9 square and 16 square pattern generator

Hello!

So in architecture, we have the 9 square diagram, and the 16 square diagram. If we imagine any number of these squares colored either black or white, we get a specific number of iterations depending on the number of white and/or black squares. I've got a script that will generate these iterations for me, but in a random method. I'd like to be able to do this in some sort of numerical order where the first white, or 'subtracted' square starts in the upper left-hand corner and moves left to right, top to bottom as I cycle through these iterations.

For example, in the 9 square problem, if I subtract 2 squares, I would expect my first iteration to be this:

The second:

The Third:

The fourth:

and so on...

I've attached the script...I'm racking my brain whether I should approach this as a binary problem, a boolean problem, or some sort of mathematics that I can't comprehend.