1. Limited time only! Sign up for a free 30min personal 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!

Measure of the Mandelbrot Set

  1. May 12, 2007 #1
    What is the Lebesgue measure of the Mandelbrot set?
  2. jcsd
  3. May 16, 2007 #2
    Is it known?
  4. May 16, 2007 #3


    User Avatar
    Science Advisor

    The mandelbrot set is not "Lebesque measurable". Is is possible that you are referring to the dimension of the set?
  5. May 17, 2007 #4
    According to Wikipedia, the measure is estimated to be 1.506 591 77 ± 0.000 000 08, and it is conjectured to be exactly [tex]\sqrt{6\pi-1} - e[/tex]

    edit: But after reading the source... I'm really not sure if I would trust that too well. However, the two large areas of the Mandelbrot set each definitely have positive measures
    Last edited: May 17, 2007
  6. May 17, 2007 #5
    How do you know that it's not Lebesgue measurable?
  7. Sep 3, 2009 #6
    << insult deleted by Mentors >> every closed set is Lebesgue measurable.

    The Mandelbrot Set is closed.

    Last edited by a moderator: Sep 3, 2009
  8. Sep 3, 2009 #7
    I know this is a very old post, but read what I just posted in reply.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Measure Mandelbrot
A Lebesgue measure and integral