Allometric scaling relations, including the 3/4 power law for metabolic rates, are characteristic of all organisms and are here derived from a general model that describes how
essential materials are transported through space-filling fractal networks of branching
tubes. The model assumes that the energy dissipated is minimized and that the terminal
tubes do not vary with body size. It provides a complete analysis of scaling relations for
mammalian circulatory systems that are in agreement with data. More generally, the
model predicts structural and functional properties of vertebrate cardiovascular and
respiratory systems, plant vascular systems, insect tracheal tubes, and other distribution
networks.