Diana Davis’s Beautiful Pentagons: blogs.scientificamerican.com/r

I briefly mentioned her regular-pentagon billiards-trajectory art in mathstodon.xyz/@11011110/10153 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. youtu.be/1hs451PfFzQ

A not-entirely-successful prototype of a 3D sliding block puzzle system - Rook cubes: youtu.be/ln_AQkjjYDc

Not one of my usual mediums, but it turns out that you can make some interesting things in Mario Maker 2. Here's Mario juggling five shells. Course ID: MQ2-MM5-MCG

What happens when half a cellular automaton runs Conway's Game of Life and the other half runs a rolling version of Rule 30 pushing chaos across the border? youtube.com/watch?v=IK7nBOLYzd, via news.ycombinator.com/item?id=2

I wish I could see a larger scale of time and space to get an idea of how far the effects penetrate. If the boundary emitted gliders at a constant rate they'd collide far away in a form of ballistic annihilation but the boundary junk and glider-collision junk makes it more complicated.

A variant of the classic 15-puzzle, where the puzzle is coiled around a cylinder. Unlike the original, this version is solvable because of the extra connection between the first and sixteenth squares of the frame. YouTube: youtu.be/rfAEgxNEOrQ

‪Oskar van Deventer is an amazingly prolific puzzle designer - he designed this sliding puzzle based on a strategy I suggested: How can four squares slide all around each other without coming apart? youtube.com/watch?v=G_RlsIe3-q

The new 14-sided dice from the Dice Lab also works pretty well as a spinning top! Full video: youtu.be/0KnRtZgvKIw

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

A zoom through a selection of cohomology fractals. With David Bachman and Saul Schleimer, music by Vi Hart. youtu.be/-g1wNbC9AxI

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

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: staff.science.uu.nl/~loffl001/

Show more

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