Security News > 2023 > April > Einstein tilings – the amazing “Hat” shape that never repeats!
As you can see, square tiles form what's known as a periodic pattern, meaning that the pattern repeats itself every so often.
Unlike periodic tilings, which repeat every so often, aperiodic tilings never repeat, no matter how carefully you choose the next piece to place, and where to place it.
Periodic tilings are a bit like rational numbers, in that eventually they repeat no matter what you do.
Penrose got the number of different shapes needed to guaranteed non-repeating tilings down to just two, but the question has lingered ever since: can you find a single shape, a single tile, that can be laid down repeatedly to cover an infinite surface without ever repeating?
Simply put, if you tile your floor, or your porch, or your driveway, or even the local football pitch with a supply of Hat tiles.
If you want to play with the concept of aperiodic tilings, why not bake yourself some Hat biscuits?