IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-3784-6_2.html

Algorithms for random fractals

In: The Science of Fractal Images

Author

Listed:
  • Dietmar Saupe

Abstract

For about 200 years now mathematicians have developed the theory of smooth curves and surfaces in two, three or higher dimensions. These are curves and surfaces that globally may have a very complicated structure but in small neighborhoods they are just straight lines or planes. The discipline that deals with these objects is differential geometry. It is one of the most evolved and fascinating subjects in mathematics. On the other hand fractals feature just the opposite of smoothness. While the smooth objects do not yield any more detail on smaller scales a fractal possesses infinite detail at all scales no matter how small they are. The fascination that surrounds fractals has two roots: Fractals are very suitable to simulate many natural phenomena. Stunning pictures have already been produced, and it will not take very long until an uninitiated observer will no longer be able to tell whether a given scene is natural or just computer simulated. The other reason is that fractals are simple to generate on computers. In order to generate a fractal one does not have to be an expert of an involved theory such as calculus, which is necessary for differential geometry. More importantly, the complexity of a fractal, when measured in terms of the length of the shortest computer program that can generate it, is very small.

Suggested Citation

  • Dietmar Saupe, 1988. "Algorithms for random fractals," Springer Books, in: Heinz-Otto Peitgen & Dietmar Saupe (ed.), The Science of Fractal Images, chapter 0, pages 71-136, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3784-6_2
    DOI: 10.1007/978-1-4612-3784-6_2
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4612-3784-6_2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.