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Fractals and Experiments

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Fractals and Disordered Systems

Abstract

Real fractals are self-similar structures that result from physical, chemical, or biological growth processes. As pointed out by Benoit Mandelbrot in his pioneering book Fractal Geometry of Nature [8.1], such structures are abundant in our surroundings. Once the attention is attuned to recognizing patterns of self-similarity in an object we find it everywhere, for example in trees, bushes, plants like the cauliflower, and in the cracks and grains of stones and rocks as well as in polymers, aggregates, and flocculates. The natural abundance of such structures must mean that there are many processes that can give rise to fractal geometry. One of the goals of the current research in this field is to unravel the common features of these processes in order to find general principles that could be characterized as laws of nature. The objective of this chapter is less ambitious. Here we shall concentrate on the kind of fractal structures that can be produced in the laboratory under controlled circumstances and try to give answers to questions like: How do you make a fractal? How do you determine its structure, in particular the fractal dimension, d f ? What are the mechanical, electrical, and magnetic properties? It is through systematic variation of the control parameters during the preparation and the subsequent detailed characterization of the specimens that we can hope to make progress in the understanding of fractal systems.

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© 1991 Springer-Verlag Berlin Heidelberg

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Kjems, J.K. (1991). Fractals and Experiments. In: Bunde, A., Havlin, S. (eds) Fractals and Disordered Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51435-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-51435-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-51437-1

  • Online ISBN: 978-3-642-51435-7

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