How to resolve the algorithm Chaos game step by step in the Perl programming language

Published on 12 May 2024 09:40 PM
#Perl

How to resolve the algorithm Chaos game step by step in the Perl programming language

Table of Contents

Problem Statement

The Chaos Game is a method of generating the attractor of an iterated function system (IFS). One of the best-known and simplest examples creates a fractal, using a polygon and an initial point selected at random.

Play the Chaos Game using the corners of an equilateral triangle as the reference points.   Add a starting point at random (preferably inside the triangle).   Then add the next point halfway between the starting point and one of the reference points.   This reference point is chosen at random. After a sufficient number of iterations, the image of a Sierpinski Triangle should emerge.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Chaos game step by step in the Perl programming language

Source code in the perl programming language

use Imager;

my $width  = 1000;
my $height = 1000;

my @points = (
    [ $width/2,         0],
    [        0, $height-1],
    [$height-1, $height-1],
);

my $img = Imager->new(
                      xsize    => $width,
                      ysize    => $height,
                      channels => 3,
                     );

my $color = Imager::Color->new('#ff0000');
my $r = [int(rand($width)), int(rand($height))];

foreach my $i (1 .. 100000) {
    my $p = $points[rand @points];

    my $h = [
        int(($p->[0] + $r->[0]) / 2),
        int(($p->[1] + $r->[1]) / 2),
    ];

    $img->setpixel(
        x     => $h->[0],
        y     => $h->[1],
        color => $color,
    );

    $r = $h;
}

$img->write(file => 'chaos_game_triangle.png');

You may also check:How to resolve the algorithm Guess the number/With feedback step by step in the MATLAB / Octave programming language
You may also check:How to resolve the algorithm Find the missing permutation step by step in the Ring programming language
You may also check:How to resolve the algorithm Van der Corput sequence step by step in the Ela programming language
You may also check:How to resolve the algorithm Higher-order functions step by step in the Aime programming language
You may also check:How to resolve the algorithm Euler's sum of powers conjecture step by step in the Fortran programming language