[image] Some exciting geometry news today. Smith, Myers, Kaplan, and Goodman-Strauss just posted a new preprint on a long unsolved geometric problem. They discovered a single connected shape which copies of (including reflections) can be used to tile the plane aperiodically. Read more about it h…

Trying to understand the approach used for the animation, as shown in the NY times article here , by Craig Kaplan, which appears to show an entire class of tilings

Yes indeed (this is the animation without the NYT paywall Aperiodic monotile animation - YouTube ) I was thinking it would be good to make a definition including this edge length variation

Brilliant, thank you. A simple definition. I will try to understand the derivation of the initial points. What is amazing to me is how simple the shape is, and the elegance of the two proofs presented in the papers. Add that to how many centuries! people have been staring at this problem, starting …

ah. from your diagram of 11 days ago, i see the derivation, 4/3 of a hexagon

It’s 3 weeks i keep seeing this subject in the news here and there, then found this chat subject, and this morning this dropped… [image] ‘The miracle that disrupts order’: mathematicians invent new ‘einstein’ shape Called ‘the hat’, the 13-sided shape can be arranged in a tile formation…

I think the Quanta one is probably the best of the articles I’ve seen on this [image] Hobbyist Finds Math’s Elusive ‘Einstein’ Tile | Quanta Magazine The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’…

An Aperiodic Monotile

Grasshopper

DanielPiker (Daniel Piker) April 1, 2023, 12:19pm 51

Here’s a definition showing the variation for a single tile. Next step - combine this with the substitution system to make the whole tiling.

monotile_family.gh (5.8 KB)
monotiles_00001

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An Aperiodic Monotile

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