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Recently, Sébastien Labbé and Peter Selinger posted a preprint (https://arxiv.org/pdf/2604.20964) that describes a sophisticated construction for the hat tiling, based on what's called a Markov partition (see the thread by @pieter at https://mathstodon.xyz/@pieter/116484517078239617 for more details).
One nice side effect of their construction is that it provides a means of rendering the hat tilin
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The other Bridges paper with my students was by Saba Molaei. Her work is inspired by the legendary Silicon Graphics logo (designed by Scott Kim!). The logo can be interpreted as a single closed path that visits every edge of a cube. Naively, that's impossible, but you can do it if you allow yourself to visit some edges *twice*. The inevitable question is: for what other polyhedra can you do this,
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So I guess I have a merch table now? The University of Waterloo created a retail collection based on the hat. Lots of fun stuff. And no, I don't get a cut of the profits. :monotile:
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Two of my graduate students have absolutely terrific papers at Bridges this year. The paper by Tuan Dung (Brian) Do is about drawing analogues of standard visual illusions in hyperbolic geometry. Some illusions carry over nicely, and some don't work, but all the results are fun to look at. I hinted at this project earlier this year as part of Genuary (image reposted here).
The full paper is at htt
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🔥 Top post: Recently, Sébastien Labbé and Peter Selinger posted a preprint ( · 103 likes + reposts
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Recently, Sébastien Labbé and Peter Selinger posted a preprint (https://arxiv.org/pdf/2604.20964) that describes a sophisticated construction for the hat tiling, based on what's called a Markov partition (see the thread by @pieter at https://mathstodon.xyz/@pieter/11648451707823…
The other Bridges paper with my students was by Saba Molaei. Her work is inspired by the legendary Silicon Graphics logo (designed by Scott Kim!). The logo can be interpreted as a single closed path that visits every edge of a cube. Naivel…
Two of my graduate students have absolutely terrific papers at Bridges this year. The paper by Tuan Dung (Brian) Do is about drawing analogues of standard visual illusions in hyperbolic geometry. Some illusions carry over nicely, and some …
The Bridges Archive has been updated with 2026 papers: https://archive.bridgesmathart.org/2026. Stop by and enjoy a trove of math-art delights!
So I guess I have a merch table now? The University of Waterloo created a retail collection based on the hat. Lots of fun stuff. And no, I don't get a cut of the profits. :monotile:
Also, this is somewhat more specialized, but here's a first draft (with no documentation) that draws just the Markov partition itself: https://www.shadertoy.com/view/s3lGDM.
As promised, here's the Shadertoy page for a GPU shader that draws the hat tiling: https://www.shadertoy.com/view/s3lGD7. Hopefully the code makes sense (I've tried to organize it to be easy to work with), and people will find fun ways to …
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The construction involves defining a fractal colouring of the plane, and sampling from the fractal using points in a lattice (the vertices of a tiling by equilateral triangles). @pieter asked about visualizing the result of sliding the lat…
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