Abstract
In the past few years a great deal of activity has been devoted to the study of fractal structures [3] in relation to physical phenomena [4,5]. The prototype fractal growth model is based on a combination of the Laplace equation and a stochastic field. The first model of this class to be formulated was Diffusion Limited Aggregation (DLA) [6]. A few years later the more general Dielectric Breakdown Model (DBM) [7] was introduced. This model used the relation between the random walk and potential theory and made clear that growth could also occur “from inside”. In addition to their intrinsic theoretical interest, these models are now believed to capture the essential features necessary to describe pattern formation in seemingly different phenomena like electrochemical deposition, deudritic growth, dielectric breakdown, viscous fingering in fluids, fracture propagation and others [4,5].
We outline the basic ideas of a new theoretical approach to fractal growth for models based on the Laplace equation and a stochastic field like Diffusion Limited Aggregation (DLA) and the Dielectric Breakdown Model (DBM). This theory clarifies the origin of fractal structures and provides a systematic method for the calculation of the fractal dimension. For a detailed description the reader should consult the original papers [1,2].
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References
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© 1988 Springer-Verlag Berlin Heidelberg
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Pietronero, L., Erzan, A., Evertsz, C. (1988). Theory of Fractal Growth. In: Jullien, R., Peliti, L., Rammal, R., Boccara, N. (eds) Universalities in Condensed Matter. Springer Proceedings in Physics, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51005-2_24
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DOI: https://doi.org/10.1007/978-3-642-51005-2_24
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