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:

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

Big update to - 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:

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

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:

Quasiperiodic bobbin lace patterns:, Veronika Irvine, Therese Biedl, and Craig S. Kaplan, via — 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:

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

Escher-like spiral tilings, by Craig Kaplan:

(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.

:chalkdust_scorpion: In this blog from our archives, @mscroggs talks about @henryseg's book on how 3D printing can help with our understanding of geometry!

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.

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!

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