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
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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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