We have discovered a novel transition rule for binary cellular automata (CA) that yields self-replicating structures across two spatial and temporal scales from sparsely populated random initial conditions. Lower-level, shapeshifting clusters frequently follow a transient attractor trajectory, generating new clusters, some of which periodically self-duplicate. When the initial distribution of live cells is sufficiently sparse, these clusters coalesce into larger formations that also self-replicate. These formations may further form the boundaries of an expanding complex on an even larger scale. This rule, dubbed ``Outlier,'' is rotationally symmetric and applies to 2D Moore neighborhoods. It was evolved through Genetic Programming during an extensive automated search for rules that foster open-ended evolution in CA. While self-replicating structures, both crafted and emergent, have been created in CA with state sets intentionally designed for this purpose, the Outlier may be the first known rule to facilitate emergent self-replication across two spatial scales in simple binary CA.

翻译：我们发现在稀疏随机初始条件下，一种新型二进制细胞自动机（CA）跃迁规则能够在两个空间与时间尺度上产生自复制结构。低级变形集群频繁遵循瞬态吸引子轨迹，生成新集群，其中部分集群周期性进行自我复制。当初始活细胞分布足够稀疏时，这些集群会聚合成更大的结构，这些结构同样能自复制。这些结构进一步可在更大尺度上构成扩张复合体的边界。该规则被命名为"Outlier"，具有旋转对称性，适用于二维Moore邻域。通过遗传编程在广泛自动化搜索中演化生成，旨在促进CA中开放性演化。尽管在专门为此目的设计状态集的CA中已创造出人工构建与涌现的自复制结构，但Outlier可能是首个在简单二进制CA中支持两个空间尺度上涌现性自复制的已知规则。