The repetition is the self-similarity, in essence the fractal nature
of the beast. Yet I believe there are points on the Mandelbrot
boundary that require an infinite calculation to determine if they're
in or out (believe because I haven't studied the maths - presumably it
has been proven one way or other). Bruno's conjecture IIUC is that
within the Mandelbrot boundary can be found points corresponding to
all possible calculations.

Cheers

On Tue, Aug 12, 2008 at 09:17:09PM -0700, Tom Caylor wrote:
> 
> Nice.  I see beauty in the Mandelbrot set.  However, there seems to be
> a lot of deja vu, similar repetition on a theme.  I have never been
> able to find anything resembling a beautiful girl, or even a mother-in-
> law, or a white rabbit.  This seems to go against your conjecture.
> 
> Tom
> 
> On Aug 12, 8:30 am, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> > On 09 Aug 2008, at 09:44, Tom Caylor wrote:
> >
> > > I believe that nature is not primarily functional. It is primarily
> > > beautiful.
> > > And this from a theist?  Yes!  This is actually to the core point of
> > > why I am a theist.  I don't blame people for not believing in God if
> > > they think God is about functionality.
> >
> > If you remember my conjecture that the Mandelbrot Set, (well, its  
> > complement in the complex plane), is Turing complete (that is  
> > equivalent in some sense to a universal dovetailing), then zooming in  
> > it gives a picture of the arithmetical multiverse or of the universal  
> > deployment. And I do find most of them wonderfully beautiful. Here is  
> > my favorite on youtube:
> >
> > http://www.youtube.com/watch?v=G0nmVUU_7IQ
> >
> > Is that not wonderful? Awesome ?
> >
> > Bruno
> >
> > http://iridia.ulb.ac.be/~marchal/
> 
-- 

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UNSW SYDNEY 2052                         [EMAIL PROTECTED]
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