Tag: tiling
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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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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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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…