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How do I create a 4 x 4 grid over the orange grid like the pink(ish) one?

The pink grid are geometries that have already been provided and are wonderful. I'm attempting to create something similar over the other orange grids.

I could do this manually, but it would take a long time.

My first attempt was a fishnet function using Creating regular polygon grid in PostGIS?. The result is the purple in the bottom right of the picture. I could fiddle with the function for a while to get the grid to be rectangular instead of square but the orange grid varies slightly in places and is completely not perfect in others. I do not want an overlapping smaller grid.

So my next idea is to take the 'perfect' geometries and a align it with the bottom left of the orange grid and 'squish' it into the orange grid area.

enter image description here

I don't know if this is A) possible or B) the best way to go about solving my problem.

Any suggestions?

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If you are trying to create quarter-quarter Sections of Public Land Survey, here is a tool.

http://ianbroad.com/creating-quarter-quarter-section-grid-python/

Also, you can freely download GCDB for most of the western US. This has data has lots/tracts and quarter-quarter Sections.

http://www.geocommunicator.gov/Geocomm/lsis_home/home/index.htm

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