Comment by gilleain

DNA is one-dimensional aperiodicity, which is ... fairly common. This sentence is one-dimensionally aperiodic!

Most biological structures are amorphous in some way, rather than strictly aperiodic. There are structures (honeycombs, for example) that are extremely regular, and especially on smaller scales (like virus capsids). Other biological structures are loosely fractal (self-similar across a narrow range) - lungs, blood systems, and so on.

I don't know of any biological structures that could accurately be described as aperiodic - like a quasicrystal - but given I'm just learning about Defense-associated reverse transcriptases, it would not surprise me if there is something out there.