This paper identifies generative replication as a form of replication which has the potential to enhance complexity in social and biological evolution, including the wondrous complexity in the biological world, and complex social institutions such as human language and business corporations. We draw inspiration from the literature on self-reproducing automata to clarify the notion of information transfer in replication processes. To enhance complexity, developmental instructions must be part of the information that is transmitted in replication. In addition to the established triple conditions of causality, similarity and information transfer, a generative replicator involves a conditional generative mechanism that can use signals from an environment and create developmental instructions. We develop a simple model, a one-dimensional linear automaton that is consistent with our four proposed conditions for a generative replicator. We show that evolution within this model will indeed approach maximal complexity, but only if our four proposed conditions are not violated. © 2010 Elsevier B.V.