  In this paper we present a model containing modifications to the
Signal-passing Tile Assembly Model (STAM), a tile-based self-assembly model
whose tiles are capable of activating and deactivating glues based on the
binding of other glues. These modifications consist of an extension to 3D, the
ability of tiles to form "flexible" bonds that allow bound tiles to rotate
relative to each other, and allowing tiles of multiple shapes within the same
system. We call this new model the STAM*, and we present a series of
constructions within it that are capable of self-replicating behavior. Namely,
the input seed assemblies to our STAM* systems can encode either "genomes"
specifying the instructions for building a target shape, or can be copies of
the target shape with instructions built in. A universal tile set exists for
any target shape (at scale factor 2), and from a genome assembly creates
infinite copies of the genome as well as the target shape. An input target
structure, on the other hand, can be "deconstructed" by the universal tile set
to form a genome encoding it, which will then replicate and also initiate the
growth of copies of assemblies of the target shape. Since the lengths of the
genomes for these constructions are proportional to the number of points in the
target shape, we also present a replicator which utilizes hierarchical
self-assembly to greatly reduce the size of the genomes required. The main
goals of this work are to examine minimal requirements of self-assembling
systems capable of self-replicating behavior, with the aim of better
understanding self-replication in nature as well as understanding the
complexity of mimicking it.
