Is The Mandelbrot Set Real?

John K Clark (
Mon, 11 Aug 1997 23:05:52 -0700 (PDT)


Eric Watt Forste <> On Mon, 11 Aug 1997 Wrote:

>>The shape of the Mandelbrot Set is more complex than the shape of
>>a grape

>John, this is a strong claim, and I for one am skeptical. Of course,
>you can keep pulling more signal out of a Mandelbrot set as you
>fall into its infinite depths, but hey, in *some* sense, we *know*
>what we are going to be getting out of it. The "fractal character"
>of the curves that emerge from increasing levels of mathematical
>magnification doesn't change much no matter how deep you go.

The Mandelbrot Set never repeats itself exactly and it's been proven that
the boundary line of it is as convoluted and random as it is possible for a
line drawn on a flat surface to be. We know for sure that the shape of
The Mandelbrot Set is infinitely complex, we don't know for sure that
anything about a grape is infinitely complex.

>Going deeply into a grape, however, you run into, well, unknown
>things. Who knows what's down in there? Superstrings? Membranes?

But is complexity really the issue here? You seem to be saying that
The Mandelbrot Set is not real because it's not complex enough, Hara was
saying it's not real because it's too complex.

John K Clark

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