  We show how to design a universal shape replicator in a self-assembly system
with both attractive and repulsive forces. More precisely, we show that there
is a universal set of constant-size objects that, when added to any unknown
hole-free polyomino shape, produces an unbounded number of copies of that shape
(plus constant-size garbage objects). The constant-size objects can be easily
constructed from a constant number of individual tile types using a constant
number of preprocessing self-assembly steps. Our construction uses the
well-studied 2-Handed Assembly Model (2HAM) of tile self-assembly, in the
simple model where glues interact only with identical glues, allowing glue
strengths that are either positive (attractive) or negative (repulsive), and
constant temperature (required glue strength for parts to hold together). We
also require that the given shape has specified glue types on its surface, and
that the feature size (smallest distance between nonincident edges) is bounded
below by a constant. Shape replication necessarily requires a self-assembly
model where parts can both attach and detach, and this construction is the
first to do so using the natural model of negative/repulsive glues (also
studied before for other problems such as fuel-efficient computation); previous
replication constructions require more powerful global operations such as an
"enzyme" that destroys a subset of the tile types.
