A tessellation is a way of filling a plane by repeating a set of figures, called tesserae, infinitely. Normally the tessellations are periodic, that is, they are repeated over and over again.
The hat tiling is the first non-periodic tiling in the plane with a single tile. The tile has been discovered in March 2023 and has been a mathematical achievement of the first order.
Below you can see the tessellation of the hat made with a single tesserae.