You can think of $line as a base 4 number.

$line = $digits[0] * 4**0
      + $digits[1] * 4**1
      + $digits[2] * 4**2
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That can also be written as

$line = ($digits[2] * 4 + $digits[1]) * 4 + $digits[0]
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You can use modulo and division

for my $num_digits (2..3) {
   for my $line (0 .. 4**$num_digits - 1) {

      my $remain = $line;
      my @digits;
      for (1..$depth) {
         push @digits, $remain % 4;
         $remain = int($remain / 4);
      }

      print(join(', ', @digits), "\n");
   }
}
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Since 4 is a power of two, bit arithmetic can be used instead.

         push @digits, $remain & 3;
         $remain >>= 2;
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