That's an excellent question, and I haven't seen it posed before. First of all, one must know that a given Julia set in fact has a well-defined dimension (the boundary of the Mandelbrot set doesn't), but I think this is well-established. I don't know what technology there is for computing dimensions of Julia sets, and of course I especially wonder whether the Mandelbrot set would be in any way "visible" in this dimension plot. On Mon, Aug 1, 2011 at 4:26 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Has anyone seen a graph {(c, H(c)) in R^3 | c in C=R^2} of the Hausdorff dimension H(c) of the Julia set of f(z) = z^2 + c, c in C ?
--Dan
Sometimes the brain has a mind of its own.
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