Irregular Shapes: Randomness in Fractal Constructions
Self-similarity seems to be one of the fundamental geometrical construction principles in nature. For millions of years evolution has shaped organisms based on the survival of the fittest. In many plants and also organs of animals, this has led to fractal branching structures. For example, in a tree the branching structure allows the capture of a maximum amount of sun light by the leaves; the blood vessel system in a lung is similarly branched so that a maximum amount of oxygen can be assimilated. Although the self-similarity in these objects is not strict, we can identify the building blocks of the structure — the branches at different levels.
KeywordsBrownian Motion Fractal Dimension Random Forest Irregular Shape Percolation Threshold
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- 1.In: Benoit B. Mandelbrot, The Fractal Geometry of Nature, Freeman, 1982, p. 1.Google Scholar
- 11.See F. M. Dekking, Recurrent Selts, Advances in Mathematics 44, 1 (1982) 78–104.Google Scholar
- 12.See R. Voss, Fractals in Nature, in: The Science of Fractal Images, H.-O. Peitgen and D. Saupe (eds.), Springer-Verlag, pages 36–37.Google Scholar
- 13.E. Guyon and H. E. Stanley (eds.), Fractal Forms, Elsevier/North-Holland and Palais de la Découverte, 1991.Google Scholar
- 21.See R. F. Voss and M. Tomkiewicz, Computer Simulation of Dendritic Electrodeposition, Journal Electrochemical Society, 132, 2 (1985) 371–375.Google Scholar