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We show that autocatalytic networks of epsilon-machines and their populationdynamics differ substantially between spatial (geographically distributed) andnonspatial (panmixia) populations. Generally, regions of spacetime-invariantautocatalytic networks---or domains---emerge in geographically distributedpopulations. These are separated by functional membranes of complementaryepsilon-machines that actively translate between the domains and areresponsible for their growth and stability. We analyze both spatial andnonspatial populations, determining the algebraic properties of theautocatalytic networks that allow for space to affect the dynamics and sogenerate autocatalytic domains and membranes. In addition, we analyzepopulations of intermediate spatial architecture, delineating the thresholds atwhich spatial memory (information storage) begins to determine the character ofthe emergent auto-catalytic organization.

How the Dimension of Space Affects the Products of Pre-Biotic Evolution:  The Spatial Population Dynamics of Structural Complexity and The Emergence of  Membranes