Current status:
Systems only go into quadrants: (X,-Y)
I may be terrible at math. Hm.

0 0
10 -10
8 -10
8 -15
12 -13
15 -11
11 -15
11 -18
15 -10
3 1
4 -1
5 -6
2 -10

Code is:

<?php
$placementfactor = floor(rand(1,4));
    if ($placementfactor === 4) { //+,+
      $newX = $host->coord_x + floor(rand(-5,5));
      $newY = $host->coord_y + floor(rand(-5,5));
    } elseif ($placementfactor === 3)  { //-,-
      $newX = $host->coord_x - floor(rand(-5,5));
      $newY = $host->coord_y - floor(rand(-5,5));
    } elseif ($placementfactor === 2) { //+,-
      $newX = $host->coord_x + floor(rand(-5,5));
      $newY = $host->coord_y - floor(rand(-5,5));      
    } else { //-,+
      $newX = $host->coord_x - floor(rand(-5,5));
      $newY = $host->coord_y + floor(rand(-5,5));      
    }

• For your examples, what were the values of $host->coord_x and $host->coord_y? If they were sufficiently positive x and negative y, that would be why you are getting these 3rd quadrant values.
• (3, 1) is not in the third quadrant, which is what makes me suspect this
• When I ran this on my computer, with debug output, $placementFactor was consistently 0. I don't know why, but this would give you "only positive" values. I'm not sure what $placementFactor is supposed to do, though. rand() is already giving you positive and negative values. You don't need the +/- jazz.
• php.net recommends mt_rand() for being faster and more random.
• rand() returns an int, so there's no need to floor() it
• If you really need $placementFactor, might I recommend making the placement rands be from 0 to 5?

Suggestion:

https://gist.github.com/adam000/93164b99c5a39025e410

@adam000 Thank you, that helps tremendously!

49 commits behind? That's mayhem.