Michael V said:

SCIENCE said:

Nice tessellation.

https://cs.uwaterloo.ca/~csk/hat/

David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss, 2023

An aperiodic monotile, sometimes called an “einstein”, is a shape that tiles the plane, but never periodically. In this paper we present the first true aperiodic monotile, a shape that forces aperiodicity through geometry alone, with no additional constraints applied via matching conditions. We prove that this shape, a polykite that we call “the hat”, must assemble into tilings based on a substitution system. The drawing above shows a patch of hats produced using a few rounds of substitution.

https://arxiv.org/abs/2303.10798

Penrose got aperiodic tessellation down to 2 tiles like 50 years ago and this kind of stuff looks like child’s play so it’s quite something that it’s taken that long to get confirmation of 1 tile.