I get the error below. Now I could set $good_ucase_numbers, $good_lcase_numbers to be static and use self:: in the constructor OR I could put them as arguments in the constructor and send them when instantiated. But I want to know why this will not work. I should be able to merge the 2 arrays in the constructor using $this-> 
Fatal error: Access to undeclared static property: Captcha::$good_ucase in C:\blah\Captcha.php on line 39
class Captcha {
public $length;
private $captcha;
protected $good_ucase = array('A', 'B', 'C');
protected $good_lcase = array('a', 'b', 'c');
protected $good_numbers = array(1, 2, 3);
protected $good_ucase_numbers, $good_lcase_numbers;
protected $font_path = '.fonts/';
protected $ucase_fonts = array('a.ttf', 'b.ttf', 'c.ttf');
protected $lcase_fonts = array('a.ttf', 'b.ttf');
public function __construct()
{
$this->$good_ucase_numbers = array_merge($this->$good_ucase, $this->$good_numbers);//ERROR HERE
$this->$good_lcase_numbers = array_merge($this->$good_lcase, $this->$good_numbers);
$this->$captcha = $this->create_captcha();
}
}
$captcha = new Captcha();