Abstract
Random walks and Sierpinski gaskets are used to introduce fractal dimensions, and diffusion limited aggregates finish this “dessert”, which is closely related to the critical exponents at the end of the previous chapter .
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- 1.
For a picture album see E. Guyon and H.E. Stanley, Fractal Forms (Elsevier, Amsterdam 1991).
- 2.
The use of the term ant to describe a random walker is used almost universally in the theoretical physics literature—perhaps the earliest reference to this colorful animal is a 1976 paper of de Gennes that succeeded in formulating several general physics problems in terms of the motion of a ‘drunken’ ant with appropriate rules for motion. Generally speaking, classical mechanics concerns itself with the prediction of the position of a ‘sober’ ant, given some set of non-random forces acting on it, while statistical mechanics is concerned with the problem of predicting the position of a drunken ant.
- 3.
Montroll and Shlesinger have written that ancient cave men (and presumably cave women) were fascinated by games of chance and would actually roll four-sided bones to randomly choose one of four possible outcomes.
- 4.
A.L. Barabási, Linked: The New Science of Networks, Perseus Books Group, Cambridge MA, 2002.
- 5.
T. Piketty, Capital in the Twenty-First Century. Belknap-Harvard University Press, Cambridge MA, 2014.
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Stauffer, D., Stanley, H.E., Lesne, A. (2017). Fractals in Theoretical Physics. In: From Newton to Mandelbrot. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53685-8_5
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DOI: https://doi.org/10.1007/978-3-662-53685-8_5
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