That script draws Serpinski's carpet:

<?php
    set_time_limit(5);

    $i = 4;        // Iterations
    $xy = 500;    // Picture size

    $img = imagecreatetruecolor($xy, $xy);

    $white = imagecolorallocate($img, 255, 255, 255);

    drawCarpet(0, 0, $xy, $xy, $i);
    function drawCarpet($a, $b, $c, $d, $n) {
        global $img, $white;

        if($n <= 0) return;

        $a1 = 2 * $a / 3 + $c / 3;
        $c1 = $a / 3 + 2 * $c / 3;
        $b1 = 2 * $b / 3 + $d / 3;
        $d1 = $b / 3 + 2 * $d / 3;
 
        imagefilledrectangle($img, $a1, $b1, $c1, $d1, $white);

        drawCarpet($a, $b, $a1, $b1, $n - 1);
        drawCarpet($a1, $b, $c1, $b1, $n - 1);
        drawCarpet($c1, $b, $c, $b1, $n - 1);

        drawCarpet($c1, $b, $c, $b1, $n - 1);
        drawCarpet($a, $b1, $a1, $d1, $n - 1);
        drawCarpet($c1, $b1, $c, $d1, $n - 1);

        drawCarpet($a, $d1, $a1, $d, $n - 1);
        drawCarpet($a1, $d1, $c1, $d, $n - 1);
        drawCarpet($c1, $d1, $c, $d, $n - 1);
    }

    header('Content-Type: image/png');
    imagepng($img);
?>