  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.
