Mammalian Circulatory System

The mammalian circulatory system exemplifies fractal branching: the aorta branches into major arteries, which branch into arterioles, which branch into capillaries - each level smaller and more numerous than the previous. This branching is approximately self-similar and fractal in structure with dimension ~3 (fills 3D space efficiently). The network enables blood to reach ~10-40 billion capillaries using only ~100,000 km of vasculature.

Evolution faced a brutal trade-off: wide vessels are easy to pump through but expensive to maintain (require more blood volume); narrow vessels are cheap but hard to pump through. Murray's Law (r₀³ = r₁³ + r₂³) describes the optimal branching ratio that emerged over hundreds of millions of years.