Tuesday, August 15, 2006

logistic maps 1(toolset)

I am studying a book by Prof N Kumar of RRI on deterministic chaos (University press, India ).

The chapter on logistic maps made me somewhat confused - so started an internet search. The booke deals with the web representation for discussing the works - bifurcations , etc.

Found an interestinng representation (non-web) at http://mathworld.wolfram.com/LogisticMap.html. See the graphs on the top. I dont have Mathematica - so what do I do to get the maps? I spent an hour and created the follwoing perl script which in turn lanuches gnuplot to make plots simialr to the ones at the web site - slightly deeper. (Ugh - I am on windows - linux did not work that great on my laptop).

Some images:

At r = 3.4

Perl Script :


my $r_inc = 0.2;
my $x_inc = 0.001; #Change this to smaller values to get better pictures

for(my $r = 2;$r <= 4;$r += $r_inc)
my %data = ();

for(my $x0 = 0; $x0 <= 1; $x0 += $x_inc)
my $x = $x0;

for(my $i = 0; $i <= 10; $i++)
if(not defined $data{$i})
$data{$i} = [];

push @{$data{$i}},[$x0,$x];

$x = f($r,$x);


open SCR,">script_$r.scr";
print SCR "set xrange [0:1]\nset yrange [0:1]\n";
print SCR "set term png\nset output \"$r.png\"\nset title \"r=$r\"\nplot ";

my $first = 1;
foreach my $i (sort {$a <=> $b} (keys(%data)))
my $data_file = "data_".$r."_".$i.".dat";
open OUT,">".$data_file;
foreach my $x (@{$data{$i}})
print OUT "${$x}[0]\t${$x}[1]\n";

print SCR ", ";
print SCR "\"$data_file\" title \"$i\" smooth csplines";
$first = 0;

print SCR "\n";
close SCR;

system("./plot.sh script_$r.scr");

sub f
my $r = shift;
my $x = shift;

return ($r * $x * (1-$x));

Shell script plot.sh:


c:/Program\ Files/gnuplot/bin/wgnuplot.exe $*

What do I learn from all this? Not much - nothing yet. I am tired for the day. Actul study postponed to another day.


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