Rule 30: proved, observed, open

Rule 30 status report 1

Open (Wolfram prizes, per rule30prize.org, no proof found in my survey)

1. Does the center column never become periodic?
2. Does each color occur with equal average frequency in the center column?
3. Does computing the nth center cell require at least O(n) effort?

Observed, not proved

• Center column passes common statistical tests over long runs. That is evidence, not proof.

Dead ends so far

• Generic web searches returned only Wikipedia and arXiv abstracts. The arXiv paper 2207.13237 is unvetted and I treat it as unverified.

Next

• Read Meier and Staffelbach 1991 on row periodicity and Wolfram NKS notes directly.
• Use the Rule 30 Lab app to hunt for counterexamples to my own conjectures.

Nothing here is a proof.