Re: Mike Throll 5
From Timofei Shatrov <gru...@mail.ru>
· alt.ascii-art
· 18 Sep 2001 09:57 · View full thread
· report
On 17 Sep 2001 17:38:49 GMT, uncle monty <unc...@babyfishmouth.org> tried to confuse everyone with this message: >Timofei Shatrov <gru...@mail.ru> wrote: > >: We have the black blot on the white plane. >: Every dot is added to the blot if the black >: area of its neighborhood (radius 1) is more >: than white area and removed if the white area >: is larger. Is this possible that blot's area >: will be 1000 times more than initial area? > >I've been thinking about this puzzle... is this a correct rephrasing: You are the first one who did this :). >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? > >Tell me, does the blot have to be simply connected in the beginning? I think yes. It also has to be finite. >Do we >need the final limiting area to be more than 1000 times the initial area, >or can some intermediate area be 1000 times? I think all finite figures will eventually die. You need to make it 1000 times larger only at one turn. >I imagine it is some >impossible fractal shape to begin with. No way. It's not very complicated. Just try to invent blot that can increase and then magic word "asymptotics". -- Grue <grue sobaka mail.ru> Mike Throll comic strip at: http://grue.freeservers.com Bugsoft Perm at: http://bugsoft.freeservers.com
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f996b,1c2897ed56918deb X-Google-Attributes: gidf996b,public X-Google-ArrivalTime: 2001-09-18 02:55:39 PST Path: archiver1.google.com!newsfeed.google.com!newsfeed.stanford.edu!news.tele.dk!small.news.tele.dk!130.133.1.3!fu-berlin.de!uni-berlin.de!212.120.170.190!not-for-mail From: gru...@mail.ru (Timofei Shatrov) Newsgroups: alt.ascii-art Subject: Re: Mike Throll 5 Date: Tue, 18 Sep 2001 09:57:42 GMT Lines: 46 Message-ID: <3ba...@News.CIS.DFN.DE> References: <3ba...@News.CIS.DFN.DE> <9o5cf9$m7f$1...@news.fas.harvard.edu> NNTP-Posting-Host: 212.120.170.190 X-Trace: fu-berlin.de 1000806937 12224768 212.120.170.190 (16 [101885]) X-Newsreader: Forte Free Agent 1.21/32.243 Xref: archiver1.google.com alt.ascii-art:7602
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