In the realm of cellular-automata-based artificial life, configurations that self-reproduce employing signals are a more advanced form than those that reproduce holistically by simple fission. One might view those signals as a very rudimentary genetic code, since they guide the formation of the “child” from its “parent.” In principle, the signals could mutate to deliver a child better suited to reproduction in this artificial world. But even the simplest signal-based replicator discovered so far requires 58 specific CA transition rules that have been carefully hand-crafted to exactly meet the requirement of self-replication. Could such a system emerge without human design? This article considers how that might occur. Specifically, it demonstrates that the application of two heuristics can increase the probability that self-replication will emerge when needed transition rules are completed at random. The heuristics are using minimum total resources (parsimony) and maintaining structural continuity. Finally, the article suggests why parsimony is effective in catalyzing the emergence of self-replication.