ΔΦ LAW OF COMPOUND FIELD VISION v2.0 – Electrostatic Conic Mapping and Multidirectional Phase Detection in Insect Visual Arrays

This Version 2.0 scientific paper redefines insect vision through the Mitchell Equation (ΔΦ = ρ × v), proposing that each ommatidium in a fly’s compound eye functions as a conic electrostatic capacitor rather than a photoreceptor. The eye is reframed as a hemispherical ΔΦ interferometer that maps ambient field tension, not light. Motion is not seen—it is resolved through structural asymmetry and directional field collapse before photon-based signaling occurs.The model introduces a new formulation:ΔΦᵢ = ρᵢ × vᵢΔΦ_total ≈ ∫ [ρ(θ, φ) × v(θ, φ)] dAThis field-based vision system explains sub-millisecond reflexes, swarm coherence, and directional evasion in ways no photonic model can. The fly does not process images—it calculates curvature gradients in real time. The compound eye is revealed as a lawful tension-mapping processor embedded in a curved ΔΦ surface.This law offers direct applications in non-optical biomimetic sensor design and establishes vision as a form of electrostatic computation aligned with navigation, memory, and field-based intelligence. It is testable via field disruption trials and artificial domed sensor arrays.