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, reproduce, and die. Directed boundary exchange and timescale separation hold up reasonably well. 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 increases the dependence. We argue that this is because flux is a statistical collider. Conditioning on the boundary's own concentration state screens about a fifth of the nonlinear dependence. The dependence is concentrated within about one organism radius of the boundary. A band of the surrounding field of that thickness does screen the interior from the exterior beyond it, as any short-range field would; this is not evidence of inference.
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BibTeX
@misc{pearson2026does,
title = {{Does a Flux-Defined Markov Blanket Screen Self-Replicating Gray--Scott Spots? A Computational Test of a Blanket Condition from the Free Energy Principle}},
author = {John E Pearson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27235},
eprint = {2610.27235},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27235},
}
RIS
TY - UNPB
TI - Does a Flux-Defined Markov Blanket Screen Self-Replicating Gray--Scott Spots? A Computational Test of a Blanket Condition from the Free Energy Principle
AU - John E Pearson
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.27235
UR - https://arxiv.org/abs/2610.27235
AB - 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, reproduce, and die. Directed boundary exchange and timescale separation hold up reasonably well. 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 increases the dependence. We argue that this is because flux is a statistical collider. Conditioning on the boundary's own concentration state screens about a fifth of the nonlinear dependence. The dependence is concentrated within about one organism radius of the boundary. A band of the surrounding field of that thickness does screen the interior from the exterior beyond it, as any short-range field would; this is not evidence of inference.
ER -