Category: Geometry
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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.
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This post is the fourth and final one in a series about Heesch numbers. Part 1 was a general introduction, and would be a good starting point if you’re unfamiliar with the topic. Part 2 covered exhaustive computations of Heesch numbers of polyominoes and polyiamonds, and likely isn’t needed to understand this final chapter. Part…
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This is the third post in a planned series of four about Heesch numbers. In the first post, I introduced some of the basic ideas behind Heesch numbers; if you’re not familiar with the topic, you may want to read it before coming back here. The second post was about Heesch numbers of simple polyforms…
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In the first post in this series, I introduced the concept of a shape’s Heesch number. In brief, if a shape doesn’t tile the plane, its Heesch number is a measure of the maximum number of times you can surround the shape with layers of copies of itself. (Shapes that do tile are defined to have…
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I love tiling theory. It’s a branch of mathematics that brings together many beautiful ideas, and that offers a lot of open questions for exploration. And of course, it gives us tools to apply mathematics in the world of art and design. Normally, in my research as a computer scientist I apply tiling theory to create…
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Anybody who has attended a Bridges conference in past ten years will be familiar with the work of Rinus Roelofs. His talks always offer an entertaining contrast: stunning and inspiring ideas in the intersection of geometry and art, balanced with his humble, low-key delivery. It was also Rinus who suggested that I try Rhino3D for…
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In 1989 I attended Shad Valley, a one-month Canadian summer program for high school students. I spent a month living on the UBC campus. Basically it was Nerd Camp, though perhaps with a more diverse range of interests and talents than you might expect from the nerd stereotype, and with a definite entrepreneurial bent. It…
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Earlier this year, at a local coffee shop, I noticed a flyer on the wall with a call for artist submissions for an upcoming show in Halton Hills. The topic of the show was Altered Books. I had never experimented with the artform of altered books before, though I had seen great examples online. I…
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I’ve been having fun experimenting with interesting visual patterns that emerge when multiple points are moved around hypocycloids. I ended up writing a Bridges conference paper on the topic, but the animated quality of the results is so crucial that it seemed absolutely necessary to create a web page to showcase the results. I had…
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The photo above is a paper model of a polyhedron that I just assembled. The model consists of four dodecagons (12-sided regular polygons) and 12 decagons (10-sided regular polygons). The holes are 28 equilateral triangles that in theory could be filled with more paper. This polyhedron has a few symmetries, and it’s customary in such…