My interest in aperiodicity originates in my interest in integer sequence extrapolation (ISE). Periodic integer sequences are not interesting to extrapolate: just find the repeating block within the sequence and you’re done. I developed many aperiodic sequences as I explored ISE; this led me to explore aperiodicity itself as a general phenomenon.

Some interesting questions have emerged from my exploration of aperiodicity:

(1) ‘Aperiodic’ is normally defined as ‘not periodic’. Does there exist a definition of aperiodicity that employs the presence of some feature rather than the absence of a feature?

(2) Aperiodicity proofs in mathematics are notoriously difficult. Can a computer create a conjecture from finite sequence data which is then provided to a mathematician to prove? If the conjecture is proven then the corresponding infinite sequence is aperiodic.

I currently don’t have an answer to any of these questions. The purpose of this post is to present the work I’ve done so far so that others can further this work if desired.