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.

Big update to https://henryseg.github.io/cohomology_fractals - 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.

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

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: https://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 https://youtu.be/ENFXnNtd3xU

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. https://henryseg.github.io/Cannon-Thurston

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. https://henryseg.github.io/Cannon-Thurston/

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. http://math.okstate.edu/people/segerman/veering.html

Mathematician working mostly in three-dimensional geometry and topology, and mathematical artist working mostly in 3D printing and virtual reality.

Joined Apr 2017

A Mastodon instance for maths people. The kind of people who make \(\pi z^2 \times a\) jokes.
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