Allometric Scaling

Kleiber's ¾ Law & Fractal Vascular Networks
1 kg
0.75
6
2

Kleiber's Law & West-Brown-Enquist Model

Metabolic rate B = B₀ · M^(3/4)    (Kleiber 1932)

Vascular: r_{k+1}/r_k = n^(-1/3)    (Murray's law → area preserving)

The ¾ exponent arises from optimization of hierarchical fractal branching networks (West, Brown, Enquist 1997). Minimizing energy dissipation with volume-filling constraint yields exactly α = 3/4. Heartbeat ~ M^(-1/4), lifespan ~ M^(1/4) — all clocks tick at the same rate per heartbeat.