Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fractals & Chaos

  1. Feb 7, 2009 #1
    Hi,

    I've read a little bit about fractals, being self repeating shapes. Is there a connections between fractals and chaotic systems?

    Thanks
     
  2. jcsd
  3. Feb 7, 2009 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The usual "interesting question" about dynamic systems in general is "where does it go in the limit?" or "what are the attracting sets?". If a system is chaotic then the attracting (limit) sets will be fractal.
     
  4. Feb 7, 2009 #3
    Yes. I think that some state space trajectories in chaotic systems follow the path of fractals.
     
  5. Feb 7, 2009 #4
    That is interesting.
    So for all chaotic systems, the limit set is a fractal. Is this always true?
    Does the reverse hold as well? (ie. Are all fractals the limit sets of some chaotic systems?)

    Lastly, how trivial is it to find one given the other?
    For example if we are given the fractal, can we find a chaotic system whose limit set is equal to the fractal?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Fractals & Chaos
  1. Chaos and not chaos (Replies: 1)

  2. Mandelbrot's Fractal (Replies: 9)

Loading...