I'd re-work that like this:

use constant LIMIT => 20; ## It's a constant. (Should do the same for 
+4)

my @palette = Imager::Color->new( 0,0,0 ); ## Set the first color to b
+lack avoids the need for $div

...
 
        my ( $re_z, $im_z, iterations ) = (0) x 3;

        while ( 1 ) {
            my $saved = $re_z; ## It's just saving a value for use lat
+er in the calculation; $temp might also do.
            $re_z = $re_z * $re_z - $im_z * $im_z + $re_c;
            $im_z = 2 * $saved * $im_z + $im_c;
            ++$iterations;

            last if $re_z * $re_z + $im_z * $im_z > 4; ## Exit and use
+ the iteration count to pick a color

            $iterations = 0, last if $iterations == LIMIT; ## beyond t
+he limit, set the iterations to 0 to pick black.
        }
        $image->setpixel( x => $x, y => $y, color => $palette[ $iterat
+ions ] )
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