Robert MacKay's Chaos Machine. Its configuration space is a genus three surface. The dynamics of the machine are equivalent to geodesic flow on the surface, which is Anosov, hence chaotic.

At ICERM this semester, Matthias Goerner made an in-space viewer for hyperbolic 3-manifolds in the geometry/topology software SnapPy starting from our cohomology fractals code. We're still working on it, but here's a path through Dehn surgery space for the fig 8 knot complement.

The video wherein David Bachman, Saul Schleimer and I finally explain what these cohomology fractals are: youtu.be/fhBPhie1Tm0

A zoom through a selection of cohomology fractals. With David Bachman and Saul Schleimer, music by Vi Hart. youtu.be/-g1wNbC9AxI

Big update to henryseg.github.io/cohomology_ - we now have all of the manifolds in the orientable SnapPy census up to 7 tetrahedra, and sliders to make linear combinations of cohomology classes (try m129). With David Bachman and Saul Schleimer.

If you're around the Oxford area on January 30th, I'll be giving a public lecture at 5pm, details: maths.ox.ac.uk/node/34486

3D Hilbert curve stained glass triptych done!

‪Braiding gears. Three gears are linked in a chain, but you can “braid” them, rearranging how they connect to each other. Full video at youtu.be/Lh7yAbw0H24

Today at lunch, I've learned about the Trash Compaction problem: Can you push objects on a grid into the compact shape of a rectangle if you're only allowed to push all objects from one side simultaneously. Akitaya, Aloupis, Löffler, and Rounds showed that the problem is NP-complete.

The fun variant of this problem talks about pushing around coconuts with a giant coconut pusher... Here are some neat slides: staff.science.uu.nl/~loffl001/

We made lots of pretty figures!

New paper on the arXiv today with Saul Schleimer, "From veering triangulations to link spaces and back again" arxiv.org/abs/1911.00006

Quasiperiodic bobbin lace patterns: arxiv.org/abs/1910.07935, Veronika Irvine, Therese Biedl, and Craig S. Kaplan, via twitter.com/bit_player/status/ — aperiodic tilings in fiber arts.

The attached image is a photo of lace (not an illustration), braided into an Ammann–Beenker tiling pattern.

‪A variant of gripping gears adds “pass-through” holes so that a solid object can pass through the connection between the gears. Joint work with Will Segerman and Sabetta Matsumoto. Full video: youtu.be/RBZG8M8_a8Y

arxiv.org/abs/1909.06947

In which we show that the knots K13n592 and K15n41127 (pictured) both have stick number 10. These are the first non-torus knots with more than 9 crossings for which the exact stick number is known.

Gripping gears: two gears mesh with and rotate around each other, with no axles and no frame. Joint work with Will Segerman and Sabetta Matsumoto. Full video at youtu.be/ENFXnNtd3xU

Escher-like spiral tilings, by Craig Kaplan: isohedral.ca/escher-like-spira

(Sadly with no angels, devils, fish, or geese, but maybe some talented artist will take up that challenge.)

Extensor cube in motion! Made by @christianp at the Talking Maths in Public conference today.

In this blog from our archives, @mscroggs talks about @henryseg's book on how 3D printing can help with our understanding of geometry! chalkdustmagazine.com/blog/vis

Added an option to view the edges of the tetrahedra in our Cannon-Thurston map explorer. This should make it easier to (eventually) explain a bit how the images are generated. henryseg.github.io/Cannon-Thur

My video on non-euclidean ray-marching virtual reality (joint work with Roice Nelson and Michael Woodard) was one of four winners of the NSF's "We Are Mathematics" competition! youtu.be/j8wx6Gol5YQ

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