Similar to what @alytile showed for the H/T/P/F metatiles (xitter.cf/alytile/status/1638093…) these are the 2 fractal tiles for the substitution system in figure 2.11 of the new aperiodic monotile paper (arxiv.org/pdf/2303.10798.pdf).
The optimal known packing of 17 equal squares into a larger square - i.e. the arrangement which minimises the size of the large square.
I should add - this packing for 17 squares is not rigid - 3 of them can slide, and one even has room to wiggle, but it's not enough to allow any of the other squares to move inward, so it doesn't change the size of the containing square.
Daniel Piker retweeted
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Mastodon: mathstodon.xyz/@Danpiker
Discord: Dan Piker#9142
I saw those clips of the tangled plug topology went viral again the other day. Lots of people in the comments were convinced it was fake and just editing tricks.
It can be hard to follow in videos with hands getting in the way, so I made an animation to hopefully make it clearer.
Here's a fun little kinematic toy that's easy to make - an equilateral orthogonal hexagon linkage with 1 degree of freedom:
With a bit of practice, you can time it so the momentum carries it through and the square opposite the one you are holding traces a sort of figure eight path