Resonant Attractor Theory (RAT) A formal principle within the Sympathetic Harmonic Resonance Framework

Abstract Recurrent natural forms—such as hexagonal crystals, spiral galaxies, branching structures, and oscillatory biological patterns—appear across disparate physical systems and scales. This work formalises Resonant Attractor Theory (RAT) within the Sympathetic Harmonic Resonance Framework (SHRF), proposing that such forms arise as stable attractor states in phase space where coherence is maximised and energetic phase correction is minimised. RAT provides a unifying explanation for why nature repeatedly manifests specific geometries while preserving individual variation, without invoking teleology or stochastic selection alone.