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.

A not-entirely-successful prototype of a 3D sliding block puzzle system - Rook cubes:

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?, via

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:

‪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?

The new 14-sided dice from the Dice Lab also works pretty well as a spinning top! Full video:

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:

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

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