Abstract
Mandelbrot1 has argued that a wide range of natural objects and phenomena are fractals; examples of fractal trees include actual trees, plants such as a cauliflower, river systems and the cardiovascular system. Here we apply the renormalization group approach2 to the collapse of fractal trees, which may be applicable to a variety of problems including cardiac arrest, failure of bronchial systems, failure of electrical distribution systems and the instability resulting in earthquakes.
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References
Mandelbrot, B. The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
Wilson, K. G. & Kogut, J. Phys. Rep. C 12, 75–200 (1974).
Harlow, D. G. & Phoenix, S. L. Adv. Appl. Probability 14, 68–94 (1982).
Meyer, P. L. Introductory Probability and Statistical Applications (Addison-Wesley, Reading, 1970).
Smalley, R. F., Turcotte, D. L. & Solla, S. A. J. geophys. Res. (in the press).
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Turcotte, D., Smalley, R. & Solla, S. Collapse of loaded fractal trees. Nature 313, 671–672 (1985). https://doi.org/10.1038/313671a0
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DOI: https://doi.org/10.1038/313671a0
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