Henry Segerman

Today, the one-week #illustratingMath workshop at @icerm.bsky.social starts. It is a week, packed with great talks on #images, #animations, #textiles, #sculptures, #dance, and #3dPrinting. All talks are being live-streamed, so go check out the schedule at icerm.brown.edu/program/topi... and join in!

I added a second post on my new Patreon, about my plans for a three-dimensional expanding racks design based on the srs net (also known as the Laves graph). See www.patreon.com/posts/135832...

The space-filling curve is the Cannon-Thurston map for a veering triangulation (with veering isosig gLLAQbecdfffhhnkqnc_120012). We prove that veering triangulations have Cannon-Thurston maps in an upcoming paper with Jason Manning.

I never got around to posting this animation I made with Saul Schleimer.This animates successively better approximations to a space-filling curve. (Or rather, you can tile the plane with the shape, and that gives the approximation to the space-filling curve.)

They generally do this by having health/damage numbers generally be very small: your attack might do three damage. Then an item that increases an effect by one makes a real difference to how you play, and feels like a real reward.

This allows the game makers to mete out many tiny rewards, although few that really make much difference to the game. There is however something of a movement (particularly in indie games) to have the items you get be meaningful upgrades, and the numbers involved be really meaningful.

There is perhaps a parallel in video game damage/health numbers. There are many games that measure how much damage your sword (or whatever) does in hundreds or even thousands. This allows for a large number of items to collect that modify your damage output by one or two percent here or there.

Come to mathstodon, where the sources of timeline bugs are presumably less opaque!

True. The cultural meaning is not that well correlated with the cardinal directions.

Feels a little odd to put a Western image of a human figure on the front cover of a book about the Alhambra?

A screenshot from a CAD program with racks arranged in a complicated pattern in space.

I finally got around to setting up a Patreon! It's at patreon.com/HenrySegerman. 
The first post is about my plans for taking the expanding racks project (youtu.be/iWknov3Xpts) from two-dimensional to three-dimensional networks. 
If you’d like to support my work, please consider joining. Thanks!

A colourful three-dimensional arrangement of gears and racks.

Working on a few three-dimensional expanding rack mechanisms. This one is based on the NbO lattice.

The Bridges 2025 conference proceedings are now online.
My article: "Fold-and-cut lines for the hat, turtle, and spectre tiles" archive.bridgesmathart.org/2025/bridges...
The full proceedings: archive.bridgesmathart.org

Some photos from the exhibition that opened at the National Museum of Mathematics Thursday, on 5th Ave in NYC. The other artists/mathematicians in the exhibition were Nicolas Belmonte, Chaim Goodman-Strauss, Edmund Harriss, Stepan Paul, Henry Segerman, and Steve Trettel.

Moving up one dimension into Apollonian sphere-packing using POPs. I put together an implementation based on Kean Walmsley’s code, which itself is built on Ron Peikert’s original work from his paper “The Fractal Dimension of the Apollonian Sphere Packing.”

#creativecoding #generative #generativeart

I’m curating an exhibition of Mathematical Art at the Australian Mathematical Society meeting in December. If you’re coming to the meeting and you create art with mathematics, please think about being involved. More information to appear at the conference website.

I'll be in NYC this week for the opening of an art exhibition at the Museum of Mathematics. "Warped Realities" showcases the work of seven artists, and includes ten of my ceramic sculptures. If you're able, please join us Thursday evening at 6:30. . momath.org/composite-ga...

Alongside the research program "Illustration as a Mathematical Research Technique" (more information here: www.ihp.fr/en/news-rese...), there will be a #MathArt exhibit from 9 April to 25 July with an open call for participation: www.ihp.fr/en/actualite....

A fractal curve divides a shape into a white and a black half.

Saul Schleimer and I got our code for generating Cannon-Thurston maps working with sagemath algebraic numbers. The old code used floating point numbers which would eventually lose precision and blow up. With algebraic numbers we can go as far as we want!

Here’s another clip from my video on expanding rack and pinion mechanisms - an expanding pythagorean triple triangle. There’s a reason why it’s easier to make this kind of triangle! Full video at
youtu.be/iWknov3Xpts

The #illustratingMath Seminar Online (IMSO) will continue on June 13th at 9am Pacific/12pm Eastern / 6pm Central Europe! Our speaker will be Carolyn Yackel on "Marrying #Mathematics with Illustrative Technique", accompanied by "Show and Ask" talks from M. Conroy and A.D. Jones.

So one of the equatorial gears rotates a bit, which is supposed to rotate the inner shell a bit. Is there enough slop in the other equatorial gears to allow for this motion?

New video on some expanding 3D printed designs based on rack and pinion mechanisms:
youtu.be/iWknov3Xpts

What if books about abstractions didn't have to stay flat?

Visualizing Mathematics with 3D Printing by Henry Segerman @henryseg.bsky.social www.3dprintmath.com Johns Hopkins University Press 2016

Model www.printables.com/model/167505... on @printables.bsky.social

#MathSky there's a new online open-access (and free) journal for mathematics and fiber arts: Interlace. Now accepting manuscripts! Editors-in-Chief: sarah-marie belcastro and Carolyn Yackel. 🧶
www.interlace-journal.org

Very cool stuff, and it's the first method (with a physical justification) I know of for making dice with differently shaped faces and probabilities. 
However, they don't pay attention to momentum, friction, or bouncing - the question now is how much those things matter.

I had to know if it worked, so I built a little simulator! Here's the setup: a little toy dinosaur and a conical spotlight, then a black hole, then a simulated piece of film (that will record when a simulated photon hits it, and accumulate them)

I’m sitting next to a 4 foot tall Hyphae lamp outside in the night with tree like shadows cast all around

For years, we've been making Hyphae lamps that fit in your hand. Now we're working on something a bit bigger #sciart

My latest coordinate-motion model with 20 pieces, based on the compound of five tetrahedra. We can assemble the 20 identical pieces into five separate tetrahedra or into one large ball. The previous 4 models in this series are available for purchase here: www.nothingyetdesigns.com/collections/...

YouTube video by 3Blue1Brown But what is Quantum Computing? (Grover's Algorithm)

New video! This covers the fundamentals of quantum computing and builds up to a step-by-step walk-through of an important algorithm in the field.

youtu.be/RQWpF2Gb-gU