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Geometry

Aperiodic Monotiles

Now that I’ve written up posts about some of the smaller projects that have occupied my time over the past 18 months or so, it’s time to talk about the Big One, the real reason I came back to this blog in the first place. I don’t want to re-tell …

Generative Zellij

Procedurally generated Zellij compositions. Click on the drawing and press the space bar to generate a new composition. Press the ‘s’ key to download an SVG file. Yes, I am somewhat ashamed to admit that a couple of years ago, I experimented with NFTs. Look: I was younger then, and …

Beyond the Great 96

The challenge when designing around a large star is to reconcile its high order of symmetry with the field of more standard shapes that surrounds it. The goal is to make the complete design appear natural and seamless. That’s an exceedingly difficult design challenge, one that increases in difficulty as …

Animated Map Colourings of Hinged Squares

Tilings like these, based on alternating arrangements of squares and rhombs, are ancient. And in the twentieth century, a few people experimented with this hinged motion. I particularly like the essay by Duncan Stuart, then a student at the UNC School of Design, though the most famous use of this …

Heesch Numbers of Unmarked Polyforms

After a few years of not writing about the subject here, I’m happy to offer an update on Heesch numbers! If you want to save time, you can skip right to the paper I wrote, or experiment with the associated dataset. Back in 2017, I wrote a series of four …