Divide the rectangle into smaller rectangles in a step-by-step cycle

Hi everyone, I want to split a rectangle into smaller rectangles like the one below. The subdivision process is carried out step by step as the arrow shown in the figure. I appreciate any of your ideas or pieces of code. Thanks all!

[Jon]

Figuring out how to do the indexing will probably not be too hard, but I am having trouble seeing the pattern as far as which rectangle is chosen as the next one to subdivide. Can you please explain further.