I wrote an article about aperiodic tiling generation

[simont]

A few weeks ago, when I heard about the shiny new aperiodic monotile that had been discovered, I immediately had to add it to the collection of grids that you can play Loopy on, in my puzzle collection.

This went fine, except for the fact that I got most of the way through implementing one algorithm for generating pieces of the tiling, and then threw it away and started again because I'd had a much better idea.

In fact, there are so many things I like about the algorithm I ended up with that I've decided it deserves a proper public writeup. So I've spent the Easter weekend hard at work on producing one. I present: https://www.chiark.greenend.org.uk/~sgtatham/quasiblog/aperiodic-tilings/

Comments

[lnr]

Thank you :) I have "enjoyed" playing it already. (It's not an easy one!)

[bens_dad]

I grew up with Altair Design's colouring pads
https://woodenbooks.com/index.php?id_category=20&controller=category
which have a lot in common with Penrose tilings.

[bens_dad]

The same team have found a new ein stein, called Spectre:
https://arxiv.org/pdf/2305.17743.pdf
This one tesselates without reflection, though it does have curves.

[simont]

Indeed yes – I'm working on implementation of that one as we speak. It will appear in Loopy in due course (current status: playable but the code needs polishing), and I'll be writing a sequel post about that one, because its metatile hierarchy is entirely different from the hat (even though the tiles themselves are so similar), so it calls for a rework of all the details of the generation algorithm.

[simont]

Now implemented in Loopy (without the optional curves), and my own writeup lives at https://www.chiark.greenend.org.uk/~sgtatham/quasiblog/aperiodic-spectre/