Enzymind Labs

"God may not play dice with the universe, but something strange is going on with the prime numbers." Paul Erdős

All aperiodic sequences and patterns have interesting relationships to integers, particularly prime numbers. The essential reason is that they are non-periodic in a regular way related to integers. If they are decimated by an integer n, the relationships between the factors of n and the integers involved in the pattern itself give rise to a kind of Moiré pattern, where the multiples of prime factors "beat" with the pattern's integral structure.

Self-similarity of the period-doubling sequence

A decimated four symbol non-cyclic system

[To Do: More examples]

[To Do: Decimation and symmetry]

"Symmetry denotes that sort of concordance of several parts by which they integrate into a whole. Beauty is bound up with symmetry." Hermann Weyl

"Symmetry is a complexity-reducing concept; seek it everywhere." Alan Perlis

Murray Gell-Mann did a nice TED talk related to self-symmetry, Beauty and truth in physics. 

Self-similarity of period-doubling sequence

A diagram demonstrating integral resampling of the period-doubling sequence (below) It is a cryptic rendering of a mystery (to me at least): how can every nth element of a sequence be a replication of the sequence itself, for every n?

[To Do: Brief mathematical treatment]