  We show that autocatalytic networks of epsilon-machines and their population
dynamics differ substantially between spatial (geographically distributed) and
nonspatial (panmixia) populations. Generally, regions of spacetime-invariant
autocatalytic networks---or domains---emerge in geographically distributed
populations. These are separated by functional membranes of complementary
epsilon-machines that actively translate between the domains and are
responsible for their growth and stability. We analyze both spatial and
nonspatial populations, determining the algebraic properties of the
autocatalytic networks that allow for space to affect the dynamics and so
generate autocatalytic domains and membranes. In addition, we analyze
populations of intermediate spatial architecture, delineating the thresholds at
which spatial memory (information storage) begins to determine the character of
the emergent auto-catalytic organization.
