PadcraftingDec 10
Mono. Ecoline Red ink in a B5 sized plot - contoured aperiodic monotiles with varying intensity measures. #penplotter #plotterart #algorist #monotiles
N-gated Hacker NewsJun 13, 2025
👒🔍📐 Here comes Nicols Hatcher, the self-proclaimed "physicist by soul," to dazzle us with a mind-numbingly riveting tale of shapes and #algorithms. Get ready to be blown away by the exhilarating world of #monotiles and SAT solvers—because that's exactly what your weekend was missing! 💤🎉
https://www.nhatcher.com/post/on-hats-and-sats/ #physicist #SATsolvers #weekendreads #HackerNews #ngated
The Hat, the Spectre and SAT solvers

Introduction In this blog post you are going to read about two things:

I'm Nicolás Hatcher
MAP Family Learning CenterMar 21, 2025

Happy belated Pi Day!!!

We've been playing with Aperiodic Monotiles, and we decided to make this video for y'all.

We missed doing this in advance of Pi Day, but we still wanted to share.

-- from the afterschool that does Music, Art, and Programming (and all sorts of other interdisciplinary fun stuff)

#Math #Monotiles #Fun #Education #Afterschool

JamesMar 6, 2024

I have a paper on #aperiodic #monotiles https://arxiv.org/abs/2403.01911

It contains proofs that Turtle tiles can't tile the place periodically.

Turtles tiles are not really monotiles. They're two tiles - it's just that the second one is a 1-dimensional cross shape. Another way of describing them is as a black 'hole' rhombus and a shape formed from gluing a rhombus to a hexagon (a shape that I call the dual Turtle). With some extra rules about how to match these shapes, these two tiles are an aperiodic tiles set.

The first rule is to force the rhombuses and hexagon shapes to snap to a hexagonal grid - a https://en.wikipedia.org/wiki/Rhombille_tiling
The second rule involves coloring the rhombuses and hexagons black and red. Red sides are only allowed to match black sides and vice versa.

In this way, it's possible to tile the plane in a non-periodic way. Here's how: https://jpdsmith.github.io/AperiodicCube/

You can spin this 3D model round to look at different angles. In particular look at the side views. It's cool that the Rhombille tiling is really a view of some 3D cubes.

Turtles, Hats and Spectres: Aperiodic structures on a Rhombic tiling

These notes derive aperiodic monotiles (arXiv:2303.10798) from a set of rhombuses with matching rules. This dual construction is used to simplify the proof of aperiodicity by considering the tiling as a colouring game on a Rhombille tiling. A simple recursive substitution system is then introduced to show the existence of a non-periodic tiling without the need for computer-aided verification. A new cut-and-project style construction linking the Turtle tiling with 1-dimensional Fibonacci words provides a second proof of non-periodicity, and an alternative demonstration that the Turtle can tile the plane. Deforming the Turtle into the Hat tile then provides a third proof for non-periodicity by considering the effect on the lattice underlying the Rhombille tiling. Finally, attention turns to the Spectre tile. In collaboration with Erhard Künzel and Yoshiaki Araki, we present two new substitution rules for generating Spectre tilings. This pair of conjugate rules show that the aperiodic monotile tilings can be considered as a 2-dimensional analog to Sturmian words.

arXiv.org
Tim DonaghyJan 2, 2024

If I had known that you could buy a set of #aperiodic #monotiles on etsy, I sure would have planned my holiday gift purchases differently.

(for reals a very fun article...)

https://www.scientificamerican.com/article/inside-mathematicians-search-for-the-mysterious-einstein-tile/

Inside Mathematicians' Search for the Mysterious 'Einstein Tile'

The quest for the einstein tile—a shape never seen before in mathematics—turned up even more discoveries than mathematicians counted on

Scientific American
Show threadRodboticSep 1, 2023
Day 3 #lasercutting #monotiles #einstein_tile hat
Michaël MaexJul 18, 2023

Finally got around to lasercutting some #monotiles and now some highschool students are playing with them 😊

I had the file ready for a long time and I forgotten where I got the vine pattern for the engraving. If anyone knows who I have to credit, let me know! #math

Show threadNalini JoshiApr 9, 2023
Many chains of #monotiles occur in this tiling (image from p.11 of arxiv.org/abs/2303.10798)
John TMar 26, 2023
You really don't know how hard it is to put together a set of #aperiodic #monotiles until you try it.
LinaMar 26, 2023

printing up some o' them sexy new #monotiles. gonna try to come up with some fun aperiodic tiling games to play with them!

read more about the shape in this post by @csk - https://mathstodon.xyz/@csk/110058791736888417

Craig S. Kaplan (@[email protected])

How small can a set of aperiodic tiles be? The first aperiodic set had over 20000 tiles. Subsequent research lowered that number, to sets of size 92, then 6, and then 2 in the form of the famous Penrose tiles. https://youtu.be/48sCx-wBs34 1/6

Mathstodon