Abstract
The concept of fractal geometry allows to look at nature in a new perspective and to consider irregularities as intrinsic entities. The main problem in this field is to understand the microscopic origin of these structures. The first step in this direction is to formulate models of fractal growth based on physical processes. This has been achieved since a few years. In addition one should be able to formulate a theory of fractal growth analogous to the Renormalization Group for critical phenomena. The attempts to apply RG methods to fractal growth turned out to be rather problematic. Recently we have introduced a new theoretical framework based on a Fixed Scale Transformation that exploits also a different invariance property than RG. This new method allows to understand the origin of fractal properties in these models and to compute analytically the value of the fractal dimension. In this paper we present a critical discussion of the field and point out the main open problems.
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© 1991 Plenum Press, New York
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Pietronero, L. (1991). Why Nature makes Fractals. In: Amar, M.B., Pelcé, P., Tabeling, P. (eds) Growth and Form. NATO ASI Series, vol 276. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1357-1_31
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DOI: https://doi.org/10.1007/978-1-4684-1357-1_31
Publisher Name: Springer, Boston, MA
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