Population Dynamics of Perception and Emergence of Translational Membranes

ABSTRACT: At root, perception converts external information from an environment to signals of use in downstream cognition. We explore a population of interacting perceptual agents whose adaptive internal structure transforms input information to outputs. We show that autocatalytic networks of structural transformations—represented by ε-transducers—spontaneously emerge. Moreover, their population dynamics—who flourishes and with whom they interact—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 ε-transducers 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 autocatalytic organization.