EMERGENT EVOLUTIONARY DYNAMICS OF SELF-REPRODUCING CELLULAR AUTOMATA

In this thesis, a new approach to the study of evolutionary processes is presented using as medium the mathematical formulation of cellular automata (CA). Previous work in this field limited the scope of analysis to focus on model construction; our emphasis is to expand this view. We investigate a system of self-reproducing loops (“evoloops”) in which mechanisms for variation and selection are considered emergent. Simple, deterministic state-transition rules result in a highly robust and flexible morphology, allowing self-replicators to modify the structure of offspring through phenotypic interaction. No explicit conditions are imposed on survival: selection criteria are an emergent property of the global system and cannot be deduced from local CA rules. As a result, populations undergo self-organized evolutionary processes leading to complex and unpredictable spatial and temporal dynamics on multiple scales. The study of these complex dynamics forms the primary focus of this thesis. Earlier investigations have largely targeted aspects of design and structural mechanics of the self-replication process. The possibility of discovering open-ended, complexity-increasing evolution has been implicitly precluded by inadequate methods of analysis and a limited subset of initial conditions. The work presented here aims to emphasize the wider potentialities of this system by addressing a number of open questions. We begin with the introduction of new mechanisms for event-driven detection, identification, and genealogy tracing, each of which operate with negligible computational overhead. Given this new framework, we show that the genealogical state-space of replicators scales exponentially with the size of replicator and that populations exhibit far greater behavioural diversity than earlier estimates would suggest. To capture the full connectivity of genealogical links spanned by these populations, we introduce the concept of a “genealogy graph” as a generalization on the familiar tree hierarchy. A classification of species based on fundamental evolutionary properties arises from this graph-based idea of genealogy and leads to the discovery of a new class of species. For a subset of these species Darwinistic selection is observed to balance replication speed with new, emergent criteria, extending evolutionary time scales by orders of magnitude. Exploration of this new genealogy space with simple, small-scale experiments, demonstrates a richness of dynamics exceeding our every expectation.