## HEXAGONAL SPACE FILLING
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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).

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* 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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