Kleiber's Law (1932): Metabolic rate B scales with body mass M as B ∝ M^(3/4) across organisms from bacteria to blue whales — 27 orders of magnitude in mass.
WBE theory (West, Brown, Enquist 1997): The exponent 3/4 emerges from the geometry of fractal supply networks (cardiovascular, vascular). A d-dimensional network filling space gives B ∝ M^((d-1)/d); for d=3 → 2/3, but self-similar branching gives 3/4.
Quarter-power scaling: lifespan ~ M^(1/4), heart rate ~ M^(-1/4), genome replication ~ M^(1/4) — all derive from the same network geometry.