Think of a number, and keep a running total starting at 0. Each turn, add your number on to the total. Then, if the old total was a multiple of your number, add one to your number. Otherwise, subtract 1.
The game ends when your number is 1.

Which starting numbers eventually get to 1? In the video, it looks like starting at 4 doesn't, but starting at 2 does.

My new sequence,, lists the numbers that eventually reach 1. I'd love to know if there's a pattern!

Show thread

Complete classification of tetrahedra whose angles are all rational multoples of \(\pi\):, via

The original paper is "Space vectors forming rational angles",, by Kiran S. Kedlaya, Alexander Kolpakov, Bjorn Poonen, and Michael Rubinstein

I've got a new sequence in the OEIS. It's to do with a really simple number game I made up. Here's a video explaining the rules

The skew dice set by The Dice Lab is out now at, featuring the most cursed d20 you're ever likely to see!
Full video at

An animation for Craig Kaplan’s art project, with Saul Schleimer. Here we fly through a cohomology fractal that happens to contain a checkerboard. You can explore it at (Open controls, go to the "cool examples" census, and choose "t12047".)

A collection of cohomology fractals for closed manifolds. The four manifolds (in reading order) are m280(1,4), s227(6,1), s400(1,3), and s861(3,1) from the SnapPy census. With David Bachman, Matthias Goerner, and Saul Schleimer.

Our big writeup, "Cohomology fractals, Cannon-Thurston maps, and the geodesic flow", is now up on the arXiv at With David Bachman, Matthias Goerner, and Saul Schleimer. We describe the relationship between cohomology fractals and Cannon-Thurston maps, we give implementation details for our software, and we investigate the limiting behaviour of cohomology fractals, as the "visual radius" increases.

Mechanical Computing Systems Using Only Links and Rotary Joints
Article by Ralph C. Merkle and Robert A. Freitas Jr. and Tad Hogg and Thomas E. Moore and Matthew S. Moses and James Ryley
In collections: Basically computer science, Things to make and do, Unusual computers
A new paradigm for mechanical computing is demonstrated that requires only two basic parts, links and rotary joints. These basic parts...
Entry: read.somethingorotherwhatever.

The dLX (pronounced "d-Lex", as in "lexicon"), is a new 60-sided, alphabetical die from The Dice Lab. Sixty is enough for us to get a letter distribution that is close to the distribution in the English language, so they can be used for word search games!

It may look like we are descending to land on an alien planet, but this is actually the new "hyperideal" view in our cohomology fractals web app. With Saul Schleimer, David Bachman, and Matthias Goerner.

Prototype skew d10 designs for The Dice Lab. We are working towards a full seven-die set of skew dice!

Experiments on reverse perspective:

Recent post by Paul Bourke with a link to a recent video,, "Hypercentric optics" by Ben Krasnow, showing how to achieve reverse perspective physically using a giant Fresnel lens

More messing around in , this time a contraption that counts to 64 in binary. Course ID: 46R-9KM-VPG

More cohomology fractals, with Saul Schleimer and Matthias Goerner. Here we are simultaneously increasing how far we see into the manifold and decreasing our field of view, until our simulation succumbs to accumulating floating point errors.

The new version of the three-manifold software SnapPy is out now at It includes the ability to fly around inside hyperbolic manifolds! Pictures at

Diana Davis’s Beautiful Pentagons:

I briefly mentioned her regular-pentagon billiards-trajectory art in but now Evelyn Lamb has a much more detailed column on her and her work.

Amazing video: how to cheat at a Battleships-like game in Zelda Wind Waker. Featuring a tool developed by speed runners that uses knowledge of the pseudo-random number generator in the game, probability distributions, and deliberately losing the first game.

Show more

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!