Help Getting Started: Matrix Permutations

I’m trying to use grasshopper (maybe C#?) to iterate a complete series of matrix permutations, but I’m having trouble getting started and I was wondering if anyone might have suggestions.

The matrix is a 6x6 grid, but instead of each square being black or white, half of the total squares are black and half are white. This would reduce the number of permutations, but each black square is associated with an adjacent white square (see attached diagram).

Each pair can aggregate up to three pairs (three contiguous black squares), but no more than three.

It might not seem terribly exciting, but it’s part of a larger academic project and a good way for me to learn how to use data structures in grasshopper (I think…).

Any suggestions or starting points would be welcome, thank you!