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.

using namespace std; typedef complex z_type; 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"); 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");
 * 1) include 
 * 2) include 
 * 3) include 
 * 4) define DB double
 * 5) define DO(x,y) for(x=0;x<y;x++)
 * 1) include
 * 1) define Re(x) x.real
 * 2) define Im(x) x.imag
 * 3) define I z_type(0.,1.)
 * 4) include "ado.cin"
 * 5) include "efjh.cin"
 * 1) define M(x,y) fprintf(o,"%6.3f %6.3f M\n",0.+x,0.+y);
 * 2) define L(x,y) fprintf(o,"%6.3f %6.3f L\n",0.+x,0.+y);

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

%