Supposedly, the placement occurrence of motifs in Penrose tilings are impossible to predict in 2, 3, or 4 dimensions. One looks a bit like a joker, another motif like a snowflake, etc. We can assume they will reoccur, much like we can assume that there are no end to prime numbers, but both of those assumptions require fancy mathematical proofs.
Whatever. My point is that some people think you can predict Penrose tiles in a higher (5th) dimension – planes upon planes colliding and multiplying, in a sense, but ironing out to something comprehensible.
Here is an earlier post on the subject:
I wanted to work with students to create this competition between subject and background. We chose a lovely spotted frog as our subject, and a not especially aggressive play on the spots and patterns in the background.