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  Everyone's droning on about the ability of AI to solve millennium prize problems in mathematics, etc., etc. But not enough people are talking about using AI to draw Islamic Geometric Patterns. I created the first version of Taprats as a class project around 1998/1999. I wrote it in Java, which means that it's almost impossible for anybody to use it these days (and it's quite janky in any case). But David Bachmann recently fed my papers into ChatGPT and came out with a...

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  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 play with it! :monotile:

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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 tiling on the GPU using a fragment shader. That's cool, because it requires a constant a...

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  In the past few years, spicy topokki chips from Korea have become one of my favourite snack foods. They're the perfect blend of sweet, spice, salt, and crunchy. They're also very hard to get in my part of the world. Needless to say, that just makes them even more delicious.

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  Yesterday, through a somewhat unlikely chain of events, I met a complete stranger who was wearing a t-shirt with a picture of me on it.

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  In my online undergraduate P5.js course, students are about to begin the module on motion and physics, including a bit of physics simulation using Matter.js. It suddenly occurred to me that I had never seen anybody put together this particular demo before, and I realized it had to be done. Messy source code at https://editor.p5js.org/isohedral/full/vJa5RiZWs.

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  Wow, I'm glad the internet enjoyed my silly demo so much. As I mentioned elsewhere, I tip my hat to the people who responded with their past implementations of the same idea. I wish the students in my undergraduate P5.js course were as enthusiastic about this material as all of you 🙃

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  There are a few different notations that are used to describe "regular" tilings (where we use "regular" in the informal sense of "simple arrangement of copies of a single shape"). The most important are probably Grünbaum and Shephard's incidence symbols for isohedral tilings, and Heesch and Kienzle's primitive tiling types. A system developed by Bigalke and Wippermann in the 1990s is intermediate between the other two. Talkin...

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  In my online undergraduate P5.js course, students are about to begin the module on motion and physics, including a bit of physics simulation using Matter.js. It suddenly occurred to me that I had never seen anybody put together this particular demo before, and I realized it had to be done. Messy source code at https://editor.p5js.org/isohedral/full/vJa5RiZWs.