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I am currently developing a technology to transform random maps into completely symmetrical ones. I haven't yet managed to fully automate this process, and some settings still need to be adjusted manually. This takes about 2-3 minutes per map, but it's still progress. With a small change to the algorithm, it's possible to generate symmetrical 2x2 random maps as well.
If you plan to play something like this, let me know, and I can generate a dozen or so layouts.