Fibonacci Tree from Grid of Boxes/Rectangles

Hello everyone

I am currently trying to generate a cull pattern for a data tree of rectangles to generate a fibonacci sequence after connecting the centroids.

The idea is that I start off with a set of boxes or rectangles (it does not necessarily has to be a grid organization).

This would be not following a grid like organization:

How can I cull those lists in order to achieve something like this?

Thanks for any help