  We construct a scheme for self-replicating square clusters of particles in
two spatial dimensions, and validate it with computer simulations in a
finite-temperature heat bath. We find that the self-replication reactions
propagate through the bath in the form of Fisher waves. Our model reflects
existing colloidal systems, but is simple enough to allow simulation of many
generations and thereby the first study of evolutionary dynamics in an
artificial system. By introducing spatially localized mutations in the
replication rules, we show that the mutated cluster population can survive and
spread with the expanding front in circular sectors of the colony.
