1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mandelbrot Set- definitive point testing

  1. Nov 19, 2008 #1
    For those of you not familiar with the mandelbrot set, it is the set of all complex numbers c for which the following transform remains finite for an infinite number of iterations:

    z --> z^2 + c

    z is 0 for the first iteration

    My question is this: How can I conclusively determine whether a number is part of the Mandelbrot Set? I am not looking for an approximation, I can do that on my own.
     
    Last edited: Nov 19, 2008
  2. jcsd
  3. Nov 19, 2008 #2
    Should I have posted this somewhere else?
     
  4. Nov 20, 2008 #3

    gel

    User Avatar

    maybe no-one knows the answer?

    I've never studied the Mandlebrot set, but can say the following

    - if c is not in the Mandlebrot set then the sequence z_n will eventually diverge, and you can prove this with certainty just by evaluating the sequence accurately enough until z becomes large.

    - for certain values of c the sequence z_n will be eventually be periodic and c will be in the Mandlebrot set, and you could compute these values as solutions of polynomials.

    - for more general points in the Mandlebrot set I doubt that there is such an algorithm.

    edit: Wikipedia seems to back up what I just said

     
    Last edited: Nov 20, 2008
  5. Nov 24, 2008 #4
    Evalutating until c becomes large doesn't work except as an approximation. c can get very large as long as it converges finitely eventually. You also cannot prove that c does not converge to a finite number or range through such evaluation.
     
  6. Nov 24, 2008 #5

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If c is sufficiently large, iterating must diverge to infinity.
    If z becomes sufficiently large, iterating must diverge to infinity.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Mandelbrot Set- definitive point testing
  1. The Mandelbrot Set (Replies: 1)

  2. Mandelbrot set (Replies: 4)

Loading...