Why rand() isn't really random?

I wanted to put random points on an image (stars in space for some little fun side project)

I have this simple script.

<?php
$gd = imagecreatetruecolor(1000, 1000);
$white = imagecolorallocate($gd, 255, 255, 255);

for ($i = 0; $i < 100000; $i++) 
{
    $x = rand(1,1000);
    $y = rand(1,1000);

    imagesetpixel($gd, round($x),round($y), $white);
}

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

Keep in mind this is just for testing, that is why I put 100000 in for loop so it shows the pattern I noticed emerging. We have 1 million pixel to use, still random X and Y creates this pattern instead:

So it is far from random. I know rand is not real random, that is why it isn't good for cryptography. But I find no information about how it works and what should I do to avoid patterns like this.