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Fractals and Experiments

  • Jørgen K. Kjems

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 our attention is attuned to recognizing patterns of self-similarity in an object we find it everywhere, for example in trees, bushes, plants such as 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.

Keywords

Fractal Dimension Fumed Silica Fractal Structure Fractal Geometry Silica Aerogel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 1996

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  • Jørgen K. Kjems

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