Linkage

I’m gradually shifting weight to my Mastodon account and away from my doomed G+, but I hope to stick with both through the end of the year to provide a gradual transition. Today’s step: the Mastodon links go first.

• Meditative geometric shapes doodled on old ledgers by Albert Chamillard (\(\mathbb{M}\)).

• Post without words: A sequence of mathematical images in search of an explanation (\(\mathbb{M}\), G+). What are these paths of randomly-placed dots that seem to explode in some sort of binary tree pattern from the bottom left corner of the images? (Don’t read the comments farther down on the post unless you want spoilers.)

• Symmetric graphs constructed as the state spaces of rolling dice of different shapes (\(\mathbb{M}\)). It doesn’t say so in the post, but Ed Pegg pointed out separately to me that if you do this with a regular octahedron (d8) you get the Nauru graph (see Ed’s new illustration of this). A dodecahedron (d12) should get you a nice 5-regular 120-vertex graph (because each face has 10 orientations) – anyone have any idea what’s known about this graph?

• 1 in 4 statisticians say they were asked to commit scientific fraud (\(\mathbb{M}\), G+, via). One of the reasons I like working in a discipline based more on proof and less on experiment: I have a difficult time imagining what “mathematical fraud” might be, or why one might be pressured to commit it. Uninteresting math, or more-complicated-than-necessary math, sure, but deliberately-wrong math? Why would you do that?

• How can we randomly sample degeneracy orderings of graphs? (\(\mathbb{M}\)). These are the orderings you get by setting a counter \(k\) to zero, and then repeatedly either removing a vertex of degree \(k\) (if there is one) or incrementing \(k\) (otherwise); they define an antimatroid. My intuition is that counting them (or generating exactly uniform samples) might be \(\#\mathsf{P}\)-complete, but I don’t have a proof.

• The 2019 class of fellows of the American Mathematical Society (\(\mathbb{M}\)). There are surprisingly many new fellows with a theoretical computer science connection, including Saugata Basu, Bonnie Berger, Aravind Srinivasan, Moshe Vardi, and Eric Vigoda.

• The geometric quilts of Irena Swanson (\(\mathbb{M}\)). Swanson is a commutative algebraist, one of the new AMS Fellows. See also her own sites on geometric quilting and tube piecing.

• The Queen of the fold-and-cut alphabet (\(\mathbb{M}\)). Two posts by Evelyn Lamb about the theorem that you can make any shape by folding and one cut, and a alphabet based on this principle by Katie Steckles with the Demaines.

  A small peeve: Lamb and Steckles omit credit for some theorem authors. If you want to design your own, the disk packing method has been implemented (I posted about this already once long ago) but I think that the straight skeleton method produces prettier folding patterns when it works (it doesn’t always).

• Little Planet Lookout, by Gyorgy Soponyai (\(\mathbb{M}\), via). Where did all the circles in this image come from? Some of them, traced by stars across the night sky, form an elliptic pencil converging to the north and south celestial poles. Others come from the latticework of a lookout tower, transformed into more pencils of circles. The horizon also appears, less clearly, as a small dark circle near the center of the image.

• New tools for self-construction in Conway’s Game of Life (\(\mathbb{M}\)). Self-constructing spaceships are getting smaller, more visually clear (not just looking like a line) and more varied. And there’s a hint of a new and improved metacell that can simulate Life or other cellular automata, with empty space as its off state, so you could start any simulation with finitely many live cells. The key to all this is new software to find glider salvos that build constellations of still lifes.

• A Space of Their Own (\(\mathbb{M}\), via). A new and under-construction database of over 600 overlooked female artists from the 15th to 19th centuries.

  “Many of their female creators were acclaimed during their lifetimes. By the time Fortune [the founder of the project] set about restoring their work – and visibility – to the public view, they were virtually unknown, even to museum staff.”

• A puzzle about representing numbers as a sum of 3-smooth numbers (\(\mathbb{M}\)). No two of the numbers in the sum can be pairwise divisible, so you can’t just use powers of two.