This thesis demonstrates for the first time that it is possible to automatically discover self-replicating structures in cellular space automata models rather than, as has been done in the past, to design them manually. Self-replication is defined as the process an entity undergoes in constructing a copy of itself. Von~Neumann was the first to investigate artificial self-replicating structures and did so in the context of cellular automata, a cellular space model consisting of numerous finite-state machines embedded in a regular tessellation. Interest in artificial self-replicating systems has increased in recent years due to potential applications in molecular-scale manufacturing, programming parallel computing systems, and digital hardware design, and also as part of the field of artificial life.