http://books.google.com/books?id=sKGz7SiCVpEC&pg=PA239&lpg=PA239&dq=hausdorf... Gives an example of two sets of Hausdorff dimension 0 whose product has dimension >= 1. I haven't yet worked through the proof to get an intuitive understanding of it. Andy On Fri, May 30, 2014 at 9:51 PM, James Propp <jamespropp@gmail.com> wrote:
Warren's argument (which might or might not be valid -- it sounds good to me but I don't work in that area) reminds me of something I was told (but never understood) 30 years ago: that the fractal dimension of the Cartesian product of two sets need not be equal to the sum of the fractal dimensions of the two sets.
Can anyone explain this to me?
Jim
P.S. After having been publically (albeit gently) scolded on MathOverflow a number of times for the way I've phrased questions, and having seen others being similarly scolded, I've now got an internalized troll in my brain who criticizes the above question ("Can anyone explain this to me?") as follows: "Well of course the answer to your question is YES: that is, there do exist people who can explain this to you. But is that what you really meant to ask? Please try to ask questions in a clearer way."
On Friday, May 30, 2014, Warren D Smith <warren.wds@gmail.com> wrote:
Just rotate the 2D Mandelbrot set to get a body of revolution with a 3D boundary given that the 2D set has 2D boundary.
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