Metabolic Scaling ¾ Law

West-Brown-Enquist fractal network theory: B ~ M^(3/4)

Slope = 3/4 (Kleiber) | Surface exponent = 2/3 | WBE prediction: 3/4
West, Brown & Enquist (1997): metabolic rate scales as B ~ M^(3/4) across 27 orders of magnitude — from bacteria to blue whales. The origin: fractal branching networks (vascular, respiratory) minimize transport costs while filling the body volume. Space-filling + terminal unit invariance forces the exponent to be exactly 3/4, not 2/3 (surface area). Quarter-power laws arise throughout biology: lifespan ~ M^(1/4), heart rate ~ M^(-1/4).