Spatial Order in Fluvial Systems: Horton's Laws Derived from Mixed Hexagonal Hierarchies of Drainage Basin Areas

Research Article| January 01, 1969 Spatial Order in Fluvial Systems: Horton's Laws Derived from Mixed Hexagonal Hierarchies of Drainage Basin Areas MICHAEL J WOLDENBERG MICHAEL J WOLDENBERG Laboratory for Computer Graphics and Spatial Analysis, Graduate School of Design, Harvard University, Cambridge, Massachusetts Search for other works by this author on: GSW Google Scholar Author and Article Information MICHAEL J WOLDENBERG Laboratory for Computer Graphics and Spatial Analysis, Graduate School of Design, Harvard University, Cambridge, Massachusetts Publisher: Geological Society of America Received: 30 Jul 1968 First Online: 02 Mar 2017 Online ISSN: 1943-2674 Print ISSN: 0016-7606 Copyright © 1969, The Geological Society of America, Inc. Copyright is not claimed on any material prepared by U.S. government employees within the scope of their employment. GSA Bulletin (1969) 80 (1): 97–112. https://doi.org/10.1130/0016-7606(1969)80[97:SOIFSH]2.0.CO;2 Article history Received: 30 Jul 1968 First Online: 02 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Facebook Twitter LinkedIn Email Permissions Search Site Citation MICHAEL J WOLDENBERG; Spatial Order in Fluvial Systems: Horton's Laws Derived from Mixed Hexagonal Hierarchies of Drainage Basin Areas. GSA Bulletin 1969;; 80 (1): 97–112. doi: https://doi.org/10.1130/0016-7606(1969)80[97:SOIFSH]2.0.CO;2 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentBy SocietyGSA Bulletin Search Advanced Search Abstract 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. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not have access to this content, please speak to your institutional administrator if you feel you should have access.