Category: Research
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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 the whole (long) story, and…
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I’ve always loved the Ishihara tests (pages printed with patterns of coloured dots, used to diagnose different forms of colour vision deficiency, or CVD). They’re beautiful works of graphic design. Years ago I bought a used copy of a complete set of tests, and framed some of them to hang in my house. Reflecting on…
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Earlier this year I created a web-based mobile puzzle game called “Slide to Unlock“. The premise is very simple, and probably easier to understand by trying it rather than reading about it. To clear a level, you must slide disks along their tracks, gradually removing those tracks until nothing is left. The sliding must be…
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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 I didn’t always make the…
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This is the second of two posts about papers that will appear at the Bridges 2021 conference. This paper is related to Islamic geometric patterns, and was co-authored with John Berglund. In this case I played a supporting role. The core ideas are very much due to John; I contributed a few bits here and…
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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 mechanism was probably Buckminster Fuller’s…
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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 posts about Heesch numbers. If…
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I’m freshly back from a weekend in Toronto, where I was participating in the Winter meeting of the Canadian Mathematical Society. I don’t normally attend math conferences, but this time around I was invited to a session entitled “The Art of Mathematics”, and it seemed natural to join in. As it happens, the session was…
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The artist M.C. Escher drew many lovely tilings, which he called “regular divisions of the plane”. He worked hard to ensure that his tilings were of lifelike animal forms such as birds and fish. He filled notebooks with hand-drawn sketches of tilings, many of which later found their way into his woodcuts. If you’d like…
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I’m thrilled to report that I’m a co-author of the article “An ultra-stable gold-coordinated protein cage displaying reversible assembly“, which was recently published in Nature. This work is the result of an exciting collaboration between biochemists, physicists, structural biologists, mathematicians, and others (including yours truly, a computer scientist!), spread over at least five countries on…
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At least year’s Bridges Conference in Stockholm, I attended a short presentation by Susan Goldstine about “self-diagramming lace”. As motivation for the new work she was presenting, Susan referenced her paper from the year before on what she calls “symmetry samplers”. Samplers are an old tradition in fibre arts. A symmetry sampler combines small swatches…
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I developed a new open-source software library for manipulating isohedral tilings, based on the work I did on this topic during my PhD. The library is available in C++ and Javascript, and I offer a few fun automated and interactive demo programs that anybody can use to play with isohedral tilings.