## Aperiodic

There are disputations among the experts how to define “aperiodic”. One possibility is to use it synonymously with nonperiodic. This is somehow a waste of this term. Others refer to an “aperiodic tiling” as one, which is created by an aperiodic set of tiles. This is unsatisfactory since this is rather a property of the set of prototiles than the tiling itself. Another definition is: A tiling is aperiodic, if its hull contains no periodic tiling. Personally, I like the latter definition (DF). Then a sequence $\ldots aaaaabaaaaaaa\ldots$. is not aperiodic (since its hull comtains the periodic sequence $\ldots aaaaabaaaaaaa\ldots$.), but the Fibonacci sequence is aperiodic.