Spatial Order in Fluvial Systems: Horton's Laws Derived from Mixed Hexagonal Hierarchies of Drainage Basin Areas
The number of stream basin areas (that is, the number of Strahler stream segments) is predicted on the basis of an hexagonal model for basin areas. It is suggested that the number of orders and the number of basins per order balance opposing tendencies for minimum overland work for streams flowing in small basins and maximum work savings in large, as opposed to small, channels. In addition, the entropy of the system approaches the maximum possible. The model agrees with empirical data in cases where the land surface is reasonably uniform with regard to structure and lithology. The necessity for approximate geometric progressions of basin areas with order creates geometric progressions of other basin parameters, leading directly to the power function relationships between variables, known as allometric growth. This model is identical to one proposed to explain the numbers of market areas per order in a system of cities. In addition, the model predicts the structure of bile ducts in one bovine liver cited in this paper.