Pieter MostertA few weeks ago I realised that the construction of generalised metallic mean tilings I posted about here https://mathstodon.xyz/@pieter/115532375133320451 can be generalised further - both the V4 and C4 symmetric tile sets are special cases of a construction that generally only has half-turn symmetry. I won't spell out all the details unless someone asks, but if you've read the pre-print in the linked post, I hope you'll be able to join the dots.
Even if you aren't interested in the details, you may be interested in this new (to my knowledge) aperiodic set of 4 tiles. Valid tilings are by translates of these tiles or 180-degree rotations of them, with arrow directions and colours required to match. In some sense this is a sibling to Ammann's A2 and A3 tile sets, so I've dubbed it A2.5, but I'm open to other suggestions.
In the following posts I'll explain how I arrived at this tile set.
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