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Top-level
One more interesting thing: the "hats" are 14-gons (counting the long edge as two), what happens when we try to draw a "straight line" by exit each tile via the edge opposite (+7) to the edge we have entered it? (Bulls in Bull Dash move like this...) The result gets very random, especially compared to the Penrose kite-and-dart (despite both being based on a hierarchical construction). 3 comments
In https://mathstodon.xyz/@zenorogue/110084091274230145 there was a bug: the centers of mirrored hats was supposed to be the mirror images of the centers of non-mirrored hats (in particular, rotate clockwise vs anti-clockwise), but they did not -- here is a fixed version (with some other minor changes). Thanks to Magma for catching this! A version of the "zooming in" animation up in the thread where the color of hats and clusters is based on their rotation (and the saturation is based on hat/cluster type), and the lowest level oscillates between the possible shapes. |
Gregory's Server
Can we zoom in forever, or do we eventually reach "atoms" with no internal structure?
This is an aperiodic tiling, so what we get depends on where we zoom in. In the first animation we pick a very specific location; in the second animation, we pick a random one.
BTW to keep all our hat threads in one place, here is the other one: https://mathstodon.xyz/@zenorogue/110073177221166901