Area of Mandelbrot Set
Date: Around 1995
Anyone got any clues about the area of the Mandelbrot set? I have thought
about using Monte Carlo, but I would rather do it by hand.
On thought is that "fractal dimension" of a set is determined by looking at
covering sets, which have areas in the usual sense. Perhaps looking at what
is known about calculating the dimension of the Mandelbrot set might suggest
something about area. This would appear to be a difficult area.
Note that the Mandelbrot set itself is not a fractal in the sense of having
a dimension less than 2 - it does have a real area! I would be surprised if
this has not already been figured out though - a lot of work has been done
on the Mandelbrot set! I would suggest you try a keyword search for "area"
and "Mandelbrot" in one of the journal abstracting services.
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Update: June 2012