Re: Mike Throll 5

Ilmari Karonen <ilt...@sci.invalid> wrote:
: In article <9oachv$795$1...@news.fas.harvard.edu>, uncle monty wrote:
:>Ilmari Karonen <ilt...@sci.invalid> wrote:
:>: In article <3ba...@News.CIS.DFN.DE>, Timofei Shatrov wrote:
:>:>On 17 Sep 2001 17:38:49 GMT, uncle monty <unc...@babyfishmouth.org> tried to
:>:>confuse everyone with this message:
:>:>
:>:>>Given an initial separation of the plane RxR into a subset A and not-A,
:>:>>and an iterative process which at each step assigns membership in A to
:>:>>each point outside A whose circular neighbourhood of radius 1 has a
:>:>>greater intersection with A than with not-A, and removes each point
:>:>>previously within A whose circular neighbourhood of radius 1 has a greater
:>:>>intersection with not-A than with A, is it possible to choose initial A
:>:>>such that its area will increase by a factor of 1000 or more during the
:>:>>process?
:>
:>:>>I imagine it is some 
:>:>>impossible fractal shape to begin with.

: Hmm.. you just gave me an idea.  Take one big blot.  Fill it with N > 1
: large circular holes, just far enough apart not to disturb each other's
: shrinking.  Now fill the *remaining* blot with smaller circular holes,
: and repeat until the holes get too small.

: Now your blot is a fractal foam.  If you make it big enough, I see no
: reason why you couldn't get an arbitrarily high area increase.  Not that
: I could prove this either, but I'm a lot more confident in making that
: conjecture than with any of my previous ideas.

: Of course, if there's a non-fractal answer, as Timofei seems to imply
: above, I still have no idea what it could be.

: ObAscii: foam
:       _..._                _     __
:    ./'     `\,---.-'"".--.(_)  /"  "\
:   ,' .'"`. ."   / .--:    : __: _    ;
:   |  `._.'-(  _: (    )__.7'   (_)_./
:  -'-._  ;  `.(_)-"`--'-.  ;  ,--.|-.
:    .--".--. /_    .---(_)/  ;_   |  :
:   ;    `;  ;(_)--`-.    `;-.(_)-'--'


ok Timofei, time to reveal the shape that solves the problem... we are 
clearly too thick to get your hints.  thanks --monty

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