Fractal boundaries are infinitely complex and seem to dissolve as we try to pin them down more precisely.
This is undoubtedly a feature of existing complex systems, but then only up to the point where the elements of the boundary dissolve at a lower scale in some other type of lesser elements.
However, the mathematical models, especially their graphic representations, are quite useful to visualize the elusiveness of boundaries, which means that any boundary element is simultaneously within the system and within its environment (or within neither).
WEIERSTRASS function expresses this characteristic through the impossibility to differentiate for any value of the function (i.e. to draw a tangent to any part of the curve).
The same principle applies to every fractal.
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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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