Nostr notes by Pieter Mostert

Peter Selinger has come up with a great way of generating hat ...

2026-04-28T21:44:35Z

Peter Selinger has come up with a great way of generating hat tilings by overlaying a triangular grid on a periodic pattern, and placing a tile at each point that is not white, with the orientation and handedness of the tile determined by the colour of the point. A more thorough explanation is given in this preprint
https://arxiv.org/pdf/2604.20964,
where he and Sébastien Labbé show that this is a Markov partition. As mentioned in the paper, I came up with a similar construction a few years ago, but it required separate steps for tiles of a given orientation modulo 120.

In this series of posts, I'll attempt to explain the connection between the two constructions, and demonstrate the analogous constructions for the hats-in-turtles and turtles-in-hats versions of the Spectre tiling. The aim is to give a sense of the main ideas, rather than a rigorous proof that this works.

Before I get into the details, here is a Markov partition for turtle tilings, where control / anchor points are located on the underside of the turtle's shell.

(1/n)

#TilingTuesday #aperiodicTilings

The magazine article headline claims that's enough gold and ...

2025-10-26T19:36:42Z

In reply to nevent1q…4gz7
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The magazine article headline claims that's enough gold and uranium to "fill Earth's oceans", when the very first line describes the amount as having approximately the same mass as Earth's oceans. I know article writers aren't always the people writing headlines, but you'd think someone at Space.com would have noticed the error and fixed it by now.

I once had a heated argument with my grade 6 teacher about the ...

2025-08-05T19:51:08Z

In reply to nevent1q…3kq9
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I once had a heated argument with my grade 6 teacher about the value of \[3\times \frac{1}{3}\]. I claimed it was 1, while she claimed it was 0.9999999 (not recurring, just the number of digits shown by the calculator), since "the calculator is always right". If I recall correctly, the controversy arose after one of my classmates had noticed that the calculator showed 0.3333333 when they calculated \[1/3\], and then observed that \[3\times 0.3333333 = 0.9999999\].

View towards Lubanzi beach, with Hole in the Wall in the distance ...

2024-10-06T16:36:47Z

View towards Lubanzi beach, with Hole in the Wall in the distance

#SilentSunday

I took a walk down to Mbolompo point this afternoon, and on the ...

2024-09-29T21:15:32Z

I took a walk down to Mbolompo point this afternoon, and on the way back came across these beautiful iridescent films produced by iron / manganese oxidising bacteria.

#SilentSunday