## STRUCTURE (Lacunar)
^{2)}

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In relation to CANTOR's triadic set, M. DUBOIS, P. ATTEN and P. BERGÉ explain as follows the nature of fractal dimensions:

"The set thus obtained is formed by rigorously ordered points, even if they seem irregularly distributed. Like all fractal objects, this set possesses a lacunar structure, which may be expressed by saying that its dimension is not whole, that it is "fractal". It is in no way a curve in view that an infinity of segments are not included. Its dimension is contained between 0 and 1 (0.63…) The same type of structure, in a qualitative sense, is to be found in a transversal section (i.e. a POINCARÉ section of the chaotic attractor constructed by contraction, stretching and folding ad infinitum of a small rectangle in the phases space. These operations transform a segment inside of the rectangle in the phases space into a set of points… whose dimension is also less than 1… As to the attractor it spreads out… in a complex fashion in a three-dimensional space. Its dimension is contained between 2 and 3." (1987, p.197).

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### Publisher

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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