".=" operation seems to get slower and slower as string gets longer.
Maybe some linear operation is being done on the string each time.
Reproduce with:

set_time_limit(3000);
for ($i = 0; $i <= 100000; ++$i) {
    $o .= "x";
}
I control-C'ed this after 135 seconds of run time.

Similar perl code runs in about one second on the same system.
Perl code is:
for ($i = 0; $i < 100000; ++$i) {
    $o .= "x";
}