Parts Entropy, Symmetry and the Difficulty of Self-Replication

A self-replicating robot (SRR) is one that can identify and assemble spare parts into an exact functional copy of itself. An SRR that is able to identify and pick up parts that are randomly scattered in an environment without prior knowledge of their location would be more robust than one that requires parts to be positioned at exactly known locations. Therefore, the degree of disorder in the environment that an SRR is able to handle is in some sense a measure of how “powerful” it is. The entropy of the ensemble of all possible configurations of parts quantifies this concept. In this paper, various issues associated with computing the entropy of ensembles of configurations of parts are explored. The effect of part symmetries is analyzed. It is shown that both the design of parts and the evaluation of an SRR’s functionality can be influenced by the knowledge of part entropies.