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.

A B C D E F G H I J K L M N O P Q R S T U V W Y Z

SELF-SIMILARITY 2)

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Property of some sets such as each part at different levels is similar to the whole.

This is particularly the case with fractals, whose forms do repeat in a similar way through decreasing dimensional scales.

Some examples of self-similar sets are:

- CANTOR's set, obtainable by sequential suppression of the median third of a segment (a process that could theoretically be repeated ad infinitum, which is also the case in the following examples)

- von KOCH's curves

- SIERPINSKY's sieves and carpets

- PEANO's curves

- MENGER's sponges (see J. GLEICK, 1987)

Self-similarity is a powerful algorithm for compressibility. It is related to chaotic attractors, through period-doubling sequences.

Self-similarity is also the most important property of holograms.

J. GLEICK explains that self-similarity: "… implies recursion, pattern inside pattern. MANDELBROT's price charts and river charts display self-similarity, because not only do they produce detail at finer and finer scales, they also produce detail with certain constant measurements" (1987, p.103).

As GLEICK states: "The self-similarity is built into the technique of constructing the curves the same transformation is repeated at smaller and smaller scales" (Ibid).

The first and best known example of selfsimilarity is found in the Golden Proportion of the ancient Greeks. Self-similarity is also related to chaos and renormalization.

It was independently discovered by K. WEIERSTRASS as his continuous, non-differentiable function (See hereafter).

→ also: ELLIOTT waves; Fields within fields

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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