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

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

‪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

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

‪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

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

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

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

GPUs are amazing. I generated these images at a full resolution of 12,288 x 24,576, each one taking a couple of minutes. My old python code would have taken most of a month to generate each of these!

There's still work to do, but our Cannon-Thurston map explorer web app is already lots of fun to play around with. You can rotate the view with WASD and move with the arrow keys. The controls tab has lots of other options: different triangulations, colouring choices, etc. With Saul Schleimer and David Bachman.
henryseg.github.io/Cannon-Thur

Cannon-Thurston maps for veering triangulations, joint work with David Bachman and Saul Schleimer.

This won't make much sense unless you're a three-manifold topologist. But in case you are, Saul Schleimer and I made a census of the first 87047 transverse veering structures, together with some analysis, and two styles of pictures of the first 5699 of them. math.okstate.edu/people/segerm

Some new hyperbolic designs, and much more, available in T-shirt form from neatoshop.com/artist/Henry-Seg

Edmund Harris and I built a MathMechs extensor diamond lattice inside of a Curvahedra Schwarz D surface.

I updated my website segerman.org to link to a few new things. There’s also a new page collecting together my virtual reality projects.

Curvahedra + MathMechs extensors = ?

A Mastodon instance for maths people. The kind of people who make $$\pi z^2 \times a$$ jokes. Use $$ and $$ for inline LaTeX, and $ and $ for display mode.