File:Logi5U1500.png

LogisticSequence versus real argument for various values of parameter.

$F(x)=\mathrm{LogisticSequence}_s(x)$ versus $x$ for

$s\!=\!3.9$, red dashed

$s\!=\!4$, green solid

$s\!=\!4.1$, blue dotted

Generator of curves

// Files efjh.cin and ado.cin should be loaded in the working directory in order to compile the 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"
#include "efjh.cin"
main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
FILE *o;o=fopen("logi5.eps","w");ado(o,164,44);
fprintf(o,"62 22 translate\n 20 20 scale\n");
#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);
fprintf(o,"1 setlinejoin 2 setlinecap\n");
for(m=-3;m<6;m++){if(m==0){M(m,-1.06)L(m,1.06)} else{M(m,-1)L(m,1)}}
for(n=-1;n<2;n++){	M(  -3,n)L(5,n)}
fprintf(o,".008 W 0 0 0 RGB S\n");

maq(4.);
DO(m,1001) { x=-3.+8.*sqrt(.001*m); y=Re(F(x)); if(m==0)M(x,y) else L(x,y);}
fprintf(o,".01 W 0 .7 0 RGB S\n");

maq(3.9);
DO(m,1001) { x=-3.+8.*sqrt(.001*m); y=Re(F(x)); if(m==0)M(x,y) else L(x,y);}
fprintf(o,".015 W 1 0 0 RGB [.03 .04] 0 setdash S\n");

fprintf(o,"1 setlinejoin 1 setlinecap\n");
maq(4.1);
DO(m,1001) { x=-3.+8.*sqrt(.001*m); y=Re(F(x)); if(y>-2) { if(m==0)M(x,y) else L(x,y);} }
fprintf(o,".015 W 0 0 1 RGB [.001 .02] 0 setdash S\n");

fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
system("epstopdf logi5.eps");
system(    "open logi5.pdf");
getchar(); system("killall Preview");
}

Generator of labels

File logi5.pdf should be generated with the code above in order to compile the Latex document below.

\documentclass[12pt]{article} %<br>
\usepackage{geometry} %<br>
\usepackage{graphics} %<br>
\usepackage{rotating} %<br>
\paperwidth 164pt %<br>
\paperheight 46pt %<br>
\topmargin -108pt %<br>
\oddsidemargin -90pt %<br>
\newcommand \sx {\scalebox} %<br>
\newcommand \ing \includegraphics %<br>
\newcommand \rot {\begin{rotate}} %<br>
\newcommand \ero {\end{rotate}} %<br>
\begin{document} %<br>
\begin{picture}(166,44) %<br>
\put( 1,1){\includegraphics{logi5}} %<br>
%\put( 64,48){\sx{.6}{$F(x)$}} %<br>
\put( 50,36){\sx{.4}{$F(x)$}} %<br>
\put(  0,41.5){\sx{.3}{$1$}} %<br>
\put(  0,22){\sx{.3}{$0$}} %<br>
\put( -1, 2){\sx{.3}{$-\!1$}} %<br>
\put( 20, 0){\sx{.3}{$-2$}} %<br>
\put( 40, 0){\sx{.3}{$-1$}} %<br>
\put( 62.5, 0){\sx{.3}{$0$}} %<br>
\put( 82.5, 0){\sx{.3}{$1$}} %<br>
\put(102.5, 0){\sx{.3}{$2$}} %<br>
\put(122.5, 0){\sx{.3}{$3$}} %<br>
\put(142.5, 0){\sx{.3}{$4$}} %<br>
\put(162, 0){\sx{.3}{$x$}} %<br>
\put(91.3,29){\sx{.3}{$s\!=\!3.9$}} %<br>
%\put(91,21){\sx{.3}{$s\!=\!4$}} %<br>
\put(92.5, 19.5){\sx{.3}{$s\!=\!4.1$}} %<br>
\end{picture} %<br>
\end{document} %<br>