• Linkage

  • Some pyramidology

    Another Wikipedia editor, “Dedhert.Jr”, recently brought Wikipedia’s square pyramid article up to Good Article standards. In honor of their achievement, I thought it might be fun to analyze the proportions of various famous pyramids.

  • Aperiodic pinwheel scheduling using Beatty sequences

    The pinwheel scheduling problem takes as input a collection of tasks, each taking unit time but needing to be repeated with some given maximum repeat time. The goal is to find a schedule: an infinite sequence of tasks to perform so that the gaps between each repetition of each task are no bigger than allowed. I drew the following illustration for Wikipedia, with the help of Adobe Illustrator’s new AI-based vector drawing features; it shows tasks A, B, and C with repeat times 2, 4, and 5, respectively, scheduled with the infinite repeating sequence ABACABAC… One real-world situation that this might model is scheduling equipment maintenance sessions, where certain kinds of equipment have different demands on how frequently they are maintained.

  • Mid-November Linkage

    • We recently installed a wall-mounted scratching pole (\(\mathbb{M}\)) to give our kittens access to the space above the bathroom false ceiling (to the upper left of this photo) and the lintel between the bathroom and bedroom (upper right). It’s their new favorite place.
  • Linkage for Halloween

  • The quadtree-balancing antimatroid

    Today’s computational geometry lecture involved the use of balanced quadtrees in finite element mesh generation, the topic of Chapter 14 of the Book of the Four Marks. Here, a quadtree is just a recursive subdivision of a square into smaller squares, obtained by some rule for deciding when to divide one square into four. In the mesh generation application, you start of by performing this sort of subdivision for “crowded” squares (containing more of the boundary of the region to be meshed than just one or two adjacent edges) and for squares within which you expect the physical properties you are simulating to have complicated behavior (like turbulence or shock waves) where smaller regions are needed for better accuracy.

  • Linkage

  • Linkage for the start of the academic year

  • Report from Graph Drawing

    I just returned from the 31st International Symposium on Graph Drawing and Network Visualization (GD ‘23), held this time in Isola delle Femmine, a small beach town on Sicily near Palermo. Despite the name it is not a separate island; the actual Isola delle Femmine is not the town, but a small barren island about a half kilometer offshore, decorated only by a ruined tower. Several conference participants (not me) swam to the island, several others were turned back by choppy water, and at least two were stung by jellyfish. Other than visiting the hotel beach I didn’t have much of a chance for sightseeing (the weather did not cooperate for the only large block of free time that I had) but I did enjoy the excellent Sicilian food and wine.

  • Linkage

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