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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CANTOR SET (Triadic) 2)

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This set, imagined by Georg CANTOR towards the end of 19th century is probably the first ever abstract representation of a fractal set.

It is constructed, starting from a segment, which is divided in three equal parts, the middle third being removed. This operation is renewed on the two subsisting segments ad infinitum (supposedly !). In this way, we should obtain finally an infinity of points… whose total length dimension, or linear measure, would be zero. The Cantor triadic set has a fractal dimension of 0.63. Another Cantor set can be constructed removing at each stage two fifth segments within the remaining part of the original segment. It has also a zero linear measure and its fractal dimension is 0.68.

The Cantor set is self similar.

If we could invert the construction process of the Cantor set (i.e. from an infinity of points to a complete segment) we would have modeled the genesis of a macrolevel system constructed from discrete parts.

Other mathematical objects of the same type are the "snowflake" Koch curve, and the Peano curve, made from an infinitely folded segment which finally would wholly cover a surface. There are also objects of the same kind in three or more dimensions.

Categories

  • 1) General information
  • 2) Methodology or model
  • 3) Epistemology, ontology and semantics
  • 4) Human sciences
  • 5) Discipline oriented

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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