Post #2672398
2026-01-22 18:53 UTC
So maybe part of what we're doing is building up a vocabulary of valid transformations from a starting rectangle to distinct sets of multiple sub-rectangles.
And then we could find some of the solutions for any given n by looking at various kinds of transformations that add some number m rectangles to a smaller solution of size n-m.
i.e. if we know an n=2 solution, and we know there's a +3 transformation, that gives us an n=5 specimen. (Which is sort of where we started!)
Replies (1)
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@joshmillard@mastodon.social 2026-01-22 18:56
I think this by itself is NOT enough to find all specimens -- there are solutions that don't proceed solely from subdividing existing rectangles -- but it feels like a fun space to explore. There's other kinds of transformations we can document as well; one is the basis of all this, transforming a square into a set of rectangles, and all our solutions for n are new members of that family. But there's other things to look at to, like...