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

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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!
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Jon
Jon 2021-11-15
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.

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