How did these checkerboards come about? I've noticed them on maps before when looking for public land in the US.
Office types gridded up manifest destiny using squares within squares and created a pre GPS coordinate system for coding up space (within central north america).
See (as starting points).
https://en.wikipedia.org/wiki/Public_Land_Survey_System
https://www.usgs.gov/faqs/do-us-topos-and-national-map-have-...
While I'm not from that part of the world I spent a few years writing interop transformations betwixt all manner of "coord systems" across the globe that predate WGS84 et al.
The PLSS grid explains the locations of many midwest US roads and townships, and "checkerboard ownership" (families | businesses buying land to surround other land and then deny access to land not paid for) was one form of early system gaming.
The foundational aspect to the question posed is that land was gridded in abstract from afar before any aportions were made, a secondary aspect was that in some regions large tracts of those squares were initially granted to various railroads on an "every second large chunk" basis, another aspect was that in the days of open cattle grazing early land cattle barons realised they didn't have to own land to graze on it and they could control access to unowned land by only paying for surrounding land or for "chokepoint" land in rough terrain.
A 'final' aspect to the story is the creation of the US National Parks movement which started a wave of "freezing" as yet unsold land as permanently held as not for private use.
A key point is that the Land Grant Act of 1850 granted checkerbordered land to railroad companies within at most 50 miles of planned rail routes .. however that practice wasn't limited to rail grants - Tribal lands were also checkerboarded by the Dawes Act and public land was released on a checkerboard basis.
You can see the checkerboard ownership even in early cattle country that had no history of railroad grants - the large squares were the unit of sale and typically the early sales were for homesteads in the midst of unclaimed land with the next sale not being "right next door" but for another homestead block in the midst of unclaimed land.
It's the appeal of owning your house, shed, assets, yards, etc. while not having to pay to own the land your cattle are moved through for seasonal pastures.
Eventally all land would presumably have been purchased .. but the National Parks started freeing things up.
There's more on this (but not the complete picture) in:
That’s interesting, there are places where public/private checkerboards emerged naturally? The wiki link only tells the land-grant and reservation part of the story.
I had a better grasp and notes on this in the late 1990s, if you read the wikipedia page closely I seem to recall they make brief passing reference to both Homestead and Dawes Acts (~ 31st congress (?) era IIRC).
The railroad grants were the largest best known example by a long shot I believe, however not the first or only example and all based on an ealier gridding abstraction and a practice of encouraging development to spread out.
There's an intertwining of rich private interests and public policy .. people with entire full PLSS squares were able to influence land release patterns and the idea of vast endless "untouched" lands where you weren't forced to have neighbours had appeal.
The ridiculous lengths these hunters had to go to in order to avoid straying onto private land is antithetical to freedom (you still need hunting licenses in Norway; and permission to hunt on private land so there are still potential issues, but worrying about a few meters and the accuracy of GPS to avoid even crossing a tiny little portion of private land is not one of them).
Also, isn't this somewhere in the mountains where there are no railroads?
Looked like a clever idea at the time, likely.