Status of ECA 105 under skew-asynchronous updating for n not divisible by 4

Determine whether elementary cellular automaton rule 105 exhibits recurrent dynamics or non‑convergent non‑recurrent dynamics under the skew‑asynchronous updating scheme when the lattice size n is not a multiple of 4, and characterize its asymptotic behavior in this regime.

Background

ECA 105 shows recurrence under fully asynchronous updates for any lattice size. Under skew‑asynchronous updates, the authors observe convergence to (0011)^{n/4} when n is divisible by 4, but they cannot classify its behavior for n not divisible by 4.

They explicitly state uncertainty about whether the dynamics in this case are recurrent or non‑convergent non‑recurrent, calling for further analysis.