The diversity and complexity of living systems on Earth have presumably emerged from a single common ancestor, and before that, from the inorganic components present on the surface of Earth. So far, it is unclear what are the \emph{algorithmic} properties of a process that would display a similar trajectory in its state space. Describing such a process entails characterizing both the state space itself, the possible emergent forms, and the evolutionary process behind the diversification and complexification of forms. Because living systems are hypothesized to correspond to attractors in chemical networks, Artificial Chemistries (AC) are well suited to explore this question because they can simulate the evolution of these networks. Combinatory Chemistry is an AC in which self-reproducing metabolisms emerge from its dynamics. Here, I extend it with a set of mutation reactions, showing that said reactions coupled with the emergent structures in the system enable a more efficient search of complex structures. I conclude that the resulting dynamics constitute an emergent self-organizing search process that could capture the properties of open-ended evolutionary processes.