Determine whether Rule 110 supports universal self-replication

Determine whether the elementary cellular automaton Rule 110 belongs to the class UniversalSelfReplicating of cellular automata that support non-trivial self-replication by constructing or ruling out self-replicating structures that perform Turing-universal computation under Rule 110 dynamics.

Background

The paper distinguishes local and global computational universality and develops a minimal local self-replicating condition, then shows that local universality does not imply self-replication. Within this framework, the authors highlight Rule 110—a 1D, 2-state CA renowned for local Turing universality—as a central test case for universal self-replication.

They note that resolving whether Rule 110 can host genuinely self-replicating, Turing-universal structures is pivotal for understanding the relationship between universality notions and replication mechanisms.

References

Many challenges remain. Determining whether specific CAs support universal self-replication is open, and Rule 110 presents a compelling test case: Conjecture Rule 110 is in \textnormal{\textsf{UniversalSelfReplicating}.}

— Self-replication and Computational Universality (2510.08342 - Cotler et al., 9 Oct 2025) in Discussion