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Visiting my sister and family for Christmas, and they have a shiny new 3D printer, so naturally we've been playing with it. Here's a hats-and-turtles jigsaw puzzle.
The puzzle was made by taking a hat tiling and its combinatorially identical turtle tiling, and making a puzzle piece from each pair of
66 views
Once at university we accidentally invented Hexagonal Quantum Chess.
Chess-like games on a hex board have been thought of before, of course. But one afternoon we had a hex board and some pieces and nothing better to do, so we tried to make up one of our own.
Our pawns were very powerful, because the
66 views
I've recently been rewriting my substitution-tiling transducers code in #RustLang, replacing the old Sage code.
One reason is that Sage is harder to run these days. It vanished from Ubuntu some time between 22.04 and 24.04 and hasn't (yet?) come back.
Another reason was that reimplementing all my al
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Last month I asked for recommendations for graph layout tools. Thanks to everyone who suggested something! I've now finished the task I wanted them for, so have some pretty (ish) pictures.
In the end, I didn't use anything more complicated than Dotty, and I didn't even use Dotty on the _full_ versio
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🔥 Top post: Visiting my sister and family for Christmas, and they have a shi · 211 likes + reposts
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Visiting my sister and family for Christmas, and they have a shiny new 3D printer, so naturally we've been playing with it. Here's a hats-and-turtles jigsaw puzzle.
The puzzle was made by taking a hat tiling and its combinatorially identical turtle tiling, and making a puzzle pi…
Late-night prototype of an alternative UI: Snooker Loopy.
Once at university we accidentally invented Hexagonal Quantum Chess.
Chess-like games on a hex board have been thought of before, of course. But one afternoon we had a hex board and some pieces and nothing better to do, so we tried to make…
It's not Tuesday any more, but here are a few more bonus pretty pictures.
There's a clever construction called the "Wieringa roof" in which you assign every vertex of a P3 rhomb tiling a z-coordinate in {1,2,3,4}, with each rhomb having co…
For #TilingTuesday, 4-colourings of the Penrose P2 and P3 tilings, via refinements of their substitution systems.
Penrose tilings must _admit_ proper 4-colourings, by the Four Colour Theorem and the Erdős–de Bruijn theorem. 4CT says that a…
Last month I asked for recommendations for graph layout tools. Thanks to everyone who suggested something! I've now finished the task I wanted them for, so have some pretty (ish) pictures.
In the end, I didn't use anything more complicated…
I was really pleased with this daft idea. And it worked! I got a successful run of it on the OS OpenData's incomplete outline of the coastline of Great Britain.
With hindsight, there are several problems with it. What if an edge of the inp…
A flow network is a graph, with each edge imagined as a pipe through which some kind of fluid can flow. Edges are annotated with _capacities_ – the maximum rate at which fluid can flow through that pipe. Some vertices are _sources_ (fluid …
Given a set S of points in the plane, the _Voronoi cell_ of a point P ∈ S is the region of the plane which is closer to P than to any other point of S. A Voronoi cell is a polygon; where two cells touch, say for points P and Q, the edge be…
What does a Voronoi diagram have to do with a flow network?
Some years ago I was trying to make 3D-printable models of Britain for a friend. (Both the whole of Great Britain as a single model, and also zooming in to model individual mounta…
Just because I expect someone will appreciate it, here's a pristine version of the larger image, containing just the Spectre tiles, without the hexagon drawn on top.
I've recently been rewriting my substitution-tiling transducers code in #RustLang, replacing the old Sage code.
One reason is that Sage is harder to run these days. It vanished from Ubuntu some time between 22.04 and 24.04 and hasn't (yet?…
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