BCSSS

International Encyclopedia of Systems and Cybernetics

2nd Edition, as published by Charles François 2004 Presented by the Bertalanffy Center for the Study of Systems Science Vienna for public access.

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The International Encyclopedia of Systems and Cybernetics was first edited and published by the system scientist Charles François in 1997. The online version that is provided here was based on the 2nd edition in 2004. It was uploaded and gifted to the center by ASC president Michael Lissack in 2019; the BCSSS purchased the rights for the re-publication of this volume in 200?. In 2018, the original editor expressed his wish to pass on the stewardship over the maintenance and further development of the encyclopedia to the Bertalanffy Center. In the future, the BCSSS seeks to further develop the encyclopedia by open collaboration within the systems sciences. Until the center has found and been able to implement an adequate technical solution for this, the static website is made accessible for the benefit of public scholarship and education.

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HEXAGONAL SPACE FILLING 2)4)

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W. CHRISTALLER (1933) and A. LÖSCH (1945) gave numerous examples of a tendency to hexagonal occupation of the geographic space. As stated by M.L. WOLDENBERG: "These writers recognized that the most efficient shape in terms of accessibility to the center of an area is the circle. Circles, however, cannot be packed into a space without leaving interstices. Hexagons are the polygons which allows the closest packing in an area, consistent with minimizing movement cost to a point". Moreover "… the overlap between circles emanating from centers is a minimum for an hexagonal lattice of centers" (1969, p.24).

The existence of a mathematical set of the various possible types of nested hexagonal hierarchies in the occupancy of space has been demonstrated by LÖSCH. The nested subsets can be trapezia, pentagons or hexagons (Ibid,.p.25).

Natural geographic irregularities may deform or even suppress the hexagonal space filling net, but it is striking to see that dissipative structures observed by BENARD and related to energy dissipation in emergent systems tend also to take hexagonal forms.

This is perfectly consistent with both classical and Prigoginian thermodynamics. As noted by C. JOSLYN, hexagonal packing "… can be shown to maximize… energy flow and thermodynamic entropy production" (1991, p.641).

Either we witness a dynamic equilibrium, with stable haxagonal space filling (sustained by a stable energy flow), or observe the progressive emergence of a new structure as a result of the "flooding" of the system by massive and sustained energy supplements, which lead the system to a higher level of organization, i.e. of entropy production.

→ Density of occupancy; Foraging theory; Isotropy; Substrate

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Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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