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.

About

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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FRACTAL 2)5)

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A figure that is self-similar at different scales.

The conceptual base of fractals is recursive self-similarity by scaling.

Fractals involve similarities generated by a template, independent of changes of scales. They are also characterized by the absence of derivative, an infinity of details, an infinite length and a fractional dimension.

The mathematical theory was established by B. MANDELBROT (1983), but numerous fractal figures where described beforehand by various authors, who did not seem to have perceived their common ground:

- LICHTENBERG's figures (18th. century!)

- KOCH 's snow flakes and curves

- SIERPINSKI's carpets

- MENGER's sponges

- PEANO's curves

- CANTOR's triadic sets

The WEIERSTRASS function is also self-similar and may lead to fractalized representations of processes.

Recently, A. EDWARDS fractalized the VENN diagrams, a very interesting and useful application, for taxonomic uses (1979, p.51-56).

Fractals describe structures and are somehow static objects, if one is not interested in the order of appearance of their components at successive self-similar levels.

Fractals are increasingly used to modelize a number of natural processes. A recent example is their application to the study of epidemics (Ph. Sabatier et aI., 1998)

There seems also to be a relation between fractals and percolation

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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