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

Fractals of rational dimension and fractals of integral powers

  1. Apr 27, 2003 #1
    What generalizations can be made concerning fractals of nonzero rational dimensions M/N (where M and N are nonzero integers)?

    How does a fractal of non-integral dimension F compare geometrically to a fractal of dimension GF, where G is a nonzero integer?
     
  2. jcsd
  3. May 1, 2003 #2
    In the first paragraph, I was concerned with a fractal space that could be raised to the integer Nth power to obtain a whole number dimensional space.

    Similarly, in the second paragraph, I wondered about the geometry of an "axis" of fractal dimension F extended to G axes to produce a GF fractal dimensional space, or moreso, comparing the geometry of int[GF] dimensional spaces of int[GF] axes for G=1, 2, 3... .
     
  4. May 1, 2003 #3
    Believe the Serpinski gasket has a fractal dimension of exactly two.
     
  5. May 4, 2003 #4
    no - triangle has a dimension of 1.58. Carpet has a dimension of 1.89.

    If its dimension was 2 it wouln't be a fractal.

    Cheers,

    ron.

    Can't help with the earlier Q.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fractals of rational dimension and fractals of integral powers
  1. Fractal Geometry (Replies: 10)

  2. Fractals & Chaos (Replies: 3)

  3. Fractal Geometry (Replies: 3)

  4. Mandelbrot's Fractal (Replies: 9)

Loading...