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The Fantastic World of Tor’ Bled-Nam

  • Michele Emmer

Abstract

Let us imagine that we have been travelling on a great journey to some far-off world. We shall call this world Tor’ Bled-Nam. Our remote sensing device has picked up a signal which is now displayed on a screen in front of us. The image comes into focus and we see. [...] What can it be? Can it be some strange looking insect? Or could it be some vast and oddly shaped alien city, with roads going off in various directions to small towns and villages nearby? Maybe it is an island — and then let us try to find whether there is a nearby continent with which it is associated. This we can do by ‘backing away’, reducing the magnification of our sensing device by a linear factor of about fifteen. Lo and behold, the entire world springs into view. [...] We may explore this extraordinary world of Tor’ Bled-Nam as long as we wish, tuning our sensing device to higher and higher degrees of magnification. We find an endless variety: no two regions are precisely alike — yet there is a general flavour that we soon become accustomed to. [...] What is this strange, varied and most wonderfully intricate land that we have stumbled upon? No doubt many readers will already know. But some will not. This world is nothing but a piece of abstract mathematics — the set known as the Mandelbrot set [1, p. 74–79].

Keywords

Fractal Dimension Fractal Geometry Mathematical Creation Eternal Truth Abstract Mathematic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    R. Penrose, The Emperor’s New Mind: Concerning Computers, Minds and The Laws of Physics. Oxford University Press, Oxford, 1989.Google Scholar
  2. 2.
    B.B. Mandelbrot, Les objets fractals. Forme, hasard et dimension. Flammarion, Paris, 1975.MATHGoogle Scholar
  3. 3.
    B.B. Mandelbrot, Fractals: Forms, Chance and Dimension. Freeman, San Francisco, 1977.Google Scholar
  4. 4.
    H.-O. Peitgen, P.H. Richter, The Beauty of Fractals, Images of Complex Dynamical Systems. Springer, Berlin, 1986.MATHCrossRefGoogle Scholar
  5. 5.
    H. Jürgens, H.-O. Peitgen, D. Saupe, The Language of Fractals. Scientific American 263: 60–67, 1990.CrossRefGoogle Scholar
  6. 6.
    R. Osserman, I frattali: le frontiere del caos. In: M. Calvesi, M. Emmer (eds.), I frattali: la geometria dell’irregolare. Istituto Enciclopedia Italiana, Roma, pp. 71–83, 1988.Google Scholar
  7. 7.
    B.B. Mandelbrot, Fractals and an Art for the Sake of Science. In: M. Emmer (ed.), The Visual Mind. MIT Press, Cambridge MA, pp. 11–14, 1993.Google Scholar
  8. 8.
    B.B. Mandelbrot, La geometria della natura. Theoria, Roma, 1989.Google Scholar
  9. 9.
    J. Mandelbrot, Fractals in Art, Science and Technology. Leonardo Almanac Online. http://www.leoalmanac.org/index.php//lea/entry/fractals in art science and technology. Last accessed 19 July 2011.Google Scholar
  10. 10.
    R. Huyghe, Formes et Forces. Flammarion, Paris, 1971.Google Scholar

Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  • Michele Emmer
    • 1
  1. 1.Department of MathematicsSapienza University of RomeItaly

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