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Christian Lawson-Perfect (christianp@mathstodon.xyz)'s status on Saturday, 14-Jun-2025 06:06:54 JST Christian Lawson-Perfect

EDIT: aperiodic *tilings*, not aperiodic *tiles*. You can arrange these tiles periodically. That'll teach me to take a second to read an abstract!
Whoah! More aperiodic monotiles! https://arxiv.org/abs/2506.07638
In conversation about 8 months ago from mathstodon.xyz permalink
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1. Domain not in remote thumbnail source whitelist: arxiv.org
  
  A Family of Non-Periodic Tilings, Describable Using Elementary Tools and Exhibiting a New Kind of Structural Regularity
  
  We present a construction of a family of non-periodic tilings using elementary tools such as modular arithmetic and vector geometry. These tilings exhibit a distinct type of structural regularity, which we term modulo-staggered rotational symmetry. The construction is self-contained and does not rely on previous tiling theories or systems.
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  scmbradley (scmbradley@mathstodon.xyz)'s status on Saturday, 14-Jun-2025 06:06:52 JST scmbradley
  in reply to
  
  @christianp this one in particular is hurting my brain
  In conversation about 8 months ago permalink
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  1. It's a tiling of the plane made of long thin wiggly tiles. You know how you sometimes get like placemats made of bits of wood where there's a rotational symmetry? It's sort of like that but... more chaotic
    https://media.mathstodon.xyz/media_attachments/files/114/666/563/799/226/792/original/86f93d91979673eb.png
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  scmbradley (scmbradley@mathstodon.xyz)'s status on Saturday, 14-Jun-2025 06:06:53 JST scmbradley
  in reply to
  
  @christianp how long until we have custom emojis of them?
  
  In conversation about 8 months ago permalink
  
  mark repeated this.

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