{$n\!=\!0.6$}\ero}
\put(768,870){\rot{53}\sx{3.1}{$n\!=\!0.4$}\ero}
\put(822,870){\rot{48}\sx{3.1}{$n\!=\!0.2$}\ero}
\put(880,867){\rot{45}\sx{3.1}{$n\!=\!0$}\ero}
\put(890,813){\rot{41}\sx{3.1}{$n\!=\!-0.2$}\ero}
\put(889,760){\rot{36}\sx{3.1}{$n\!=\!-0.4$}\ero}
\put(889,712){\rot{32}\sx{3.1}{$n\!=\!-0.6$}\ero}
\put(889,671){\rot{29}\sx{3.1}{$n\!=\!-0.8$}\ero}
\put(889,633){\rot{26}\sx{3.1}{$n\!=\!-1$}\ero}
\put(905,518){\rot{13}\sx{3.1}{$n\!=\!-2$}\ero}
\put(900,422){\rot{4}\sx{3.1}{$n\!=\!-4$}\ero}
\put(874,392){\rot{.01}\sx{3.1}{$n\!\rightarrow\!-\infty$}\ero}
\end{picture}
\end{document}

%

References

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Date/TimeThumbnailDimensionsUserComment
current19:00, 18 September 2013Thumbnail for version as of 19:00, 18 September 20132,088 × 2,088 (893 KB)T (talk | contribs)Iterates of the linear function $T(z)=A+B z$ for $A\!=\!1$, $B\!=\!2. $y=T^n(x)$ is plotted versus $x$ for various values of $n$. Category:Linear function Category:Iteration Category:Explicit plot Category:C++ Cateogry:Latex

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