  A general and basic model of primordial evolution--a soup of reacting
finitary and discrete processes--is employed to identify and analyze
fundamental mechanisms that generate and maintain complex structures in
prebiotic systems. The processes--$\epsilon$-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 autocatalysis. Moreover, this is facilitated by local
components that have low structural complexity, but high generality. In effect,
the finitary process soup spontaneously 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.
