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Fractals


J Dale Jacquette


Pages 223 - 224



Fractals are geometrical figures that exhibit increasingly fine structures at every successive level of magnification. Fractals are produced either through physical processes or by algorithm via recursively iterated functions. The most striking and beautiful examples are constructions produced by computer color graphics executing repeated applications of relatively simple operations at every level of scale that in principle ramify indefinitely, presenting thereby an appearance like that of a naturally occurring object. The naturalseeming aspect of fractals has encouraged the use of fractal geometry in studying the mathematics of many physical and organic phenomena, such as structures of dendrites, crystal growth, neural network articulation, and biological, geographical and cosmic developmental events related to chaos theory.




1Philosophy Institute, University of Bern



1 Edgar, G. A., ed., (1993), Classics on Fractals, Reading: Addison-Wesley.

2 Mandelbrot, B. B., (1977), Fractals:

3 Form, Chance and Dimension, San Francisco: W.H. Freeman.

4 Rietman, E., (1989), Exploring the Geometry of Nature: Computer Modeling of Chaos, Fractals, Cellular Automata, and Neural Networks, New York: McGraw-Hill.

5 Yamaguti, M.; Hata, M.; Kigami, J., (1997), Mathematics of Fractals, Providence: American Mathematical Society.

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