mathBlock(Inactive, see other accounts) @mathBlock

@BretDevereaux @AtienzaElias I wonder what your have to say about his take on the Dark Ages?: slatestarcodex.com/2017/10/15/wer…

@dimden @demomikke I've tried that several times and have not gotten it to work. (old pic of warning below)

Link to the post: mathblock8128.wordpress.com/2024/04/13/tur…

The most recent post on the blog is a follow up of my re-worked non-peridoicity proof for the Turtle #aperiodic #monotile. It is rather dry, but it explains the 'even' distribution of reflected tiles in the Turtle(thus Hat) tilings and sharpens that finding.

I've re-worked my proof that the Turtle #aperiodic #monotile cannot tile the plane periodically, so that it may serve as a proper starting point for future explorations. mathblock8128.wordpress.com/2024/03/20/tur…

@alytile It seems that you have coloured the original F metatiles white as well as the tile in the H metatile directly connected to it. However, there are a few F metatiles here that aren't coloured white. Why did you choose not to colour them the same?

The new tiles look and substitute like this:

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These can also be also be modified for the Turtle tile. Using the metatiles and substitutions in these pictures...

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Here's something for those still interested in the Hat or Turtle #aperiodic #monotile. If you take one of the two tiles below, place one on a plane and then try to fill the rest of the plane with Hat tiles, it seems that the position of every Hat tile is already determined.

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@ZenoRogue I posted about this elsewhere, but I thought of this hyperbolic prototile thinking about the binary tile and some stuff I was working on. All lengths labelled are Euclidean apparent lengths in the half-plane representation(assuming I did it right).

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If you start with a #spectre #aperiodic #monotile tiling, and just keep the oddballs, you can flip each one and smush them together to get a new tiling. However, you are left with gaps, which become the new oddballs.

@mathBlock I didn't realize I had to follow the 26 posts, so I was confused by your comment. (I am new to twitter.) Here's a version where I use the edge instead of the vertex to avoid having to extend the outlet past the boundary. And I use one decoration instead of two.

@AndrewR88968514 For the Hat/Turtle tiling, this edge consistency forces the 'odd'(reflected) tiles to exit the same way as the other tiles.

@AndrewR88968514 See Figure 3.1 in arxiv.org/abs/2305.17743 to see what I'm talking about with the edges.

@apu_yokai @mananself @JimPropp @robinhouston @cinderBlock_496 Sorry for the late reply. I don't think I've solved this per se, but I believe I've made progress working with Turtle tiles. See , replies, and the linked blog posts for details.

mathBlock(Inactive, see other accounts) @mathBlock

3 years ago

Made a follow-up to mathblock8128.wordpress.com/2023/08/15/the…, linked in reply. (Hopefully no mistakes)

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The blog post at (mathblock8128.wordpress.com/2023/09/16/spa…) has more details and further discussion. It is strongly suggested to read the previous post in the quoted/linked tweet() first.

mathBlock(Inactive, see other accounts) @mathBlock

3 years ago

Made a follow-up to mathblock8128.wordpress.com/2023/08/15/the…, linked in reply. (Hopefully no mistakes)

1 2 6 940 0

*Note on step 3: It may terminate w/o filling the outline if there exists a ‘loop’ of hexagons and fixed rhombs. Our example outline does not produce those, so it can be completely filled in.

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Made a follow-up to mathblock8128.wordpress.com/2023/08/15/the…, linked in reply. (Hopefully no mistakes)