Imagine the tiling is on a wall outside, and goes on for miles.

Now imagine you wanted to take a photo of the tiling.

With squares, or triangles, you could take two different photos of the wall in two different places, but the photos would be identical. You wouldn't be able to tell them apart.

With 'the hat' the two different photos would be different.

In reality, eventually, 'the hat' tiling does repeat, but not anywhere near enough for it to be noticeable.

For some shapes, you can tile them in a simple, repetative way.

For example, you can put a load of squares together, and no matter which bit of the tiling you look at, it always has the same pattern.

The same thing happens with triangles.

With 'the hat', whichever bit of tiling you look at, the pattern is always different.

It's the first time this has been done using only a single shape of tile.

I use a single duvet.