Primes vs Composites When N is prime, every non-zero state is reachable and the automaton produces unique, non-repeating patterns. The ring ℤp has no zero divisors, so the totalistic rule explores the full state space.
When N is composite, the pattern reveals the factor structure. For example N=6 = 2×3 produces interference between the N=2 and N=3 sub-patterns, and N=4 = 2² shows nested copies of the Rule 150 triangle.