自复制相图：在细胞自动机规则空间中确定生命可能的区域
The Self-Replication Phase Diagram: Mapping Where Life Becomes Possible in Cellular Automata Rule Space
AI总结：
研究通过分类所有262144个外总istic二进制细胞自动机规则，确定支持模式繁殖的条件，揭示背景稳定性与近似质量守恒为主要因素。
摘要：
什么底物特征允许生命存在？我们详尽分类了所有262144个外总istic二进制细胞自动机规则，采用Moore邻域进行自复制分类，并在(λ,F)平面上生成相图。其中20152个规则（7.69%）支持模式繁殖，集中在低规则密度（λ≈0.15-0.25）和低至中等背景稳定性（F≈0.2-0.3）的弱超临界区域（Derrida系数μ=1.81对复制体 vs. 1.39对非复制体）。自复制规则更接近质量守恒（质量平衡0.21 vs. 0.34），并推广到k=3 Moore规则。三级检测层次（模式繁殖、扩展长度确认和因果扰动）估计了1.56%的因果自复制率。自复制率在等效检测下随着邻域大小单调增加：von Neumann 4.79%，Moore 7.69%，扩展Moore 16.69%。这些结果将背景稳定性和近似质量守恒确定为自复制相边界的主要轴。
英文摘要：
What 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
