The fourth dimension of life: Fractal geometry and allometric scaling of organisms

Fractal-like networks effectively endow Life with an additional fourth spat ial dimension. This is the origin of quarter-power scaling that is so perva sive in biology, Organisms have evolved hierarchical branching networks tha t terminate in size-invariant units, such as capillaries, Leaves, mitochond ria, and oxidase molecules. Natural selection has tended to maximize both m etabolic capacity, by maximizing the scaling of exchange surface areas, and internal efficiency, by minimizing the scaling of transport distances and times. These design principles are independent of detailed dynamics and exp licit models and should apply to virtually all organisms.