© 2012 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (



In this analysis natural systems are posed to subsystemize in a manner facilitating both structured information/energy sharing and an entropy maximization process projecting a three-dimensional, spatial, outcome. Numerical simulations were first carried out to determine whether n × n input-output matrices could, once entropymaximized, project a three-dimensional Euclidean metric. Only 4 × 4 matrices could; a small proportion passed the test. Larger proportions passed when grouped random patterns on and within two- and three-dimensional forms were tested. Topographical patterns within 31 stream basin systems in the state of Kentucky, USA, were then similarly investigated, anticipating that the spatial configuration of elevations within each basin would provide evidence of evolutionary control when interpreted as internal group relations. Twenty-eight of thirty-one of the systems pass the test unambiguously, with the remaining three approaching or reaching passage when sampling density is increased. Two measures of subsystem-level redundancies are also introduced; these show: (1) surprisingly, minimized internal redundancy levels at the four subsystems level of analysis of the stream systems (as opposed to the five or six, in contrast with the simulations), and (2) much lower average levels than those obtained in the simulations at the same dimensions, both suggesting a preferred evolutionary path under real world conditions.


Biodiversity | Hydrology