Primordial evolution in the finitary process soup

A general and basic model of primordial evolution-a soup of reacting fini- tary and discrete processes-is employed to identify and analyze fundamental mechanisms that generate and maintain complex structures in prebiotic sys- tems. The processes?-machines as defined in computational mechanics-and their interaction networks both provide well defined notions of structure. This enables us to quantitatively demonstrate hierarchical self-organization in the soup in terms of complexity. We found that replicating processes evolve the strategy of successively building higher levels of organization by autocataly- sis. Moreover, this is facilitated by local components that have low structural complexity, but high generality. In e\uaeect, the finitary process soup sponta- neously evolves a selection pressure that favors such components. In light of the finitary process soup’s generality, these results suggest a fundamental law of hierarchical systems: global complexity requires local simplicity