Does a Flux-Defined Markov Blanket Screen Self-Replicating Gray--Scott Spots? A Computational Test of a Blanket Condition from the Free Energy Principle

Abstract

Friston's free energy principle holds that a system separated from its environment by a Markov blanket---a boundary whose states statistically screen its interior from its exterior---can be treated as performing approximate Bayesian inference, and that such blankets arise wherever coupling is short-range. We test this blanket condition in a concrete nonlinear pattern-forming system: self-replicating spots in a reaction-diffusion model that persist, compete, and reproduce. Directed boundary exchange and timescale separation hold up reasonably well, with qualifications. A flux-defined blanket does not screen interior from exterior. Flux removes only part of the linear dependence, and a nonlinear test shows that conditioning on flux \emph{increases} the dependence, consistent with conditioning on a collider, since flux is a joint function of concentrations on both sides of the boundary. The dependence is concentrated within about one organism radius of the boundary. A band of the surrounding field that thick screens the interior from the exterior beyond it, as any short-range field would, which is not evidence of inference.