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Pieter Mostert

pieter@mathstodon.xyz

<p>I&#39;m a former potter with a maths background, and currently work with data at a rural education NGO in South Africa.</p>

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    #SilentSunday

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    For any fellow fans of Angine de Poitrine, they just released their second album: https://anginedepoitrine.bandcamp.com/album/vol-ii If you aren&amp;#39;t (yet) a fan, take a listen to their KEXP performance: https://www.youtube.com/watch?v=0Ssi-9wS1so #anginedepoitrine

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    I wish I&amp;#39;d thought to install an AI-slop blocker for youtube sooner. This seems to be working great so far, although unfortunately there isn&amp;#39;t a version for Android: https://addons.mozilla.org/en-US/firefox/addon/ai-channel-blocker-for-youtube/ #aislop

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    Taking some time away from the herd. #sea #cow

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    As a follow up to last week&amp;#39;s post on Markov partitions for Hat (hat and turtle) and Spectre (hats in turtles and turtles in hats) tilings (https://mathstodon.xyz/@pieter/116484517078239617), here is a way of colouring such tilings. For each control point, we colour the tile according to its distance from the boundary of the fractal window it lies in. The first image shows a patch of a turtle tiling using the colour map in the second. Control points that lie near the boundary of the fra...

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    Peter Selinger now has an app https://www.mathstat.dal.ca/~selinger/hat-partition/ that lets you create hat tilings using the Markov partition described in his paper with Sébastien Labbé (https://arxiv.org/abs/2604.20964). For a printable version of this, see Sébastien&amp;#39;s blog post: http://www.slabbe.org/blogue/2026/03/a-construction-of-the-hat-tilings-by-a-markov-partition/ #aperiodicMonotile #tiling

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    #silentSunday

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    Peter Selinger has come up with a great way of generating hat tilings by overlaying a triangular grid on a periodic pattern, and placing a tile at each point that is not white, with the orientation and handedness of the tile determined by the colour of the point. A more thorough explanation is given in this preprint https://arxiv.org/pdf/2604.20964, where he and Sébastien Labbé show that this is a Markov partition. As mentioned in the paper, I came up with a similar construction a few years ago...