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<blockquote style="position: relative; padding-left: 55px;"><section><a href="https://mathstodon.xyz/users/christianp/statuses/114666484438540778">Christian Lawson-Perfect (christianp@mathstodon.xyz)'s status on Saturday, 14-Jun-2025 06:06:54 JST</a><a href="https://mathstodon.xyz/@christianp" title="christianp@mathstodon.xyz"><img src="https://gnusocial.jp/avatar/88801-48-20231101090538.webp" width="48" height="48" alt="Christian Lawson-Perfect" style="position: absolute; left: 0; top: 0;">Christian Lawson-Perfect</a></section><article><p>EDIT: aperiodic *tilings*, not aperiodic *tiles*. You can arrange these tiles periodically. That'll teach me to take a second to read an abstract!</p><p>Whoah! More aperiodic monotiles! <a href="https://arxiv.org/abs/2506.07638" rel="nofollow noreferrer">https://arxiv.org/abs/2506.07638</a></p></article><footer><a rel="bookmark" href="https://gnusocial.jp/conversation/5197164#notice-10195700">In conversation</a><time datetime="2025-06-14T06:06:54+09:00" title="Saturday, 14-Jun-2025 06:06:54 JST">about 8 months ago</time> <span>from <span><a href="https://mathstodon.xyz/@christianp/114666484438540778" rel="external" title="Sent from mathstodon.xyz via ActivityPub">mathstodon.xyz</a></span></span><a href="https://mathstodon.xyz/@christianp/114666484438540778">permalink</a><h4>Attachments</h4><ol><li><article><header><div>Domain not in remote thumbnail source whitelist: arxiv.org</div><h5><a href="https://arxiv.org/abs/2506.07638">A Family of Non-Periodic Tilings, Describable Using Elementary Tools and Exhibiting a New Kind of Structural Regularity</a></h5><div></div></header><div>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.</div><footer></footer></article></li></ol></footer></blockquote>

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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 conversationabout 8 months ago from mathstodon.xyzpermalink
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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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