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  "path": "/abs/2603.25239v1",
  "publishedAt": "2026-03-27T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Don Yin"
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  "textContent": "**Authors:** Don Yin\n\nWhat substrate features allow life? We exhaustively classify all 262,144 outer-totalistic binary cellular automata rules with Moore neighbourhood for self-replication and produce phase diagrams in the $(λ, F)$ plane, where $λ$ is Langton's rule density and $F$ is a background-stability parameter. Of these rules, 20,152 (7.69%) support pattern proliferation, concentrated at low rule density ($λ\\approx 0.15$--$0.25$) and low-to-moderate background stability ($F \\approx 0.2$--$0.3$), in the weakly supercritical regime (Derrida coefficient $μ= 1.81$ for replicators vs. $1.39$ for non-replicators). Self-replicating rules are more approximately mass-conserving (mass-balance 0.21 vs. 0.34), and this generalises to $k{=}3$ Moore rules. A three-tier detection hierarchy (pattern proliferation, extended-length confirmation, and causal perturbation) yields an estimated 1.56% causal self-replication rate. Self-replication rate increases monotonically with neighbourhood size under equalised detection: von Neumann 4.79%, Moore 7.69%, extended Moore 16.69%. These results identify background stability and approximate mass conservation as the primary axes of the self-replication phase boundary.",
  "title": "The Self-Replication Phase Diagram: Mapping Where Life Becomes Possible in Cellular Automata Rule Space"
}