Allometric Scaling — West Fractal Networks

West-Brown-Enquist (1997): metabolic rate scales as M^(3/4) because of space-filling fractal vascular networks. Explore how network branching geometry dictates metabolic exponents.

Fractal Vascular Network

Kleiber's Law: B ~ M^β

Network Parameters

β = (D+1)/(D+2) [WBE]
D=3: β = 3/4 (mammals)
D=2: β = 2/3 (surface-limited)
r_k = r_0 · n^{-1/3}

Branching n2 Levels L7 Length ratio γ0.71 Radius ratio ε0.79

β = 0.750
Fractal dim: 3.000

Metabolic Rate vs Mass

Log-log plot. Slope = β. Dashed = β=3/4.