ΔΦ BIOLOGICAL REGENERATION – COMPUTATIONAL FRAMEWORK v1.0 Gradient-Aligned Field Dynamics as a Model for Structured Recovery and Morphological Persistence

This work presents a computational framework demonstrating that gradient-aligned field dynamics governed by the Mitchell Equation (ΔΦ = ρ × v) produce structured convergence, persistence under perturbation, and recovery following disruption. Controlled simulations show that systems with directional gradient alignment consistently form stable attractor states and re-converge toward those states after lesion, while stochastic systems fail to maintain or recover structure.The results establish a proof-of-mechanism for field-guided structural recovery. In particular, the simulations reveal that rapid error minimization alone does not produce stable structure; instead, sustained directional coherence is required for convergence, persistence, and regeneration-like behavior.We interpret these findings as evidence that structured systems can be understood as dynamic attractors maintained by field flow. Recovery is not achieved through stored templates but through re-convergence to these attractor states under continued field dynamics.This framework is consistent with experimental observations in bioelectricity research, including work by Michael Levin, which demonstrates that voltage gradients influence morphological outcomes. We therefore propose the hypothesis that biological regeneration may involve similar field-guided attractor dynamics.The model is explicitly computational and generates testable predictions, including the role of gradient coherence in regeneration, the impact of field disruption on recovery, and the potential to redirect structure through externally imposed gradients. These predictions provide a direct path for experimental validation.